ICCAM2009

14 th International Congress on Computational and Applied 

Mathematics 

(ICCAM2009) 

29 September - 2 October 2009 

Antalya - TURKEY 

i

iv 

ICCAM2009 

Programme 

and 

Submitted Abstracts Book

SCIENTIFIC COMMITTEE 

Marc Goovaerts (Chair) – Katholieke Universiteit Leuven 

Omer L. Gebizlioglu (Vice Chair) – Ankara University 

Zhong-zhi Bai – Chinese Academy of Sciences 

Ismihan Bayramoglu – Izmir University of Economics 

Jan Dhaene – Katholieke Universiteit Leuven 

Ken Hayami – National Institute of Informatics/Japan 

Abdul Q.M. Khaliq – Middle Tennessee State University 

Mihael Perman – Institute for Mathematics, Physics and Mechanics/S 

G. Wilhelm Weber – Middle East Technical University 

Luc Wuytack – University of Antwerp 

ORGANIZING COMMITTEE 

Omer L. Gebizlioglu (Chair) – Ankara University 

Serkan Eryilmaz (Vice Chair) – Izmir University of Economics 

Devin Sezer (Vice Chair) – Middle East Technical University 

Fatih Tank (Vice Chair) – Kirikkale University 

Ersan Akyildiz – Middle East Technical University 

Bulent Karasozen – Middle East Technical University 

Dolun Oksoy – Ankara University 

Sevgi Y. Oncel – Kirikkale University 

Cihan Orhon – Ankara University 

Birdal Senoglu – Ankara University 

v

14 th International Congress 

on 

Computational and Applied Mathematics 

(ICCAM2009) 

29 September‐2 October, 2009 

Antalya, Turkey 

Congress Programme 

29 September 2009, Tuesday 

12:00‐18:00 Registration 

16:00‐18:00 Tutorial Session 

Place: Hall 1 

• “Global Optimization In Practice” 

Janos D. Pinter 

18:30‐20:00 Welcome Cocktail 

Place: Cocktail Hall 

30 September 2009, Wednesday 

08:30‐09:00 Registration 

09:00‐09:30 Opening Session 

Place: Hall 1 

Welcome and Opening Talks 

09:30‐10:30 Invited Talk Session 

Place: Hall 1 

Chair: Marc Goovaerts 

• “Dependence Modelling With Copulas” 

Roger B. Nelsen 

10:30‐11:00 Tea‐Coffee Break 

11:00‐12:30 Parallel Sessions 1 

Session1.1: Applied Probability and Stochastic Processes I 

Place: Hall 1 

Chair: Refail Kasımbeyli 

• Andrei Bourchtein, L. Bourchtein 

Dependence of the PageRank vector on the artificial links 

• Serkan Eryilmaz, Funda Iscioglu 

Multi‐state system reliability under stress‐strength setup 

• Agah Kozan, H. Tanil 

On distributions of bottom m scores after ℓth change 

• Guvenc Arslan 

A Variant of the Choquet‐Deny Theorem with Application to Characterizaiton 

Session1.2: Computational Methods in Physical and Social Sciences I 

Place: Hall 2 

Chair: Masai Watanabe 

• Canan Bozkaya, Tulay Kocabıyık 

Streamwise oscillations of a cylinder beneath a free surface: Part 1. Free surface 

effects on vortex formation modes 

• Canan Bozkaya, Tulay Kocabıyık 

Streamwise oscillations of a cylinder beneath a free surface: Part 2. Free surface 

effects on fluid forces 

• Nail Akhmediev, J. M. Soto‐Crespo, A. Ankiewicz 

Rogue waves: power of mathematics in understanding the phenomenon 

• Ali Reza Ashrafi , M. Saheli 

The Eccentric Connectivity Index of Nanotubes and Nanotori

Session1.3: Differential Equations I 

Place: Hall 3 

Chair: Bulent Karasozen 

• Mesliza Mohamed, H.B. Thompson, M. Jusoh 

First‐Order Three‐Point Boundary Value Problems at Resonance 

• Pavel Krutitskii 

Boundary value problems for the Helmholtz equation in domains bounded by closed 

curves and open arcs 

• Adem Kilicman, Hassan Eltayep, Fudziah Ismail 

On the Partial Differential Equations with Non‐Constant Cefficients and Convolution 

Method 

• Gulnur Celik Kizilkan, Kemal Aydin 

Step size strategies on the numerical integration of the systems of differential 

equations 

Session1.4: Mathematical Programming I 

Place: Hall 4 

Chair: M.Fernanda P.Costa 

• Eren Ozceylan, T. Paksoy 

Modeling Facility Location and Supplier Selection with Supplier’s Product Quality and 

Contract Fee for Strategic Supply Chain Design 

• Sureyya Ozogur Akyuz, G. Ustunkar, G. W. Weber 

On Numerical Optimization Methods for Infinite Kernel Learning 

• Alireza Davoodi 

A DEA based approach for solving the multiple objective shortest path problem 

• Fatma Yerlikaya Ozkurt, G.W. Weber, A. Ozmen 

Robustification of CMARS 

Session1.5: Numerical Analysis and Software I 

Place: Hall 5 

Chair: Kuniyoshi Abe 

• Suzan Cival Buranay, A.A. Dosiyev 

A high accurate difference‐analytical method for solving Laplace's equation on 

polygons with nonanalytic boundary conditions 

• Kamile Sanli Kula, Fatih Tank, Turkan Erbay Dalkilic 

An Application of a New Fuzzy Robust Regression Algorithm to Actuarial Science 

• Fudziah Ismail, A. Karimi, N. Md Ariffin, M. Abu Hassan 

Comparison of Exponentially fitted Explicit Runge‐Kutta methods for Solving ODEs 

• Fereidoon Khadem, M. A. Fariborzi Araghi 

Numerical Integration of a Fuzzy Riemann Double Integral 

12:30‐13:30 Lunch Break 


Session2.1: Approximation and Interpolation I 

Place: Hall 1 

Chair: Gulen B. Tunca 

• Halil Gezer, H. Aktuglu 

Statistical Convergence for Set‐Valued Functions 

• Elias Berriochoa, A. Cachafeiro 

Hermite‐Birkhoff interpolation problems on the roots of the unity 

• Liping Yang, X. Xie 

Weak and strong convergence theorems for a finite family of $I‐$asymptotically 

nonexpansive mapping 

• Serife Bekar, H. Aktuglu 

q‐Statistical Convergence 

• Anvarjon Ahmedov, Norashikin Abdul 

Approximation of the functions from $LLog^2(S^N)$ by Fourier‐Laplace series 

• Yunus Hassen, Barry Koren 

A novel 2D finite‐volume method for advection problems with embedded moving‐ 

boundaries

Session2.2: Numerical Linear Algebra I 

Place: Hall 2 


• Venancio Tomeo, Jesus Abderraman 

Explicit Representation of Hessenbergians: Application to General Orthogonal 

Polynomials 

• Fatih Yilmaz, Humeyra Kıyak, Irem Gurses, Mehmet Akbulak, Durmus Bozkurt 

The Powers of Anti(2k+1)‐Diagonal Matrices and Fibonacci Numbers 

• Fatih Yilmaz, Humeyra Kıyak, Irem Gurses, Mehmet Akbulak, Durmus Bozkurt 

On computing powers for one type of matrice by Pell and Jacobsthal Numbers 

• Hasan Huseyin Gulec, N. Taskara, K. Uslu 

On the properties of generalized Fibonacci and Lucas numbers with binomial coefficients 

• Seiji Fujino, Y. Kusakabe, M. Harumatsu 

IDR‐based relaxation methods for solving linear systems 

• Kensuke Aishima, T. Matsuo, K. Murota, M. Sugihara 

A Shift Strategy for Superquadratic Convergence in the dqds Algorithm for Singular 

Values 

Session2.3: Optimization I 

Place: Hall 3 

Chair: Ana Maria A.C.Rocha 

• Lino Costa, Isabel Espírito Santo, Edite M.G.P. Fernandes 

A Hybrid Genetic Pattern Search Augmented Lagrangian Method for Constrained Global 

Optimization 

• Herman Mawengkang 

Production Planning under Stochastic Demand for Fish Processed Product at North 

Sumatera Province, Indonesia 

• Mahnaz Mirbolouki, F. Hosseinzadeh Lotfia, N.Nematollahi, M.H. Behzadi, M.R. Mozaffari 

Centralized Resource Allocation with Stochastic Data 

• Ana Maria A. C. Rocha, Tiago F. M. C. Martins, Edite M. G. P. Fernandes 

On the augmented Lagrangian methodology in a population based global optimization 

algorithm 

• Eman Hamad Al‐Shemas, A. Hamdi 

A Regularized Modified Lagrangian Method for Nonlinearly Constrained Monotone 

Variational Inequalities 

• Miguel Gabriel Villarreal‐Cervantes, Carlos Alberto Cruz‐Villar, Jaime Alvarez‐Gallegos 

A new multiobjective differential evolution strategy for scattering uniformly the Pareto 

solution set for designing mechatronic systems 

Session2.4: Special Functions 

Place: Hall 4 

Chair: Patricia J.Y.Wong 

• Lidia Fernandez, T. E. Perez, M. A. Pinar 

On Koornwinder classical orthogonal polynomials 

• Rabia Aktas, A.Altın, F. Taşdelen Yeşildal 

A note on a family of two variable polynomials 

• Cem Kaanoglu, Mehmet Ali Ozarslan 

Some generalizations of multiple Hermite polynomials via Rodrigues formula 

• Emine Ozergin, M.A. Ozarslan, A. Altin 

Extension of Gamma, Beta and Hypergeometric Functions 

• Onur Karaoglu, Ayse Betul Koc, Haldun Alpaslan Peker, Yildiray Keskin, Yucel Cenesiz, Galip 

Oturanc, Sema Servi 

Application of Padé approximation of differential transform method to the solution of 

prey and predator problem 

• Pablo Sanchez‐Moreno, A. Zarzo, J.S. Dehesa 

Jensen divergence based on Fisher's information 

Session2.5: Statistics and Data Analysis I 

Place: Hall 5 

Chair: Ismihan Bayramoglu 

• Mustafa Cagatay Korkmaz, Coskun Kus, Asir Genc 

Weibull‐Negative Binomial Distribution 

• Yeliz Mert Kantar, Birdal Senoglu, Omer L. Gebizlioglu 

Comparison of a New Robust Test and Non‐parametric Kruskal‐Wallis Test in One‐way 

Analysis Of Variance Model 

• Neslihan Iyit, A. Genc

General Linear Model (GLM) Approach to Repeated Measurements Data Involving 

Univariate Analysis of Variance (ANOVA) and Multivariate Analysis of Variance 

(MANOVA) Techniques 

• Alper Sinan, A. Genc 

Comparing Estimation Results in Nonparametric and Semiparametric Models 

• Noor Akma Ibrahim, N. Poh Bee 

Confidence Intervals for Mean Time to Failure in Two‐Parameter Weibull with Censored 

Data 

• Tutut Herawan, Mustafa Mat Deris 

Rough Set‐based Functional Dependency Approach for Clustering Categorical Data 


16:15‐18:30 

Parallel Sessions 3 

Session 3.1: Mathematical Modeling, Analysis, Applications I 

Place: Hall 1 

Chair: Alejandro Zarzo 

• Turkan Erbay Dalkilic, Aysen Apaydin 

Parameter Estimation by ANFIS in Cases Where Outputs are Non‐Symmetric Fuzzy 

Number 

• Fatemesadat Salehi S.M.H. Karimian, H. Alisadeghi 

A Multizone Overset Algorithm for the Solution of Flow around Moving Bodies 

• Nihal Yokus, E. Bairamov 

Spectral Singularities of Sturm‐Liouville Problems with Eigenvalue Dependent Boundary 

Conditions 

• Zeynep Eken, S.Sezer 

Vague DeMorgan Complemented Lattices 

• Zainidin Karimovich Eshkuvatov 

Approximating the singular integrals of Cauchy type with weight function on the interval 

• Bulent Karasozen, Ayhan Aydin 

Lobatto IIIA‐IIIB Discretization for the Strongly Coupled Nonlinear Schr\"odinger Equation 

Session 3.2: Approximations and Interpolation II 

Place: Hall 2 

Chair: Miguel Angel Fortes 

• Hussain Mohammed Al‐Qassem , L. Cheng, Y. Pan 

Rough oscillatory singular integrals on Rⁿ 

• Raffaele D'Ambrosio, E. Esposito, B. Paternoster 

Exponentially fitted two‐‐step hybrid methods for y''=f(x,y) 

• Nazri Mohd Nawi, Rozaida Ghazali, Mohd Najib Mohd Salleh 

Improving the Gradient based search Direction to Enhance Training Efficiency of Back 

Propagation based Neural Network algorithms 

• F. Tasdelen Yesildal, Gurhan Icoz 

On Linear positive operators including q‐Konhauser Polynomials 

• Veronica Biga, Daniel Coca, Visakan Kadirkamanathan, Stephen A. Billings 

An Alternative Region‐Based Active Contour Model Using Cauchy‐Schwartz Divergence 

• Gulen Bascanbaz Tunca, Yalcin Tuncer 

On Chlodovsky variant of multivariate beta operator 

Session 3.3: Nonlinear Equations and Mathematical Modeling 

Place: Hall 3 

Chair: Ersan Akyıldız 

• Enes Yilmaz, M. U. Akhmet, D. Arugaslan 

Stability analysis of recurrent neural networks with deviated argument of mixed type 

• Turgut Tollu, N. Taskara, K. Uslu 

The Periodicity of Solutions of a Rational Difference Equations x(n+1)=[ p(n).x(n‐k)+x(n‐ 

(k+1))]/[ q(n)+x(n‐(k+1))] with (k+1)th Periodic Coefficients 

• Emine Hekimoglu, N. Taskara, K. Uslu 

On the behavior of solutions of a rational system x(n+1)=1/[y(n‐1)] , y(n+1)=x(n‐ 

1)/[x(n).y(n‐2)] 

• Behzad Ghanbary, Jafar Biazar 

A modification on some improved Newton's method without direct function evaluations 

• Patricia J. Y. Wong, Fengmin Chen 

Error Inequalities for Discrete Hermite Interpolation 

• Josep Arnal 

Parallel Newton‐like methods for solving systems of nonlinear equations

Session 3.4: Computational Methods in Physical and Social Sciences II 

Place: Hall 4 

Chair: Jose M.Matias 

• Demet Ersoy, V. Yakhno 

Deriving Elastic Fields in an Anisotropic Bi‐material 

• Sengul Kecelli, V. Yakhno 

A Boundary Value Problem of the Frequency‐Dependent Maxwell's System for Layered 

Materials 

• Sevgi Yurt Oncel, Omer L. Gebizlioglu, Fazil Aliyev 

Multiple Logistic Regression A Study on the Multiple Logistic Regression Analysis To 

Determine Risk Factors For The Smoking Behavior 

• Yoji Otani, M. Watanabe, L. Ying, K. Yamamoto, Hashentuya 

Numerical simulation of tsunami generated in North Pacific Ocean near Japan 

• Ata Olah Abbasi, B. Vosoughi Vahdat 

A new numerical method for solving 2D Electrical Impedance Tomography Inverse 

Problem 

• Tertia Delia Nova, H. Mawengkang, M. Watanabe 

Control strategy of avian influenza based on modeling and simulation 

Session 3.5: Mathematical Programming II 

Place: Hall 5 

Chair: Venancio Tomeo 

• Eren Ozceylan, T. Paksoy, N.Y. Pehlivan 

Fuzzy Optimization of A Multi Stage Multi Item Closed‐Loop Flexible Supply Chain 

Network Under Fuzzy Material Requirement Constraints 

• Gerhard‐Wilhelm Weber, E. Kropat, C.S. Pedamallu 

Identification, Optimization and Dynamics of Regulatory Networks under Uncertainty 

• Erkki Laitinen , I. Konnov, O. Kashina 

Multi‐Criteria Optimization for Distribution of Spatial Resources 

• Mahnaz Mirbolouki, F.Hosseinzadeh Lotfi, G.R. Jahanshahloo, M.H. Behzadi 

Finding Efficient and Inefficient Outlier Layers by Using Skewness Coefficient 

• Hendaru Sadyadharma, Z. Nasution, H. Mawengkang 

Multi‐Objective Optimization Model for Solving Risk‐Based Environmental Production 

Planning Problem in Crude Palm Oil Industry 

• Sacha Varone, David Schindl 

Staff scheduling with priority constraints 

1 October 2009, Thursday 


Place: Hall 1 

Chair: Gerhard Wilhelm Weber 

• “NULISS:Non‐Uniform Local Interpolatory Subdivision Surfaces” 

Lucia Romani 


10:30‐12: 45 

Parallel Sessions 4 

Session 4.1: Mathematical Modeling, Analysis, Applications II 

Place: Hall 1 

Chair: Alireza Ashrafi 

• Fatma Tasdelen Yesildal, Burak Sekeroglu, H.M. Srivastava 

Some Properties of Q‐Biorthogonal Polynomials 

• İsmail Yaslan 

Positive solutions for nonlinear first‐order m‐point boundary value problem on time 

scale 

• Fengmin Chen, Patricia J. Y. Wong 

Error Estimates for Discrete Spline Interpolation 

• Masaji Watanabe, F. Kawai 

Computational analysis for microbial depolymerization processes of xenobiotic 

polymers based on mathematical models and experimental results 

• Tahir Khaniyev, I. Unver, Z. Mammadova 

Asymptotic Results for a Semi‐Markovian Random Walk with a Normal Distributed 

Interference of Chance

• Mustafa Kahraman, Nurgul Gokgoz, Hakan Oktem 

A Model of Vascular Tumor Growth by Hybrid Systems 

Session 4.2: Applied Probability and Stochastic Processes II 

Place: Hall 2 

Chair: Roger B. Nelsen 

• M.R. Akramin M. Mazwan Mahat, A. Juliawati, A.H. Ahmad, A.R.M. Rosdzimin 

Probability Failure Analysis for Cracked Structure 

• Burak Uyar, H. Tanil 

On exceedances based on the list of top m scores after ℓth change 

• Jose M. Matias, T. Rivas, C. Ordonez, J. Taboada 

Functional Approach Using New $L^{\ast }a^{\ast }b^{\ast }$ color functions to 

evaluate colour changes in granites after desalination using different methods 

• Ceren Eda Can, M. Rainer 

On LIBOR and swap market models: calibration to caps and swaption markets 

• Zhaoning Shang, Marc Goovaerts 

Analytical Recursive Algorithm for Path‐dependent Option Pricing with Stochastic 

Time 

• Rovshan Aliyev, T.Kesemen , T.Khaniyev 

On the Semi‐Markovian Random Walk with Delay and Weibull Distributed 

Interference of Chance 

Session 4.3: Computational Methods in Physical and Social Sciences III 

Place: Hall 3 

Chair: Hassan Yousefi‐Azari 

• Jisheng Kou, Xiuhua Wang, Yitian Li 

A nonlinear preconditioner for Jacobian‐free Newton‐Krylov methods 

• Ludmila Bourchtein, Andrei Bourchtein 

A splitting semi‐implicit scheme for large‐scale atmospheric dynamics model 

• Dogan Yildiz, Atif Evren 

Multilevel Factor Modeling as an Alternative in Evaluating the Performance of 

Statistics Education in Turkey 

• Selcuk Han Aydin, M. Tezer Sezgin 

Stabilized FEM Solution of Steady Natural Convection Flow in a Square Cavity 

• Hanieh Khalili Param , F. Bazdidi 

Investigation of Large Eddy Simulation and Eddy‐Viscosity Turbulence Models 

Applicable to Film Cooling Technique 

• Eun Heui Kim, C. Lee, B. Englert 

Transonic problems in multi‐dimensional conservation laws 

Session 4.4: Mathematical Programming III 

Place: Hall 4 

Chair: Herman Mawengkang 

• Masoud Allame, B. Vatankhahan, S. Abbasbandy 

Modified iteration methods to solve system Ax=b 

• Eren Ozceylan, T. Paksoy 

A Multi‐Objective Mixed Integer Programming Model for Multi Echelon Supply Chain 

Network Design and Optimization 

• Ali Osman Cibikdiken, Kemal Aydin 

Effect of Floating Point Aritmetic on Monodromy Matrix Computation of Periodic 

Linear Difference Equation System 

• Mohammad Hassan Behzadi, F. Hosseinzadeh Lotfi, N. Nematollahi, M. Mirbolouki 

Ranking Decision Making Units with Stochastic Data by Using Coefficient of Variation 

• Gurkan Ustunkar, S. Özöğür‐Akyüz, U. Sezerman, G. W. Weber, N. Baykal 

Application of Advanced Machine Learning Methods For SNP Discovery in Complex 

Disease Association Studies 

• Ulas Ozen, S. A. Tarim, M. K. Dogru, R. Rossi 

An Efficient Computational Method for Non‐Stationary (R,S) Inventory Policy with 

Service Level Constraints 

Session 4.5: Statistics and Data Analysis II 

Place: Hall 5 

Chair: Fatih Tank 

• Senol Erdogmus, E. Koc, S. Ayhan 

A Comprehensive Kansei Engineering Algorithm: An application of the university web 

page design

• Guvenc Arslan, I. Ozmen, B.O. Turkoglu 

A JAVA Program for the Multivariate Zp and Cp Tests and Its Application 

• Ovgu Cidar, Y. Tandogdu 

Smoothing the Covariance Based on Functional Principal Component Analysis 

• Yucel Tandogdu 

Functional Predictor and Response Variables Under Non‐Gaussian Conditions 

• Mustafa Cagatay Korkmaz, Coskun Kus, Asir Genc 

Exponential‐Negative Binomial Distribution 

• Tutut Herawan, Mustafa Mat Deris 

Soft Set Theory for Maximal Association Rules Mining 



Place: Hall 1 

Chair: Omer L. Gebizlioglu 

• “Ordered Random Variables‐Recent Developments” 

Ismihan Bayramoglu 

15:30‐19:00 Tour to the old town fortress/marina and museum visit 

20:00 Congress Dinner 


2 October 2009, Friday 

Session 5.1: Mathematical and Computational Finance 

Place: Hall 1 

Chair: Jan Dhaene 

• Koen Van Weert, Jan Dhaene, Marc Goovaerts 

Approximations for Optimal Portfolio Selection Problems 

• Gerhard‐Wilhelm Weber, Kasirga Yildirak, Efsun Kurum 

A Classification Problem of Credit Risk Rating Investigated and Solved by 

Optimization of the ROC Curve 

• Muhammed‐Shahid Ebrahim, Ike Mathur 

Structuring Pension Funds Optimally 

• Refail Kasimbeyli, G. Ozturk, O. Ustun 

Multi‐class classification algorithms based on polyhedral conic functions and 

application to companies listed on the Istanbul Stock Exchange 

Session 5.2: Cryptography 

Place: Hall 2 

Chair: Ersan Akyıldız 

• Ferruh Ozbudak, M. Cenk 

Efficient Multiplications in 

• Baris Bulent Kirlar 

On the elliptic curves y 2 =x 3 ‐c with embedding degree one 

• Mohammed Mahmoud Jaradat 

On the basis number of the lexicographic product of two graphs and some related 

problems 

• Frank J. Kampas, Janos D.Pinter 

Nonlinear Optimization in Mathematica with MathOptimizer 

Session 5.3: Differential equations II 

Place: Hall 3 

Chair: Josep Arnal 

• Muhammad Asif Gondal, A. Ostermann 

Exponential Runge‐‐Kutta methods for option pricing in jump‐diffusion models 

• Mesliza Mohamed, M. Jusoh 

Discrete First‐Order Four‐Point Boundary Value Problem 

• Yucel Cenesiz, Y. Keskin, A. Kurnaz 

The Solution of the Bagley‐Torvik Equation with the Generalized Taylor Collocation 

Method

• Ahmet Duman, Kemal Aydin 

Sensitivity of Schur Stable Linear Systems with Periodic Coefficients 

Session 5.4: Numerical Linear Algebra II 

Place: Hall 4 

Chair: Serkan Eryilmaz 

• Maxim Naumov, A. Bourchtein 

On the Modification of an Eigenvalue Problem that Preserves an Eigenspace 

• Kuniyoshi Abe, G. L. G. Sleijpen 

A Variational Algorithm of the GPBi‐CG Method for Solving Linear Systems 

• Soheil Salahshour, Tofigh Allahviranloo 

Fully fuzzy linear system: New point of view 

• Tofigh Allahviranloo, Soheil Salahshour 

Fuzzy Linear System: Satisfactory Level of Solution 

Session 5.5: Approximation and Interpolation III 

Place: Hall 5 

Chair: Dmitri V. Alexandrov 

• Havva Kaffaoglu, N. Mahmudov 

On q‐Szász‐‐Durrmeyer Operators 

• M. Cetin Kocak 

Ostrowski’s Fourth‐order Iterative Method Solves Cubic Equations of State 

• Hatice Gul Ince, G. Bascanbaz Tunca, A. Erencin 

On Bivariate Bernstein‐Chlodovsky Operator 

• Yoseph Hashemi, A. Jahangirian 

Implicit Fully Mesh‐Less Method for Compressible Viscous Flow Calculations 


11:00‐12:30 

Paralel Sessions 6 

Session6.1: Applied Probability and Stochastic Processes III 

Place: Hall 1 

Chair: Kasirga Yildirak 

• Mustafa Kemal Dogru, G.J. van Houtum, A.G. de Kok 

Newsvendor Characterizations for One‐Warehouse Multi‐Retailer Inventory Systems 

with Discrete Demand under the Balance Assumption 

• Ismail Kinaci, B. Saracoglu 

Modified Maximum Likelihood Estimators for Logistic Distribution under Type‐II 

Progressively 

• Azizah Hanim Nasution , A. Syahrin, H. Mawengkang 

Modeling Coordination Relationships of School Communities to Achieve 

Environmental Behavior Using Influence Diagram 

• Vilda Purutcuoglu, M. L. Tiku 

Testing unit root and comparison of estimates 

Session6.2: Computational Methods in Physical and Social Sciences IV 

Place: Hall 2 

Chair: Lucia Romani 

• Dmitri V. Alexandrov, A.P.Malygin, I.V.Alexandrova 

Nonlinear Dynamics of Leads 

• Reza Zolfaghari 

An Inverse Problem of Finding Control Parameter in a Parabolic Equation 

• Mohammad Moalemi, F. Bazdidi 

Analysis of Laminar Film Boiling on a Vertical Surface Using a Coupled Level‐Set and 

Volume‐of‐Fluid Technique 

• Hassan Yousefi‐Azari, A.R. Ashrafi, M.H. Khalifeh 

Topological Indices of Graph Operations 

Session6.3: Quadrature and Integral Equations 

Place: Hall 3 

Chair: Tahir Khaniyev 

• Nik Mohd Asri Nik Long, M. Yaghobifar, Z. K. Eshkuvatov 

New approach for the construction of the solutions of Cauchy integral equation of 

the first kind 

• Mohammad Ali Fariborzi Araghi, Sh. Sadigh Behzadi

The Use of variational iteration method to Solve a nonlinear Volterra‐Fredholm 

integro‐differential equations 

• Tomoaki Okayama, T. Matsuo, M. Sugihara 

Modified Sinc‐collocation methods for Volterra integral equations of the second kind 

and their theoretical analysis 

• Nagehan Akgun, M. Tezer Sezgin 

Differential Quadrature Solution of 2D Natural Convection in a Cavity Under a 

Magnetic Field 

Session6.4: Mathematical Modeling, Analysis, Applications III 

Place: Hall 4 

Chair: Seiji Fujino 

• Abdelouahed Kouibia , M. Pasadas 

Approximation by div‐rot variational splines 

• Bulent Karasozen, Fikriye Yilmaz 

Solving Distributed Optimal Control Problems for the Unsteady Burgers Equation in 

COMSOL Multiphysics 

• Farnaz Derakhshan 

Formalizing Dynamic Assignment of Rights and Responsibilities to Agents 

• Ali Deliceoglu, F. Gurcan 

Topology of two separation bubbles with opposite rotations in a double‐lid‐driven 

rectangular cavity 

Session6.5: Numerical Analysis and Optimization 

Place: Hall 5 

Chair: Janos D. Pinter 

• Adigozal Dosiyev 

The Block‐Grid Method for Solving Laplace's Boundary Value Problem with 

Singularities 

• Johan Hendrik DeKlerk 

Analytical and numerical evaluation of finite‐part integrals 

• Nematollah Fouladi, M. Darbandi 

Automatic Zone Decomposition in Iterative Solution of Differential Equations over 

Unstructured Grids 

• Alireza Naderi, M. Darbandi 

An Extended Implicit Pis Scheme to Efficent Simulation of Turbulent Flow with 

Moving Boundaries 


13:30‐16:10 

Paralel Sessions 7 

Session 7.1: Optimization II 

Place: Hall 1 

Chair: Gerhard W. Weber 

• Jorge A. Ruiz‐Vanoye, Joaquín Pérez‐Ortega, Rodolfo A. Pazos R., Ocotlán Díaz‐Parra 

Survey of Polynomials Transformations between NP‐Complete problems 

• Jorge A. Ruiz‐Vanoye, Joaquín Pérez‐Ortega, Rodolfo A. Pazos R., Ocotlán Díaz‐Parra 

Application of Formal Languages in the Polynomial Transformations of Instances 

Between Np‐Complete Problems 

• Serap Kemali, Gabil R. Adilov 

Some Inequalities for Increasing Positively Homogeneous Functions 

• Aydin Karakoca, A. Genc 

A Comparative Study on Parameter Estimations in Multivariate Nonlinear Model 

• M. Fernanda P. Costa, Edite M.G.P. Fernandes, A. Ismael F. Vaz 

Interior point filter line search strategies for large scale optimization: practical 

behavior 

• Farhad Hosseinzadeh Lotfi, H. Nikoomaram,A. Toloie Eshlaghy,M.A.Afshar Kazemi,R. 

Sharifi,M. Ahadzadeh Namin 

Interval Malmquist productivity in DEA analysis and its application in determining 

the regress and progress of Islamic Azad university's departments 

• Radek Matousek, Martin Kuba 

HC12‐Highly Scalable Optimization Algorithm

Session 7.2: Mathematical Modeling, Analysis, Applications IV 

Place: Hall 2 

Chair: Andrei Bourchtein 

• Atif Evren, Dogan Yildiz 

Parameter Interval Estimations through Chebyshev‐ type inequalities for Nonlinear 

Regression Models 

• Alejandro Zarzo, L. Fernandez, P. Martinez‐Gonzalez, B. Soler 

Special functions, non‐linearity and algebraic and differential properties: 

Computational aspects. 

• Zubeyde Ulukok, Ramazan Turkmen 

Trace Inequalities for Matrices 

• Mine Menekse Yilmaz, Sevilay Kirci Serenbay 

The Convergence of Family of Integral Operators with Positive Kernel 

• Miguel Angel Fortes, P. Gonzalez, M. Pasadas 

Approximation of patches by C r ‐finite elements of Powell‐Sabin type 

• Alejandro Fuentes‐Penna , Jorge A. Ruiz‐Vanoye, Ocotlán Díaz‐Parra 

Application of Formal Languages in the Polynomial Transformations of Instances 

Between Np‐Complete Problems 

• Farhad Hosseinzadeh Lotfi, A.Toloie Eshlagy, M.R. Mozaffari, Z. Ghalej Beigi, 

K.Gholami 

Large Sensitivity of Ranking 

Session 7.3: Probability Modeling and Computing 

Place: Hall 3 

Chair: Birdal Senoglu 

• Mohammad Khodabakhshi 

Super efficiency in stochastic data envelopment analysis: An input relaxation 

approach 

• Sukru Acitas, Birdal Senoglu 

Two Level Fractional Factorials with Long‐Tailed Symmetric Error Distributions 

• Alvaro Rodolfo De Pierro, E.X. Miqueles 

X‐ray Fluorescence Computed Tomography: Inversion Methods 

• Anders Andersson , B. Nilsson 

Using Dirichlet‐to‐Neumann operators and Conformal Mappings with Approximate 

Curve Factors in Waveguide Problems 

• Mila Milan Stojakovic 

Imprecise probability and application in finance 

• Mehdi Zamani 

An Efficient 2‐D Model for Analysis of Nonuniform Rock Masses 

Session 7.4: Mathematical Modeling and Data Analysis 

Place: Hall 4 

Chair: Pablo Sanchez‐Moreno 

• Tugba Sarac 

A new hybrid algorithm for quadratic knapsack problem 

• Ahmet Pekgör, A. Genc 

Criteria Function Efficiency Against Outliers in Nonlinear Regression 

• Nergiz Kasımbeyli, Tugba Sarac 

A two‐objective integer programming mathematical model for a one‐dimensional 

assortment problem 

• A. Asgharzadeh, R. Valiollahi 

Estimation of reliability P(Y < X) for the proportional reversed hazard models using 

lower record data 

• Ceren Eda Can, N. Erbil, G. W. Weber 

Libor Market Model as a Special Case of Parameter Estimation in Nonlinear 

Stochastic Differential Equations (SDEs) 

• Koray Kalafatcilar, Yılmaz Akdi, Kıvılcım Metin‐Özcan 

Alternative Long‐run analysis of Services and Goods SectorsInflation in Turkey by 

Fractional and Asymmetric Cointegration Methods 

• Seyhmus Yardımcı 

Some Relations Between Functionals On Bounded Real Sequences

Session 7.5: Mathematical Modeling and Computing 

Place: Hall 5 

Chair: Guvenc Arslan 

• Shamsul Qamar, S. Mukhtar, S. Noor, A. Seidel‐Morgenstern 

Efficient numerical techniques for solving batch crystallization models 

• Handan Cerdik Yaslan, Valery G. Yakhno 

Equations of anisotropic elastodynamics as a symmetric hyperbolic system:deriving 

the time‐dependent Green's function 

• Abbas Toloie Eshlaghy, Mohammadali Afshar Kazemi,Ebrahim Nazari Farokhi,Bahareh 

Sagheb 

Measuring the importance and the weight of decision makers 

• Abbas Toloie Eshlaghy, Nasim Rastkhiz Paydar,Khadijeh Joda,Neda Rastkhiz Paydar 

Sensivity analysis for criteria values in decision making matrix of SAW method 

• Modjtaba Ghorbani , A.R. Ashrafi, M. Saheli 

Rational Eigenvalues of Fullerenes 

• G.H. Fath‐Tabar, A.R. Ashrafi 

Bounds on Estrada Index of Fullerenes 

• Sinem Sezer, Ilham A.aliev 

A Characterization of the Riesz Potentials Space With the Aid of a Composite 

Wavelet Transform 

16:10‐16:30 Tea‐Coffe Break 

16:30‐17:00 Closing Session 

Place: Hall 1 

Information and Closing Talks

CONTENTS 

Committees v 

Invited Paper 1 - Dependence Modeling with Copulas 1 


Invited Paper 2 - NULISS: Non-Uniform Local Interpolatory Subdivision 

Surfaces 2 

Lucia Romani 

Invited Paper 3 - Ordered Random Variables - Recent Developments 3 


Tutorial - Global Optimization In Practice 4 


Parallel Sessions 1 5 

Dependence of the PageRank vector on the artificial links 8 

Andrei Bourchtein 

Multi-state system reliability under stress-strength setup 9 

Serkan Eryilmaz 

On distributions of bottom m scores after l-th change 10 

Agah Kozan 

A Variant of the Choquet-Deny Theorem with Application to Characterizaiton 11 

Guvenc Arslan 

Streamwise oscillations of a cylinder beneath a free surface: Part 1. 

Free surface effects on vortex formation modes 13 

Canan Bozkaya 

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viii 

Streamwise oscillations of a cylinder beneath a free surface: Part 2. 

Free surface effects on fluid forces 14 

Canan Bozkaya 

Rogue waves: power of mathematics in understanding the phenomenon 15 

Nail Akhmediev 

The Eccentric Connectivity Index of Nanotubes and Nanotori 16 

Ali Reza Ashrafi 

First-Order Three-Point Boundary Value Problems at Resonance 18 

Mesliza Mohamed 

Boundary value problems for the Helmholtz equation in domains 

bounded by closed curves and open arcs 19 

Pavel Krutitskii 

On the Partial Differential Equations with Non-Constant Coefficients 

and Convolution Method 20 

Adem Kilicman 

Step size strategies on the numerical integration of the systems of 

differential equations 21 

Gulnur Celik Kizilkan 

Modeling Facility Location and Supplier Selection with Suppliers 

Product Quality and Contract Fee for Strategic Supply Chain Design 

23 

Eren Ozceylan 

On Numerical Optimization Methods for Infinite Kernel Learning 24 

Sureyya Ozogur Akyuz 

A DEA based approach for solving the multiple objective shortest 

path problem 25 

Alireza Davoodi 

Robustification of CMARS 26 

Fatma Yerlikaya Ozkurt 

A high accurate difference-analytical method for solving Laplace’s 

equation on polygons with nonanalytic boundary conditions 28 

Suzan Cival Buranay

An Application of a New Fuzzy Robust Regression Algorithm to Actuarial 

Science 29 

Kamile Sanli Kula 

Comparison of Exponentially fitted Explicit Runge-Kutta methods 

for Solving ODEs 40 

Fudziah Ismail 

Numerical Integration of a Fuzzy Riemann Double Integral 31 

Fereidoon Khadem 


Statistical Convergence for Set-Valued Functions 36 

Halil Gezer 

Hermite-Birkhoff interpolation problems on the roots of the unity 37 

Elias Berriochoa 

Weak and strong convergence theorems for a finite family of 

I−asymptotically nonexpansive mapping 38 

Liping Yang 

q-Statistical Convergence 39 

Serife Bekar 

Comparison of Exponentially fitted Explicit Runge-Kutta methods 

for Solving ODEs 40 


A novel 2D finite-volume method for advection problems with embedded 

moving-boundaries 41 

Yunus Hassen 

Explicit Representation of Hessenbergians: Application to General Orthogonal 

Polynomials 44 

Venancio Tomeo 

The Powers of Anti(2k+1)-Diagonal Matrices and Fibonacci Numbers 45 

Fatih Yilmaz 

On computing powers for one type of matrice by Pell and Jacobsthal Numbers 46 

ix

x 

Fatih Yilmaz 

On the properties of generalized Fibonacci and Lucas numbers with 

binomial coefficients 47 

Hasan Huseyin Gulec 

IDR-based relaxation methods for solving linear systems 48 

Seiji Fujino 

A Shift Strategy for Superquadratic Convergence in the dqds Algorithm 

for Singular Values 49 

Kensuke Aishima 

A Hybrid Genetic Pattern Search Augmented Lagrangian Method for 

Constrained Global Optimization 51 

Lino Costa 

Production Planning under Stochastic Demand for Fish Processed 

Product at North Sumatera Province, Indonesia 52 

Herman Mawengkang 

Centralized Resource Allocation with Stochastic Data 53 

Mahnaz Mirbolouki 

Special functions, non-linearity and algebraic and differential properties: 

Computational aspects 54 

Ana Maria A. C. Rocha 

A Regularized Lagrangian Method for Nonlinearly Constrained Monotone 

Variational Inequalities 55 

Eman Hamad Al-Shemas 

A new multiobjective differential evolution strategy for scattering uniformly 

the Pareto solution set for designing mechatronic systems 56 

Miguel Gabriel Villarreal-Cervantes 

On Koornwinder classical orthogonal polynomials 59 

Lidia Fernandez 

A note on a family of two variable polynomials 60 

Rabia Aktas 

Some generalizations of multiple Hermite polynomials via Rodrigues formula 61

Cem Kaanoglu 

Extension of Gamma, Beta and Hypergeometric Functions 62 

Emine Ozergin 

Application of Padé approximation of differential transform method 

to the solution of prey and predator problem 63 

Onur Karaoglu 

Jensen divergence based on Fisher’s information 168 

Pablo Sanchez-Moreno 

Weibull-Negative Binomial Distribution 66 

Mustafa Cagatay Korkmaz 

Comparison of a New Robust Test and Non-parametric Kruskal-Wallis 

Test in One-way Analysis Of Variance Model 67 

Yeliz Mert Kantar 

General Linear Model (GLM) Approach to Repeated Measurements 

Data Involving Univariate Analysis of Variance (ANOVA) and Multivariate 

Analysis of Variance (MANOVA) Techniques 68 

Neslihan Iyit 

Comparing Estimation Results in Nonparametric and Semiparametric 69 

Alper Sinan 

Confidence Intervals for Mean Time to Failure in Two-Parameter 

Weibull with Censored Data 70 

Noor Akma Ibrahim 

Rough Set-based Functional Dependency Approach for Clustering 

Categorical Data 71 

Tutut Herawan 


Parameter Estimation by ANFIS in Cases Where Outputs are Non- 

Symmetric Fuzzy Number 76 

Turkan Erbay Dalkilic 

A Multizone Overset Algorithm for the Solution of Flow around Mov- 

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xii 

ing Bodies 77 

Fatemesadat Salehi 

Spectral Singularities of Sturm-Liouville Problems with Eigenvalue 

Dependent Boundary Conditions 78 

Nihal Yokus 

Vague DeMorgan Complemented Lattices 79 

Zeynep Eken 

Approximating the singular integrals of Cauchy type with weight function 

on the interval 80 

Zainidin Karimovich Eshkuvatov 

Lobatto IIIA-IIIB Discretization for the Strongly Coupled Nonlinear 

Schrödinger Equation 81 

Bulent Karasozen 

Rough Oscillatory Singular Integrals on R n 83 

Hussain Mohammed Al-Qassem 

Exponentially fitted two–step hybrid methods for y ′′ = f(x, y) 84 

Raffaele D’Ambrosio 

Improving the Gradient based search Direction to Enhance Training 

Efficiency of Back Propagation based Neural Network algorithms 85 

Nazri Mohd Nawi 

Approximation Properties of Q-Konhauser Polynomials 86 

Gurhan Icoz 

Modeling An Alternative Region-Based Active Contour Model Using 

Cauchy-Schwartz Divergence 87 

Veronica Biga 

On Chlodovsky variant of multivariate beta operator 88 

Gulen Bascanbaz Tunca 

Stability analysis of recurrent neural networks with deviated argument 

of mixed type 90 

Enes Yilmaz 

The Periodicity of Solutions of the Rational Difference Equation

xn+1 = pnxn−k+x n−(k+1) 

qn+x n−(k+1) 

D. Turgut Tollu 

On the behavior of solutions of a rational system x(n + 1) = 1/[y(n − 

1)], y(n + 1) = x(n − 1)/[x(n).y(n − 2)] 92 

Emine Hekimoglu 

A modification on some improved Newton’s method without direct 

function evaluations 93 

Behzad Ghanbary 

Error Inequalities for Discrete Hermite Interpolation 94 

Patricia J. Y. Wong 

Parallel Newton-like methods for solving systems of nonlinear equations 95 

Josep Arnal 

Deriving Elastic Fields in an Anisotropic Bi-material 97 

Demet Ersoy 

A Boundary Value Problem of the Frequency-Dependent Maxwell’s 

System for Layered Materials 99 

Sengul Kecelli 

A Study on the Multiple Logistic Regression Analysis to Determine 

Risk Factors for the Smoking Behavior 101 

Sevgi Yurt Oncel 

Numerical simulation of tsunami generated in North Pacific Ocean 

near Japan 102 

Yoji Otani 

A new numerical method for solving 2D Electrical Impedance Tomography 

Inverse Problem 103 

Ata Olah Abbasi 

Control strategy of avian influenza based on modeling and simulation 104 

Tertia Delia Nova 

Fuzzy Optimization of A Multi Stage Multi Item Closed-Loop Flexible 

Supply Chain Network Under Fuzzy Material Requirement Constraints 106 

Eren Ozceylan 

xiii 

91

xiv 

Identification, Optimization and Dynamics of Regulatory Networks 

under Uncertainty 107 

Gerhard-Wilhelm Weber 

Using Dirichlet-to-Neumann operators and Conformal Mappings with 

Approximate Curve Factors in Waveguide Problems 108 

Erkki Laitinen 

Finding Efficient and Inefficient Outlier Layers by Using Skewness Coefficient 109 


Multi-Objective Optimization Model for Solving Risk-Based Environmental 

Production Planning Problem in Crude Palm Oil Industry 110 

Hendaru Sadyadharma 

Staff scheduling with priority constraints 111 

Sacha Varone 


Some Properties of Q-Biorthogonal Polynomials 116 

Fatma Tasdelen Yesildal 

Positive solutions for nonlinear first-order m-point boundary value 

problem on time scale 117 

Ismail Yaslan 

Error Estimates for Discrete Spline Interpolation 118 

Fengmin Chen 

Computational analysis for microbial depolymerization processes of 

xenobiotic polymers based on mathematical models and experimental results 119 

Masaji Watanabe 

Asymptotic Results for a Semi-Markovian Random Walk with a Normal 

Distributed Interference of Chance 120 

Tahir Khaniyev 

A Model of Vascular Tumor Growth by Hybrid Systems 121 

Mustafa Kahraman 

Probability Failure Analysis for Cracked Structure 123

M.R. Akramin 

On exceedances based on the list of top m scores after l-th change 124 

Burak Uyar 

Functional Approach Using New L ∗ a ∗ b ∗ color functions to evaluate 

colour changes in granites after desalination using different methods 125 

Jose M. Matias 

On LIBOR and swap market models: calibration to caps and swaption markets126 

Ceren Eda Can 

Analytical Recursive Algorithm for Path-dependent Option Pricing 

with Stochastic Time 127 

Zhaoning Shang 

On the Semi-Markovian Random Walk with Delay and Weibull Distributed 

Interference of Chance 128 

Rovshan Aliyev 

A nonlinear preconditioner for Jacobian-free Newton-Krylov methods 130 

Jisheng Kou 

A splitting semi-implicit scheme for large-scale atmospheric dynamics model 131 

Ludmila Bourchtein 

Multilevel Factor Modeling as an Alternative in Evaluating the Performance 

of Statistics Education in Turkey 132 

Dogan Yildiz 

Stabilized FEM Solution of Steady Natural Convection Flow in a 

Square Cavity 133 

Selcuk Han Aydin 

Investigation of Large Eddy Simulation and Eddy-Viscosity Turbulence 

Models Applicable to Film Cooling Technique 134 

Hanieh Khalili Param 

Transonic problems in multi-dimensional conservation laws 135 

Eun Heui Kim 

Modified iteration methods to solve system Ax = b 137 

Masoud Allame 

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xvi 

A Multi-Objective Mixed Integer Programming Model for Multi Echelon 

Supply Chain Network Design and Optimization 138 

Eren Ozceylan 

Effect of Floating Point Aritmetic on Monodromy Matrix Computation 

of Periodic Linear Difference Equation System 139 

Ali Osman Cibikdiken 

Ranking Decision Making Units with Stochastic Data by Using Coefficient 

of Variation 140 

Mohammad Hassan Behzadi 

Application of Advanced Machine Learning Methods For SNP Discovery 

in Complex Disease Association Studies 141 

Gurkan Ustunkar 

An Efficient Computational Method for Non-Stationary (R, S) Inventory 

Policy with Service Level Constraints 142 

Ulas Ozen 

A Comprehensive Kansei Engineering Algorithm: An application of 

the university web page design 144 

Senol Erdogmus 

A JAVA Program for the Multivariate Zp and Cp Tests and Its Application 145 

Guvenc Arslan 

Smoothing the Covariance Based on Functional Principal Component Analysis 146 

Ovgu Cidar 

Functional Predictor and Response Variables Under Non-Gaussian Conditions 147 

Ovgu Cidar 

Exponential-Negative Binomial Distribution 148 


Soft Set Theory for Maximal Association Rules Mining 149 

Tutut Herawan 


Approximations for Optimal Portfolio Selection Problems 154

Koen Van Weert 

A Classification Problem of Credit Risk Rating Investigated and 

Solved by Optimization of the ROC Curve 155 


Structuring Pension Funds Optimally 156 

Muhammed-Shahid Ebrahim 

Multi-class classification algorithms based on polyhedral conic functions 

and application to companies listed on the Istanbul Stock Exchange 157 

Refail Kasimbeyli 

Efficient Multiplications in F 5 5n and F 7 7n 159 

Ferruh Ozbudak 

On the elliptic curves y 2 = x 3 − c with embedding degree one 161 

Baris Bulent Kirlar 

On the basis number of the lexicographic product of two graphs and 

some related problems 162 

Mohammed Mahmoud Jaradat 

Global Optimization In Practice 163 


Exponential Runge–Kutta methods for option pricing in jumpdiffusion 

models 165 

Muhammad Asif Gondal 

Discrete First-Order Four-Point Boundary Value Problem 166 


The Solution of the Bagley-Torvik Equation with the Generalized Taylor 

Collocation Method 167 

Yucel Cenesiz 

Jensen divergence based on Fisher’s information 168 

Pablo Sanchez-Moreno 

On the Modification of an Eigenvalue Problem that Preserves an Eigenspace 170 

Maxim Naumov 

xvii

xviii 

A Variational Algorithm of the GPBi-CG Method for Solving Linear Systems 171 

Kuniyoshi Abe 

Fully fuzzy linear system: New point of view 172 

Soheil Salahshour 

Fuzzy Linear System: Satisfactory Level of Solution 173 

Tofigh Allahviranloo 

On q-Szász–Durrmeyer Operators 175 

Havva Kaffaoglu 

Ostrowskis Fourth-order Iterative Method Solves Cubic Equations of State 176 

M. Cetin Kocak 

On Bivariate Bernstein-Chlodovsky Operator 177 

Hatice Gul Ince 

Implicit Fully Mesh-Less Method for Compressible Viscous Flow Calculations 178 

Yoseph Hashemi 


Newsvendor Characterizations for One-Warehouse Multi-Retailer Inventory 

Systems with Discrete Demand under the Balance Assumption 182 

Mustafa Kemal Dogru 

Modified Maximum Likelihood Estimators for Logistic Distribution 

under Type-II Progressively Hybrid Censored Data 183 

Ismail Kinaci 

Modeling Coordination Relationships of School Communities to 

Achieve Environmental Behavior Using Influence Diagram 184 

Azizah Hanim Nasution 

Testing unit root and comparison of estimates 185 

Vilda Purutcuoglu 

Nonlinear Dynamics of Leads 187 

Dmitri V. Alexandrov 

An Inverse Problem of Finding Control Parameter in a Parabolic Equation 188

Reza Zolfaghari 

Analysis of Laminar Film Boiling on a Vertical Surface Using a Coupled 

Level-Set and Volume-of-Fluid Technique 189 

Mohammad Moalemi 

Topological Indices of Graph Operations 190 

Hassan Yousefi-Azari 

New approach for the construction of the solutions of Cauchy integral 

equation of the first kind 192 

Nik Mohd Asri Nik Long 

The Use of variational iteration method to Solve a nonlinear Volterra- 

Fredholm integro-differential equations 193 

Mohammad Ali Fariborzi Araghi 

Modified Sinc-collocation methods for Volterra integral equations of 

the second kind and their theoretical analysis 194 

Tomoaki Okayama 

Differential Quadrature Solution of 2D Natural Convection in a Cavity 

Under a Magnetic Field 195 

Nagehan Akgun 

Approximation by div-rot variational splines 197 

Abdelouahed Kouibia 

Solving Distributed Optimal Control Problems for the Unsteady 

Burgers Equation in COMSOL Multiphysics 198 


Formalizing Dynamic Assignment of Rights and Responsibilities to Agents 199 

Farnaz Derakhshan 

Topology of two separation bubbles with opposite rotations in a 

double-lid-driven rectangular cavity 200 

Ali Deliceoglu 

The Block-Grid Method for Solving Laplace’s Boundary Value Problem 

with Singularities 202 

Adigozal Dosiyev 

xix

xx 

Analytical and numerical evaluation of finite-part integrals 203 

Johan Hendrik DeKlerk 

Automatic Zone Decomposition in Iterative Solution of Differential 

Equations over Unstructured Grids 204 

Nematollah Fouladi 

An Extended Implicit Pis Scheme to Efficent Simulation of Turbulent 

Flow with Moving Boundaries 205 

Alireza Naderi 


Survey of Polynomials Transformations between NP-Complete problems 210 

Jorge A. Ruiz-Vanoye 

Application of Formal Languages in the Polynomial Transformations 

of Instances Between Np-Complete Problems 211 


Some Inequalities for Increasing Positively Homogeneous Functions 212 

Serap Kemali 

A Comparative Study on Parameter Estimations in Multivariate Nonlinear 

Model 213 

Aydin Karakoca 

Interior point filter line search strategies for large scale optimization: 

practical behavior 214 

M. Fernanda P. Costa 

Interval Malmquist productivity in DEA analysis and its application 

in determining the regress and progress of Islamic Azad university’s 

departments 223 

Farhad Hosseinzadeh Lotfi 

Parameter Interval Estimations through Chebyshev-Type Inequalities 

for Nonlinear Regression Models 217 

Atif Evren 

Special functions, non-linearity and algebraic and differential properties: 

Computational aspects 218

Alejandro Zarzo 

Trace Inequalities for Matrices 219 

Ramazan Turkmen 

The Convergence of Family of Integral Operators with Positive Kernel 220 

Mine Menekse Yilmaz 

Approximation of patches by C r -finite elements of Powell-Sabin type 221 

Miguel Angel Fortes 

Project Scheduling Problem 222 

Alejandro Fuentes-Penna 

Interval Malmquist productivity in DEA analysis and its application 

in determining the regress and progress of Islamic Azad university’s 

departments 223 


Super efficiency in stochastic data envelopment analysis: An input 

relaxation approach 225 

Mohammad Khodabakhshi 

Two Level Fractional Factorials with Long-Tailed Symmetric Error 

Distributions 226 

Sukru Acitas 

X-ray Fluorescence Computed Tomography: Inversion Methods 227 

Alvaro Rodolfo De Pierro 

Using Dirichlet-to-Neumann operators and Conformal Mappings with 

Approximate Curve Factors in Waveguide Problems 228 

Anders Andersson 

Imprecise probability and application in finance 229 

Mila Milan Stojakovic 

A new hybrid algorithm for quadratic knapsack problem 232 

Tugba Sarac 

Criteria Function Efficiency Against Outliers in Nonlinear Regression 233 

Ahmet Pekgor 

xxi

xxii 

A two-objective integer programming mathematical model for a onedimensional 

assortment problem 234 

Nergiz Kasimbeyli 

Estimation of reliability P (Y < X) for the proportional reversed hazard 

models using lower record data 235 

A. Asgharzadeh 

Libor Market Model as a Special Case of Parameter Estimation in 

Nonlinear Stochastic Differential Equations (SDEs) 236 

Ceren Eda Can 

Alternative Long-Run Analysis of Services and Goods Sectors Inflation 

in Turkey by Fractional and Asymmetric Cointegration Methods 237 

Koray Kalafatcilar 

Some Relations Between Functionals On Bounded Real Sequences 238 

Seyhmus Yardimci 

Efficient numerical techniques for solving batch crystallization models 240 

Shamsul Qamar 

Equations of anisotropic elastodynamics as a symmetric hyperbolic 

system:deriving the time-dependent Green’s function 241 

Handan Cerdik Yaslan 

Measuring the importance and the weight of decision makers 244 

Abbas Toloie Eshlaghy 

Sensitivity analysis for criteria values in decision making matrix of 

SAW method 245 


Rational Eigenvalues of Fullerenes 246 

Modjtaba Ghorbani 

Bounds on Estrada Index of Fullerenes 247 

G.H. Fath-Tabar 

A characterization of the Riesz potentials space with the aid of a 

composite wavelet transform 248 

Sinem Sezer

xxiii 

Author Index 249

Dependence Modeling with Copulas 


Department of Mathematical Sciences 

Lewis & Clark College, Portland 

Oregon 97219 

USA 

Abstract: Copulas have proven to be remarkably useful for modeling dependence in 

a variety of settings. In this talk we will survey important aspects of the theory of 

copulas that make them well suited for dependence modeling. We will discuss methods 

for constructing one and two parameter families, dependence properties (e.g., tail 

dependence), applications (e.g., extreme value theory, Schur-constant survival models), 

simulation techniques, etc. We will also discuss cautions about and limitations to the use 

of these copulas. We conclude with several open problems. 

1

2 

NULISS: Non-Uniform Local Interpolatory Subdivision 

Surfaces 

Lucia Romani 

email: lucia.romani@unimib.it 

University of Milano-Bicocca, Italy 

Via R. Cozzi 53, 20125 Milano - Italy 

(Joint work with: C. Beccari and G. Casciola) 

Abstract: A greater and greater interest for numerical algorithms providing high-quality 

surfaces passing through the vertices of a given control mesh has grown with the bursting 

diffusion and the increasing request of graphical tools in several fields like computer 

graphics, scientific visualization and industrial, medical, biological, topographic, geological 

applications. In all these contexts, it is essential to provide a shape that faithfully 

mimics the behavior of the underlying control net and at the same time reproduces its 

salient features, when present. In this work we address these issues by the definition 

of a non-uniform interpolatory surface subdivision scheme where the insertion rules depend 

on a proper local parameterization of the control net at each refinement level. Before 

starting the subdivision process, a parameter value is attached to each edge of the original 

mesh, depending on the geometrical configuration of its neighboring edges. The proposed 

non-uniform refinement algorithm, although non-stationary, is linear and efficient since 

the local parameterization is automatically computed only once before starting the subdivision 

process, and recursively updated at each refinement step. The computed set of 

parameters, chosen accordingly to the local geometry of the mesh, allows us to generate a 

limit surface that closely resembles the initial control net, independently of the valences 

of vertices and faces. Moreover, special features like circular sections, sharp edges and 

corners are consistently supported by opportunely setting the local edge parameters.

Ordered Random Variables - Recent Developments 


email: ismihan.bayramoglu@ieu.edu.tr 

Department of Mathematics, Izmir University of Economics 

Balcova, Izmir 

Turkey 

Abstract: Order statistics have wide applications in many areas where the use of the 

arranged sample is important. For example, in statistical models of many experiments of 

reliability analysis, life time studies, in testing of strength of materials, etc., the realizations 

arise in nondecreasing order, therefore the use of order statistics is necessary. Order 

statistics are extensively used in statistical inferences, in the estimation theory and hypothesis 

testing. Order statistics and their properties have been studied extensively since 

the early part of the last century, and recent years have seen a particularly rapid growth. 

Nowadays, the theory of general models of ordered random variables arouses interest of 

many researchers. The distributions of ordered random variables for independent and 

identically distributed random variables are well studied in both discrete and continuous 

cases. 

We will discuss some general models of ordered random variables, basic distribution theory 

and applications. Some new results on distribution of order statistics in the case 

of exchangeable random variables will be presented. These results allows wide spread 

applications in modelling of various lifetime data, biomedical sciences, reliability and 

survival analysis, actuarial sciences etc., where the assumption of independence of data 

can not be accepted and the exchange- ability is more realistic assumption. 

3

4 

Global Optimization In Practice 


email: janos.pinter@ozyegin.edu.tr 

Department of Industrial Engineering 

Ozyegin University 

Istanbul - Turkey 

Abstract: The objective of global optimization (GO) is to find the best possible solution 

of nonlinear models, in the presence of multiple local optima. As of today (2009), GO 

implementations are available for compiler platforms, optimization modeling languages, 

and integrated scientific-technical computing systems. These tools can effectively assist 

engineers and scientists to develop and solve their advanced optimization models. 

In this presentation we discuss the state-of-art in GO software development, and present 

a number of interesting applications, including numerical challenges and real-world case 

studies.

30 September 2009, 11:00-12:30 

PARALLEL SESSIONS 1

Session 1.1: Applied Probability and Stochastic Processes I 

Chair: Refail Kasimbeyli 

Place: Hall 1 

7

8 

Dependence of the PageRank vector on the artificial links 

Andrei Bourchtein 

email: burstein@terra.com.br 

Rua Anchieta 4715, bloco K, ap.304 Pelotas 96015-420 

Brazil 

(Joint work with: L. Bourchtein) 

Abstract: In this study we present an analysis of the influence of artificial links (dangling 

vector) attributed to the dangling nodes of the web link matrix on the principal 

eigenvectors of that matrix, which is a part of the algorithm used by Google to rank web 

pages. We clarify when the choice of the dangling vector does not change the original 

eigenvectors and give an evaluation for perturbations of the principal eigenvectors when 

they are subject to modification.

Multi-state system reliability under stress-strength setup 

Serkan Eryilmaz 

email: serkan.eryilmaz@ieu.edu.tr 

Department of Mathematics, Izmir University of Economics 

Balcova, Izmir 

Turkey 

(Joint work with: Funda Iscioglu) 

Abstract: Multi-state reliability models have been found to be more flexible for modeling 

engineering systems. In this study, multi-state k-out-of-n and multi-state consecutive 

k-out-of-n systems are considered in a stress-strength setup. The states of the system are 

assigned considering the number of components whose strengths are above (below) the 

multiple stresses avaliable in an environment. The exact state probabilities of the corresponding 

systems are computed and the results are illustrated for various stress-strength 

distributions. Properties of large systems are also investigated. 

Keywords. Consecutive k-out-of-n systems; Multi-state systems; Stress-strength 

reliability. 

9

10 

On distributions of bottom m scores after l-th change 

Agah Kozan 

email: agah.kozan@ege.edu.tr 

Department of Statistics, Faculty of Science, Ege University 

35100 Bornova, Izmir 

Turkey 

(Joint work with: H. Tanil) 

Abstract: Consider an infinite sequence which contains independent and identically 

distributed (iid) continuous random variables with distribution function (df) F. Tanil 

(2009) derived the joint and marginal probability density functions of top m scores after 

l-th change. In this study, using the concept of ordered random variables, we obtain the 

joint and marginal probability density functions of bottom m scores after l-th change. 

In addition, we give a structure function to construct the distribution functions, the 

moments, and the characteristic functions of the bottom m scores.

A Variant of the Choquet-Deny Theorem with Application 

to Characterizaiton 

Guvenc Arslan 

email: guvenca@baskent.edu.tr 

Baskent University, 

Balca Campus, Department of Statistics and Computer Sciences 

06810 Ankara - Turkey 

Abstract: In this paper a variant of the Choquet-Deny theorem is obtained and used to 

prove two recent characterization results of the uniform distribution based on spacings 

of order statistics and records. These two results are combined in one relation using this 

variant of the Choquet-Deny theorem. 

11

12 

Session 1.2: Computational Methods in Physical and Social 

Sciences I 

Chair: Masai Watanabe 

Place: Hall 2

Streamwise oscillations of a cylinder beneath a free surface: 

Part 1. Free surface effects on vortex formation modes 

Canan Bozkaya 

email: canan@mun.ca 

Department of Mathematics and Statistics 

Memorial University of Newfoundland 

A1C 5S7, St. John’ s 

Canada 

(Joint work with: Serpil Kocabiyik) 

Abstract: A computational study of two-phase flow problem based on a viscous incompressible 

two-fluid model with an oscillating cylinder is performed. Specifically, twodimensional 

flow past a circular cylinder subject to forced streamwise oscillations beneath 

a free surface is considered. The numerical simulations are carried out using the 

computational fluid dynamics code developed by Dr. S. Kocabiyik’s research group at 

Memorial University of Newfoundland. This computational code is based on the finite 

volume method for solving the two-dimensional continuity and unsteady Navier-Stokes 

equations in their pressure-velocity formulation and has been successfully applied to the 

problem of uniform flow past cylinders including oscillating cylinders using both single 

and two-phase flow models. The numerical simulations are carried out at the Reynolds 

number of R = 200 for fixed displacement amplitude A = 0.13 for the Froude numbers 

F r ≈ 0.0; F r = 0.2, 0.4, and the cylinder submergence depths, h = 0.25, 0.5, 0.75 

when the forcing cylinder oscillation frequency-to-natural vortex shedding frequency ratio, 

f/f0=1.5, 2.5, 3.5. The main objective of this study is to address the alterations of 

the near-wake region, in particular, the flow regimes and the locked-on vortex formation 

modes, due to the presence of the free surface. The equivorticity patterns, streamlines 

and pressure distribution contours are used for the numerical flow visualization. This 

computational investigation has shown that both the near wake structure and the free 

surface deformations are very sensitive to the Froude number F r, and to the cylinder 

submergence depth, h. For small Froude numbers the surface deformations are minimal 

and they become substantial as F r increases. As F r increases to 0.4 and h decreases to 

0.25, the localized interface sharpening and wave breaking occur. This introduces a substantial 

quantity of opposite signed vorticity from the free surface which interacts with 

the upper vorticity shedding layer through diffusion and thereby, substantially changes 

the wake evolution. These findings are in accord with that of previous studies for the 

cases of uniform flow past stationary and oscillating cylinders in the presence of a free 

surface. 

13

14 

Streamwise oscillations of a cylinder beneath a free surface: 

Part 2. Free surface effects on fluid forces 

Canan Bozkaya 

email: canan@mun.ca 

Department of Mathematics and Statistics 

Memorial University of Newfoundland 

A1C 5S7, St. John’ s 

Canada 

(Joint work with: Serpil Kocabiyik) 

Abstract: This study presents the results of a two-dimensional computational study of 

the free surface flow past a circular cylinder forced to perform streamwise oscillations in 

the presence of an oncoming uniform flow. In Part 1, we have examined the effects of the 

inclusion of the free surface on the vortex-shedding modes in the near wake region for 

the same problem at the Reynolds number of R = 200 for fixed displacement amplitude 

A = 0.13 when the forcing frequency-to-natural shedding frequency ratio, f/f0, ranges 

1.5-3.5. The numerical simulations are carried out using basically the same two-phase 

flow model and finite volume code as that used in Part 1 for numerical simulation of the 

unsteady Navier-Stokes equations in their primitive variable formulation. The objective 

of this study is to examine the effect of the cylinder submergence depths, h = 0.25, 0.5, 

0.75 and the frequency ratios, f/f0 =1.5, 2.5, 3.5 on fluid forces as well as the total 

mechanical energy transfer at two values of the Froude numbers F r = 0.2, 0.4. The time 

histories of the in-line (drag) and transverse (lift) force coefficients are plotted as well as 

their power spectrum densities and Lissajous trajectories. The mean and the root-meansquare 

lift and drag force coefficients, are also predicted to determine the free surface 

effects on the fluid forces. It is interesting to note that irrespective of the values of h 

and f/f0, the total mechanical energy transfer is negative, indicating the energy transfer 

from the cylinder to the fluid unlike transverse oscillation case. However, the changes 

in the absolute values of the energy transfer is observed depending on the values of h 

and f/f0, resulting in variations in the amount of the mechanical energy transfer from 

cylinder to fluid at each F r.

Rogue waves: power of mathematics in understanding the 

phenomenon 

Nail Akhmediev 

email: nna124@rsphysse.anu.edu.au 

Optical Sciences Group, Research School of Physics and Engineering 

Institute of Advanced Studies 

Australian National University 

Canberra, ACT 0200 

Australia 

(Joint work with: J.M. Soto-Crespo, A. Ankiewicz) 

Abstract: ”Rogue waves”, ”freak waves”, ”killer waves” and similar names have been 

the topic of several recent publications related to giant single waves appearing in the 

ocean ”from nowhere”. Hitherto, we do not have a complete understanding of this phenomenon 

due to the difficult and risky observational conditions. Those who experience 

these phenomena while being on a ship would be busy saving their lives rather than 

making measurements. It is difficult to explain the high amplitudes that can occur in the 

open ocean using linear theories based on the superposition principles. Nonlinear theories 

of ocean waves are more likely to explain why the waves can ”appear from nowhere” 

than linear theories. The reason for the phenomenon can lie in the instability of a certain 

class of initial conditions that tend to grow exponentially and hence have the possibility 

of increasing up to very high amplitudes. Rogue waves can be described as ”waves that 

appear from nowhere and disappear without a trace”. This expression can be applied 

both to rogue waves in the ocean and rational solutions of the nonlinear Schroedinger 

equation (NLSE). There is a hierarchy of rational solutions of ’focussing’ NLSE with 

increasing order and with progressively increasing amplitude. The solutions can describe 

”rogue waves” with virtually infinite amplitude. They can appear from smooth initial 

conditions that are only slightly perturbed in a special way, and are given by our exact 

solutions. Thus, a slight perturbation on the ocean surface can dramatically increase 

the amplitude of the singular wave event that appears as a result. We also numerically 

calculated chaotic waves of the focusing NLSE, starting with a plane wave modulated 

by relatively weak random waves. We show that the peaks with highest amplitude of the 

resulting wave composition (rogue waves) can be described in terms of exact solutions 

of the NLSE in the form of the collision of Akhmediev breathers. 

15

16 

The Eccentric Connectivity Index of Nanotubes and 

Nanotori 

Ali Reza Ashrafi 

email: akilicman@putra.upm.edu.my 

Department of Mathematics 

University of Kashan 

Kashan - Iran 

(Joint work with: M. Saheli) 

Abstract: Let G be a molecular graph. The eccentric connectivity index ξ(G) of G is 

defined as ξ(G) = 

u∈V (G) degG(u)εG(u), where degG(u) denotes the degree of vertex 

u and εG(u) is the largest distance between u and any other vertex v of G. In this 

paper an exact formula for the eccentric connectivity index of T UC4C8(S) nanotubes 

and nanotori are given.

Session 1.3: Differential Equations I 

Chair: Bulent Karasozen 

Place: Hall 3 

17

18 

First-Order Three-Point Boundary Value Problems at 

Resonance 


email: mesliza@perlis.uitm.edu.my 

Jabatan Matematik, Universiti Teknologi MARA, Kampus Arau 02600 Arau, Perlis 

Malaysia 

(Joint work with: H.B. Thompson, M. Jusoh) 

Abstract: We consider three-point boundary value problems for a system of first-order 

equations in perturbed systems of ordinary differential equations at resonance. We obtain 

new results for the above boundary value problems with nonlinear boundary conditions. 

In particular, we consider a system of first-order equations which is arising from scalar 

second-order equation. The existence of solutions is established by applying a version of 

Brouwer’s Fixed Point Theorem which is due to Miranda.

Boundary value problems for the Helmholtz equation in 

domains bounded by closed curves and open arcs 

Pavel Krutitskii 

email: biem@mail.ru 

KIAM, Department 4, Miusskaya Sq. 4, Moscow 125047 

Russia 

Abstract: Boundary value problems for the Helmholtz equation are studied in planar 

domains bounded by closed curves and open arcs. Either Dirichlet or Neumann bondary 

condition is specified on the whole boundary (i.e. on both closed curves and open arcs). 

Theorems on existence and uniqueness of a classical solution are proved. The integral 

representation for a solution in the form of potentials is obtained. Each boundary value 

problem is reduced to the uniquely solvable Fredholm equation of the 2-nd kind and index 

zero for the density in potentials. Dirichlet and Neumann problems for the propagative 

Helmholtz equation are studied for exterior domain [5-8], while problems for dissipative 

Helmholtz equation [1-4] are studied in both interior and exterior domains. Problems in 

domains bounded by closed curves and problems in the exterior of open arcs in a plane 

are particular cases of our problems. 

References: 

1. Krutitskii P.A. // Hiroshima Math.J., 1998, v.28, 149-168. 

2. Krutitskii P.A. // ZAMM, 1997, v.77, No.12, p.883-890. 

3. Krutitskii P.A. // Zeitschr. Analys. Anwend., 1997, v.16, No.2, p.349-362. 

4. Krutitskii P.A. // Int.J.Maths.Math.Sci., 1998, v.21, 209-216. 

5. Krutitskii P.A. // Nonlin. Anal., TMA, 1998, v.32, 135-144. 

6. Krutitskii P.A. // J. Math. Kyoto Univ., 1998, v.38, No.3, p.439-452. 

7. Krutitskii P.A. // Math. Comp. Simul., 2000, v.52, 345-360. 

8. Krutitskii P.A. // ZAMM, 2000, v.80, No.8, p.535-546. 

19

20 

On the Partial Differential Equations with Non-Constant 

Coefficients and Convolution Method 

Adem Kilicman 

email: akilicman@putra.upm.edu.my 


University Putra Malaysia 

43400 UPM, Serdang 

Selangor - Malaysia 

(Joint work with: Hassan Eltayeb) 

Abstract: The purpose of this study is to compute solutions of some explicit initialboundary 

value problems for the one-dimensional wave equation with non constant coefficients 

by means of the Laplace transform which in general has no solution.

Step size strategies on the numerical integration of the 

systems of differential equations 

Gulnur Celik Kizilkan 

email: gckizilkan@selcuk.edu.tr 

Selcuk University, Science Faculty, Math Department, Kampus/Konya - TURKEY 

(Joint work with: K. Aydin) 

Abstract:In this study, the step size strategies have been obtained such that the local 

error is smaller than desired error level in the numerical integration of 

and 

X ′ (t) = AX(t) 

X ′ (t) = AX(t) + ϕ(t, X) 

equation systems in interval [t0, T ]. The algorithms have been given that calculate step 

sizes and numerical solutions according to these strategies and numerical solutions. The 

algorithms have been supported by the numerical examples. 

21

22 

Session 1.4: Mathematical Programming I 

Chair: M Fernanda P. Costa 

Place: Hall 4

Modeling Facility Location and Supplier Selection with 

Suppliers Product Quality and Contract Fee for Strategic 

Supply Chain Design 

Eren Ozceylan 

email: eozceylan@selcuk.edu.tr 

Selcuk University, Industrial Engineering Department, Campus 42100, Konya 

Turkey 

(Joint work with: T. Paksoy) 

Abstract: This paper proposes a novel mixed integer linear programming model for 

solving supply chain network design problems including deterministic parameters, choice 

of multi-quality products of suppliers, supplier engagement contracts, and single-period 

contexts with total profit maximizing. The strategic level of supply chain planning and 

tactical level planning of supply chain are aggregated to propose an integrated model. 

The model integrates location and capacity choices for suppliers, plants, distribution 

centers and retailers selection, product range assignment and production flows according 

to suppliers product quality choices. There is a trade-off between product quality which 

is transported from suppliers and its production costs in manufacturers. There are three 

quality levels for a product according to its procurement: First Quality, Second Quality 

and Third Quality. Decision maker has to choose the supplier which he/she will work with 

evaluating its engagement fee and its quality. Engagement decisions whether will be or 

not, for the suppliers are binary decision variables and the production and transportation 

flow decisions have continuous decision variables. An integrated supply chain network 

system consists of multiple suppliers, manufacturers, distribution centers, retailers are 

considered. Finally, the proposed model is discussed with a numerical example. 

23

24 

On Numerical Optimization Methods for Infinite Kernel 

Learning 

Sureyya Ozogur Akyuz 

email: sozogur@sabanciuniv.edu 

Faculty of Engineering and Natural Sciences, Vision and Pattern Recognition Lab. 

Sabanci University, Orhanli Tuzla, 34956, Istanbul - Turkey 

(Joint work with: G. Ustunkar, G. W. Weber) 

Abstract: A subfield of artificial intelligence, machine learning (ML), is concerned with 

the development of algorithms that allow computers to “learn”. ML is the process of 

training a system with large number of examples, extracting rules and finding patterns 

in order to make predictions on new data points (examples). The most common machine 

learning schemes are supervised, semi-supervised, unsupervised and reinforcement 

learning. These schemes apply to natural language processing, search engines, medical 

diagnosis, bioinformatics, detecting credit fraud, stock market analysis, classification of 

DNA sequences, speech and hand writing recognition in computer vision, to encounter 

just a few. In this study, we focus on optimization methods for developing Support Vector 

Machines (SVMs) which is one of the most powerful methods currently in machine learning. 

In ML algorithms, one of the crucial issues is the representation of the data. Discrete 

geometric structures and, especially, linear separability of the data play an important role 

in ML. If the data is not linearly separable, a kernel function transforms the nonlinear 

data into a higher-dimensional space in which the nonlinear data are linearly separable. 

As the data become heterogeneous and large-scale, single kernel methods become 

insufficient to classify nonlinear data. Convex combinations of kernels were developed to 

classify this kind of data in Bach et. al. 2004. Nevertheless, selection of the finite combinations 

of kernels is limited up to a finite choice. In order to overcome this discrepancy, 

a novel method of “infinite” kernel combinations for learning problems which is named 

by Infinite Kernel Learning (IKL) has recently been proposed by Özö˘gür-Akyüz et.al. 

2008, with the help of infinite and semi-infinite programming regarding all elements in 

kernel space. This will provide to study variations of combinations of kernels when considering 

heterogeneous data in real-world applications. Looking at all infinitesimally fine 

convex combinations of the kernels from the infinite kernel set, the margin is maximized 

subject to an infinite number of constraints with a compact index set and an additional 

(Riemann-Stieltjes) integral constraint due to the combinations. After a parametrization 

in the space of probability measures, it becomes semi-infinite. In this study, we built IKL 

model with well known numerical methods of semi-infinite programming and compared 

the numerical results. We improved the discretization method for our specific model and 

proposed two new algorithms. The simulation of the IKL is performed on different data 

sets from UCI machine learning repository. Finally, we proved the convergence of the numerical 

methods and we analyzed the conditions and assumptions of these convergence 

theorems such as optimality and convergence.

A DEA based approach for solving the multiple objective 

shortest path problem 

Alireza Davoodi 

email: alirzd@yahoo.com 

Department of Mathematics, Islamic Azad University, Neyshabur Branch, Neyshabur, Iran 

Abstract: Finding the shortest (least costly) path in a network is one of the important 

and interesting subjects in network flow problems. When each arc has just one type of 

cost, there exist some simple methods to find the shortest path. But if there are more than 

one type of cost (vector of cost), the non-dominated path plays the role of the best path. 

In this case a Multiple Objective problem is created to find the non-dominated path. 

In this paper a DEA based approach is introduced to find the non-dominated path(s) 

in a multiple cost network. This method can determine all non-dominated paths and 

the best one. Finally, when the priority and importance of these costs are different from 

each other, a modified model is introduced to solve them which is capable of identifying 

non-dominated paths based on the incorporating of Weight Restrictions in DEA models. 

25

26 

Robustification of CMARS 

Fatma Yerlikaya Ozkurt 

email: fatmayerlikaya@gmail.com 

Middle East Technical University Department of Mathematics and Institute of Applied 

Mathematics Inonu Bulvari 06531 Ankara - Turkey 

(Joint work with: G.W. Weber, A. Ozmen) 

Abstract: CMARS developed at IAM, METU, as an alternative approach to a wellknown 

regression tool MARS from data mining and estimation theory, is based on a 

penalized residual sum of squares (PRSS) for MARS as a Tikhonov regularization (T.R.) 

problem. CMARS treated this problem by a continuous optimization technique called 

Conic Quadratic Programming (CQP) which is permitting to use interior point methods. 

CMARS is particularly powerful in handling complex and heterogeneous data. In 

this presentation, we include the existence of uncertainty in the future scenarios into 

CMARS. In fact, generally, those data include noise in both input and output variable: 

the data of the regression problem is not exactly known or cannot be exactly measured, 

or the exact solution of the problem cannot be implemented due to inherent inaccuracy 

of the devices. Furthermore, the data can undergo small changes by variations in the 

optimal experimental design. This altogether leads to uncertainty in constraints and objective 

function. To overcome this difficulty, we refine to use our CMARS algorithm by 

important robust optimization which purposes to find an optimal or near optimal solution 

that is feasible for every possible realization of the uncertain scenario. We analyze 

how uncertainty enters the CMARS model, firstly, with complexity terms in the form of 

integrals of squared first and second order derivatives of the model functions and, then, 

the discretized TR and, finally, the CQP form of the problem. Then, we employ robust 

optimization as developed by Aharon Ben-Tal, Laurent El Ghaoui et al.. In this study, 

we present the new Robust CMARS (RCMARS) in theory, method and applied to real 

life problems, we discuss structural frontiers and give and outlook to future research.

Session 1.5: Numerical Analysis and Software I 

Chair: Kuniyoshi Abe 

Place: Hall 5 

27

28 

A high accurate difference-analytical method for solving 

Laplace’s equation on polygons with nonanalytic boundary 

conditions 

Suzan Cival Buranay 

email: suzan.buranay@emu.edu.tr 

Department of Mathematics, Eastern Mediterranean University 

Gazimagusa, Cyprus, Mersin 10 

Turkey 

(Joint work with: A. Dosiyev) 

Abstract: In most of existing high accurate methods (see [1], [2]) for solving Laplace’s 

boundary value problems with singularities, boundary functions on the sides that cause 

the singularity are given as analytic functions of the arclength measured along the boundary 

of the polygon. The boundary functions being nonanalytic on the mentioned sides 

arise difficulties on the methods based on series expansion of the exact solution around 

the singular points. In this presentation, we develop the high accurate Block Grid Method 

[2] for the solution of the Dirichlet problem on polygons by combining finite difference 

approximation of Laplace’s equation with the approximation of the special integral representation 

of the exact solution for nonanalytic boundary functions around the singular 

points. 

References 

[1] Z.C. Li, Combined Methods for Elliptic Problems with Singularities, Interfaces and 

Infinities. Kluwer Academic Publishers, Dordrech, Boston and London, 1998. 

[2] A.A. Dosiyev, The high accurate block-grid method for solving Laplace’s boundary 

value problem with singularities, SIAM J. Numer. Anal.,42,1, 153-178, 2004.

An Application of a New Fuzzy Robust Regression 

Algorithm to Actuarial Science 

Kamile Sanli Kula 

email: kamilesanlikula@gmail.com 

Ahi Evran University 

Faculty of Arts and Sciences 


40200 Kirsehir - Turkey 

(Joint work with: Fatih Tank, Turkan Erbay Dalkilic) 

Abstract: In this study, a fuzzy robust regression method is proposed to construct 

a model that describes the relation between dependent and independent variables in 

insurance. Our approach is an alternative to ordinary least squares and classical robust 

regression methods in insurance. Furthermore, a new model which contains data on 

month of and number of payments, is proposed. This new approach allows to determine 

total claim amounts in the related month as an alternative to the model suggested by 

Rousseeuw et. al. 

29

30 

Comparison of Exponentially fitted Explicit Runge-Kutta 

methods for Solving ODEs 


email: fudziah i@yahoo.com.my 

Department of Mathematics, Universiti Putra Malaysia 

43400, Serdang, Selangor 

Malaysia 

(Joint work with: A. Karimi, N. Md Ariffin, M. Abu Hassan) 

Abstract: Based on the near-optimal RK44M method derived by Dormand (1996) we 

constructed the exponentially fitted Runge-Kutta method using the technique introduced 

by Simos (1998) and also the technique suggested by Berghe et. al (1999) resulting in 

two types of exponentially fitted Runge-Kutta methods. Numerical experiments based 

on the two techniques as well as the original RK44M are tabulated and compared in 

terms of accuracy, which clearly shown the advantage of the technique used by Berghe.

Numerical Integration of a Fuzzy Riemann Double Integral 

Fereidoon Khadem 

email: khadem f2000@yahoo.com 

Department of Mathematics, Zanjan Branch 

Islamic Azad University 

Zanjan - Iran 

(Joint work with: M.A. Fariborzi Araghi) 

Abstract: In this paper, the double fuzzy Riemann integrals and their numerical integration 

are proposed. At first, we introduce a double fuzzy Riemann integral whose 

integrand is a fuzzy-valued function and limits of integration are crisp real numbers. For 

this purpose, we prove a theorem to show the a-level set of the double fuzzy integral 

which is a closed interval where end points are double crisp Riemann integrals.In this 

case, we apply the double Simpson’s rule in order to approximate these double integrals. 

Also we present an algorithm to approximate the value of the membership function of the 

double fuzzy integral in a given point like r in 0-level. Finally, two numerical examples 

are solved to illustrate the efficiency of the proposed method. 

31

30 September 2009, 13:30-15:45 

PARALLEL SESSIONS 2

Session 2.1: Approximation and Interpolation I 

Chair: Gulen B. Tunca 

Place: Hall 1 

35

36 

Statistical Convergence for Set-Valued Functions 

Halil Gezer 

email: halil.gezer@emu.edu.tr 

Department of Mathematics, Eastern Mediterranean University, 

Gazimagosa, Cyprus, Mersin 10, Turkey 

(Joint work with: H. Aktuglu) 

Abstract: In this paper we consider statistical convergence for set-valued functions. We 

also prove a Korovkin Type Approximation Theorem for set valued functions in the sense 

of statistical convergence.

Hermite-Birkhoff interpolation problems on the roots of the 

unity 

Elias Berriochoa 

email: esnaola@uvigo.es 

Universidad de Vigo, Facultad de Ciencias Campus as Lagoas s/n 32004 Ourense, Spain 

(Joint work with: A. Cachafeiro) 

Abstract: We consider a general Hermite-Birkhoff interpolation problem on the n-roots 

of the unity, {z1, · · · , zn}, that is, given p nonnegative different integers ν1, · · · , , νp and 

p n-dimensional vectors (u1,ν1 · · · un,ν1 ) · · · (u1,νp · · · un,νp ), the problem is to find a 

polynomial p(z) of lower degree satisfying the conditions: 

p (j) (zi) = ui,ν j for i = 1, · · · , n j = ν1, · · · , νp. 

An important topic in the Hermite-Birkhoff problem is the existence and uniqueness of 

the solution. If in the previous problem we say that it uses p derivatives ν1, · · · , νp, in 

our contribution we deal with ν1 = 0 and we study: 

(1) Existence and uniqueness for the problem with 2 derivatives. 

(2) Existence and uniqueness for the problem with 3 derivatives. 

(3) We give an algorithm to decide when the problem with p derivatives has unique solution. 

Taking into account the previous results we obtain analogous Hermite-Birkhoff interpolation 

problems for four privileged nodal systems on the bounded interval. Finally 

we present algorithms to obtain explicit solutions of the Hermite-Birkhoff interpolation 

problems with a low cost on the unit circle as well as on the bounded interval, (see [1]) 

. 

References 

1. E. Berriochoa, A. Cachafeiro, Algorithms for solving Hermite Interpolation problems 

using the Fast Fourier Transform, J. Comput. Appl. Math. accepted. 

2. I.J. Schoenberg, On Hermite-Birkhoff interpolation, J. Math. Anal. Appl. 16 (1966), 

538-543. 

37

38 

Weak and strong convergence theorems for a finite family of 

I−asymptotically nonexpansive mapping 

Liping Yang 

email: yanglping2003@126.com 

University of Minho, Department of Mathematics for Sciencie and Technology - Portugal 

(Joint work with: X. Xie) 

Abstract: The purpose in this paper first introduce the class of I−asymptotically nonexpansive 

nonself-maps. Then, an iteration scheme for approximating common fixed points 

of a finite family of Ii−asymptotically nonexpansive nonself-mappings belonging to this 

class (when such common fixed points exist) is constructed,and strong and weak convergence 

theorems are proved. Our theorems improve and generalize important related 

results of the previously known results in this area.

q-Statistical Convergence 

Serife Bekar 

email: serife.bekar@emu.edu.tr 



(Joint work with: H. Aktuglu) 

Abstract: In the present work we introduced a q-analogue of the Cesaro Matrix of order 

one and we define a new type of convergence, called q-Statistical convergence. 

39

40 

Comparison of Exponentially fitted Explicit Runge-Kutta 

methods for Solving ODEs 


email: fudziah i@yahoo.com.my 

Department of Mathematics, Universiti Putra Malaysia 


Malaysia 

(Joint work with: A. Karimi, N. Md Ariffin, M. Abu Hassan) 

Abstract: Based on the near-optimal RK44M method derived by Dormand (1996) we 

constructed the exponentially fitted Runge-Kutta method using the technique introduced 

by Simos (1998) and also the technique suggested by Berghe et. al (1999) resulting in 

two types of exponentially fitted Runge-Kutta methods. Numerical experiments based 

on the two techniques as well as the original RK44M are tabulated and compared in 

terms of accuracy, which clearly shown the advantage of the technique used by Berghe.

A novel 2D finite-volume method for advection problems 

with embedded moving-boundaries 

Yunus Hassen 

email: yunus.hassen@cwi.nl 

CWI & Fac. Aeros. Eng, TU Delft 

MAS2: Modeling, Simulation & Analysis (CWI) Science Park 123 

1098 XG Amsterdam 

Netherlands 

(Joint work with: Barry Koren) 

Abstract: In this work, we present an accurate method, using a novel immersedboundary 

approach, for solving advection problems numerically. As is standard in the 

immersed-boundary methods, moving bodies are embedded in a fixed, two-dimensional, 

Cartesian grid. We employ the method of lines — a higher-order cell-averaged fixedgrid 

finite-volume method for the spatial discretization and the explicit Euler’s scheme 

for the time integration. The essence of the present method is that specific fluxes in 

the vicinity of a moving body are computed in such a way that they accurately and 

monotonously accommodate the boundary conditions valid on the moving body. The 

immersed-boundary method, in general, is a method in which boundary conditions are 

indirectly incorporated into the governing equations. It is very suitable for simulating 

flows around flexible, moving and/or complex bodies (see4 for a comprehensive review). 

Basically, the bodies of interest are just embedded in non-deforming Cartesian grids that 

do not conform to the shape of the body. The governing equations are modified to include 

the effect of the embedded bodies (EBs). Doing so, mesh (re)generation difficulties associated 

with body-fitted grids are obviated; and, the underlying regular fixed grid allows 

to use a simple data structure as well as simpler numerical schemes over a majority of 

the domain. Here, considering we have a solid-body immersed inside a fluid domain, we 

obtain the discrete EBs associated with individual control volumes, at any given time. 

The body is immersed into the fixed, Cartesian, finite-volume grid and the points of intersections 

of the boundaries of the immersed body with the walls of each computational 

cell are detected. Then, these discrete EBs are accurately aligned with the grid lines 

and the fluxes that are affected by the EBs are especially modified. As a result, these 

fixed-grid fluxes (indirectly) incorporate the embedded-boundary conditions associated 

with the respective moving EBs (see1 for details). To suppress wiggles, tailor-made limiters 

are introduced for the special fluxes. Over the majority of the domain, where we 

do not have influence of EBs, we use standard methods, i.e. van Leer’s κ-scheme3 and 

Koren’s κ= 1 

3 -limiter,2 on the underlying regular fixed-grid. Moreover, for the temporal 

discretization, we employ a special technique — the time integration is locally adaptive. 

Depending on the crossing of finite-volume walls by an EB, time steps are split in the 

vicinity of each EB, to avoid an abrupt flux-reversal. As a result, we achieve a gradual 

transition of the fluxes, in time, at those walls. To validate our method, we consider a 

unit hypothetical ‘cylinder’ of arbitrary radius, as an initial solution for the quantity to 

be advected. The sharp discontinuities of the initial solution are assumed to be infinitely 

41

42 

thin EBs (‘wall of the cylinder’) going with the flow. The ‘cylinder’ is then placed at 

an arbitrary initial location and advected with the Molenkamp velocity field. 5 An exact 

solution for this problem is computed with the method of characteristics. The numerical 

results obtained for linear scalar advection problems are remarkably very accurate, 

without requiring much computational overhead. They show a significant improvement 

in resolution over those computed using the standard methods. It is anticipated that the 

method can be easily extended to real fluid-flow equations. 

References 

1. Y. Hassen & B. Koren: Finite-volume discretizations and immersed boundaries, in: 

B. Koren, C. Vuik (Eds.), Lect. Notes Comput. Sci. Eng. 71 (2009), Springer-Verlag, 

Berlin (in press). 

2. B. Koren: A robust upwind finite-volume method for advection, diffusion and source 

terms, in: C.B. Vreugdenhil, B. Koren (Eds.), Notes Numer. Fluid Mech. 45 (1993), 

Vieweg, Braunschweig, pp.117–138. 

3. B. van Leer: Upwind-difference methods for aerodynamic problems governed by the 

Euler equations, in: B.E. Engquist, S. Osher, R.C.J. Somerville (Eds.), Lect. Appl. 

Math. 22(2) (1985), Amer. Math. Soc., Providence, RI, pp.327-336. 

4. R. Mittal & G. Iaccarino: Immersed boundary methods, Annu. Rev. Fluid Mech. 37 

(2005), 239–261. 

5. C.R. Molenkamp: Accuracy of finite-difference methods applied to the advection equation, 

J. Appl. Meteor. 7 (1968), 160–167.

Session 2.2: Numerical Linear Algebra I 


Place: Hall 2 

43

44 

Explicit Representation of Hessenbergians: Application to 

General Orthogonal Polynomials 

Venancio Tomeo 

email: tomeo@estad.ucm.es 

University Complutense of Madrid, Statistic School 

Avda Puerta de Hierro s/n. 28040 - Madrid 

Spain 

(Joint work with: Jesus Abderraman) 

Abstract: An explicit representation for the determinant of any upper Hessenberg 

matrix in Cn×n , with non nulls subdiagonal terms, is achieved by means of a quasitriangular 

matrix with the same determinant value. It gives rise to a representation 

with nested functions on matrix elements hi,j from the original Hessenberg matrix. Like 

an interesting application, this representation is introduced on polynomials belonging 

to general orthogonal sequences on the complex plane { Pn(z)} ∞ n=0 , whose terms are 

Pn(z) = |Inz − Dn|, with Dn a upper Hessenberg matrix. Here the polynomials are 

monic without loss of generality. The compact representation is valid for any known, or 

unknown, class of general orthogonal polynomials. Comparison with recognized representations 

of some orthogonal polynomials illustrates its generality.

The Powers of Anti(2k+1)-Diagonal Matrices and Fibonacci 

Numbers 

Fatih Yilmaz 

email: fyilmaz@selcuk.edu.tr 

Selcuk University, Faculty of Science 


42003 Selcuklu, Konya 

(Joint work with: Humeyra Kiyak, Irem Gurses, Mehmet Akbulak, Durmus Bozkurt) 

Abstract: At this study, we consider arbitrary integer powers of anti(2k+1)diagonal 

n-square matrices (n=4k, k=1,2,...). We compute integer powers of this matrix and give 

a formula with Fibonacci numbers and also investigate some properties of the matrix. 

References 

[1] A. P. Stakhov, Fibonacci matrices, a generalization of the Cassini Formula, and a 

new coding theory, Chaos, Solitons and Fractals, 30 (2006) 56-66. 

[2] M. Basu, B. Prasad, The generalized relations among the code elements for Fibonacci 

coding theory, Chaos, Solitons and Fractals, 10.1016/j.chaos.2008.09.030. 

[3] T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience Publication, 

2001. 

45

46 

On computing powers for one type of matrice by Pell and 

Jacobsthal Numbers 

Fatih Yilmaz 

email: fyilmaz@selcuk.edu.tr 



42003 Selcuklu, Konya 

(Joint work with: Humeyra Kiyak, Irem Gurses, Mehmet Akbulak, Durmus Bozkurt) 

Abstract: We compute arbitrary positive integer powers of the following matrices 

A=pentadiag(-1,0,1,0,-1) related with Pell and Jacobsthal numbers. Also we investigate 

some properties of this matrices.

On the properties of generalized Fibonacci and Lucas 

numbers with binomial coefficients 

Hasan Huseyin Gulec 

email: hhgulec82@gmail.com 

Selcuk University, Science Faculty, Department of Mathematics 

Konya - Turkey 

(Joint work with: N. Taskara, K. Uslu) 

Abstract:In this study, new properties of generalized Fibonacci and Lucas sequences 

G(n), n=1,2,... with binomial coefficients have been obtained by using properties of 

Fibonacci F(n) and Lucas L(n) numbers with binomial coefficients. 

47

48 

IDR-based relaxation methods for solving linear systems 

Seiji Fujino 

email: fujino@cc.kyushu-u.ac.jp 

Kyushu University 

6-10-1 Hakozaki Higashi-ku, Fukuoka 812-8581 

Japan 

(Joint work with: Y. Kusakabe, M. Harumatsu) 

Abstract:The classical Jacobi, GS(Gauss-Seidel) and SOR (Successive Over- 

Relaxation) methods are well known. Moreover the GS and SOR methods have been 

used for solution of problems which stem from a variety of applications. The GS and 

SOR methods, however, have some issues in reality. Because the GS and SOR methods 

greatly depend on spectrum of iteration matrix. In my talk, we extend IDR (Induced 

Dimension Reduction) Theorem proposed by Sonneveld and van Gijzen in 2008 to the 

residual of the conventional iterative methods, and accelerate its convergence and stability 

of the conventional methods. Through numerical experiments, we reveal significant 

effect of accelerated residual of the Sonneveld typed Jacobi, GS and SOR methods.

A Shift Strategy for Superquadratic Convergence in the dqds 

Algorithm for Singular Values 

Kensuke Aishima 

email: Kensuke Aishima@mist.i.u-tokyo.ac.jp 

University of Tokyo, 7-3-1, Hongo, Bunkyoku, Tokyo- Japan 

(Joint work with: T. Matsuo, K. Murota, M. Sugihara) 

Abstract: In 1994, the dqds algorithm was proposed by Fernando–Parlett [2] to compute 

the singular values of bidiagonal matrices to high relative accuracy. The dqds algorithm 

is currently implemented in LAPACK as DLASQ routine which has a complicated shift 

strategy evolved in order to achieve high efficiency. In ICCAM2008, we proved that 

DLASQ enjoys a superquadratic convergence, based on a convergence theory of the 

dqds algorithm established in [1]. In this talk, we will present a simple and novel shift 

strategy for the superquadratic convergence in the dqds algorithm. We will also present 

a numerical example to illustrate the superquadratic convergence. 

References 

1. K. Aishima, T. Matsuo, K. Murota and M. Sugihara: On Convergence of the dqds 

Algorithm for Singular Value Computation, SIAM J. Matrix Anal. Appl., Vol. 30 

(2008), pp. 522–537. 

2. K. V. Fernando and B. N. Parlett: Accurate singular values and differential qd algorithms, 

Numer. Math., Vol. 67 (1994), pp. 191–230. 

49

50 

Session 2.3: Optimization I 

Chair: Ana Maria A.C.Rocha 

Place: Hall 3

A Hybrid Genetic Pattern Search Augmented Lagrangian 

Method for Constrained Global Optimization 

Lino Costa 

email: lac@dps.uminho.pt 

Production and Systems Department 

Campus de Gualtar, Braga 

Portugal 

(Joint work with: Isabel Espirito Santo, Edite M.G.P. Fernandes ) 

Abstract: Hybridization of genetic algorithms with local search approaches can enhance 

their performance in global optimization. Genetic algorithms, as most population based 

algorithms, require a considerable number of function evaluations. This may be an important 

drawback when the functions involved in the problem are computationally expensive 

as it occurs in most real world problems. Thus, in order to reduce the total number of 

function evaluations, local and global techniques may be combined. Moreover, the hybridization 

may provide a more effective tradeoff between exploitation and exploration 

of the search space. In this study, we propose a new hybrid genetic algorithm based on 

a local pattern search that relies on an augmented Lagrangian function for constrainthandling. 

The local search strategy is applied to a subset (the elite) of the population. 

Numerical results with a set of benchmark constrained problems are provided. 

51

52 

Production Planning under Stochastic Demand for Fish 

Processed Product at North Sumatera Province, Indonesia 

Herman Mawengkang 

email: mawengkang@usu.ac.id 

Department of Mathematics, The University of Sumatera Utara 

FMIPA USU, Medan 

Indonesia 

Abstract: Marine fisheries plays an important role in the economic development of Indonesia. 

Besides being the most affordable source of animal protein in the diet of most 

people in the country, this industrial sector could provide employment to thousands who 

lives at coastal area. In this paper we consider the management of small scale traditional 

business at North Sumatera Province which performs processing fish into several 

local seafood products. The inherent uncertainty of data (e.g. demand, fish availability), 

together with the sequential evolution of data over time leads the production planning 

problem to a nonlinear mixed-integer stochastic programming model. We use scenario 

generation based approach for solving the model.

Centralized Resource Allocation with Stochastic Data 


email: mirbolouki.mahnaz@gmail.com 


Science and Research Branch 


Tehran, Iran 

(Joint work with: F. Hosseinzadeh Lotfia, N.Nematollahi, M.H. Behzadi, M.R. Mozaffari) 

Abstract:Data Envelopment Analysis (DEA) is a technique based on mathematical programming 

for evaluating the efficiency of homogeneous Decision Making Units (DMUs). 

In this technique inefficient DMUs are projected on to the frontier which constructed 

by the best performers. Centralize Resource Allocation (CRA) is a method in which all 

DMUs are projected on to the efficient frontier through solving just are DEA model. The 

indent of this paper is to present the Stochastic Centralized Resource Allocation (SCRA) 

in order to allocate centralized resource where inputs and outputs are stochastic. The 

concept discussed throughout this paper is illustrated using aforementioned example. 

keywords: Data envelopment analysis, Normal distribution, Quadratic programming, 

Resource allocation. 

53

54 

Special functions, non-linearity and algebraic and differential 

properties: Computational aspects 

Ana Maria A. C. Rocha 

email: arocha@dps.uminho.pt 

University of Minho, Dept. Production and Systems 

Campus de Gualtar 4710-057 Braga- Portugal 

(Joint work with: Tiago F. M. C. Martins, Edite M. G. P. Fernandes) 

Abstract: This paper implements the augmented Lagrangian methodology in a stochastic 

population based algorithm for solving nonlinear constrained global optimization 

problems. This class of global optimization problems is very important and frequently 

encountered in engineering applications. The method approximately solves a sequence of 

simple bound global optimization subproblems using a swarm intelligent algorithm. This 

is a stochastic population based algorithm that simulates fish swarm behaviors inside 

water. Fish in the swarm attempts to swarm, chase or search, in order to avoid danger 

and look for food. The best fish in the swarm corresponds to the best solution found. 

Based on this solution, the Lagrange multipliers as well as the penalty parameter are 

updated in the outer iterations of the algorithm. Several widely used benchmark problems 

are solved in a performance evaluation of the new algorithm when compared with 

other techniques.

A Regularized Modified Lagrangian Method for Nonlinearly 

Constrained Monotone Variational Inequalities 

Eman Hamad Al-Shemas 

email: e al shemas@hotmail.com 

PAAET,College of basic Education, Mathematics Department 

Main Capus - Shamiya 

Kuwait 

(Joint work with: A. Hamdi) 

Abstract: In this paper, we propose a new method for solving structured variational 

inequality problems. The proposed scheme combines the recent decomposition algorithm 

introduced by Deren Han [math. comp. modelling 37 (2003) 405-418] with the proximal - 

like techniques. under mild appropriate assumptions, we show that the method generates 

convergent sequences. 

55

56 

A new multiobjective differential evolution strategy for 

scattering uniformly the Pareto solution set for designing 

mechatronic systems 

Miguel Gabriel Villarreal-Cervantes 

email: gvillarr@cinvestav.mx 

Av. Instituto Politecnico Nacional 

2508 Col. San Pedro Zacatenco, C.P. 07360 Mexico, D.F. 

Mexico 

(Joint work with: Carlos Alberto Cruz-Villar, Jaime Alvarez-Gallegos) 

Abstract: Many processes and products in the area of mechanical and electrical engineering 

are showing an increasing integration of mechanical system with its embedded 

control system. This integration results in integrated systems called mechatronic systems. 

The design of mechatronic system involves the finding an optimal balance between 

the performance of the basic mechanical structure and the performance of the overall 

control system, and this synergy results in innovative solutions which have a better 

global performance. So, during the design phase of a mechatronic system, changes in the 

mechanical structure and the controller must be evaluated simultaneously. Nevertheless, 

the design in complex mechatronic systems is not an easy task. Design problems with 

multiple performance criteria require to formulate them as Pareto-based multi-objective 

optimization problems where the best compromise should be found by evaluating several 

incommensurable and often conflicting objectives. Multi-objective strategies based on 

differential evolution has been applied for solving multi-objective optimization problems 

since they can solve nonlinear, non-differentiable and discontinuous problems. Nevertheless, 

when the problem is dynamic as in the case of designing mechatronic systems, 

those strategies difficultly find a good Pareto front and they lack of a mechanism for 

distributing the solutions along the Pareto front. The dynamic problem has the main 

characteristics of having performance indexes and constraints varying on time. In addition, 

differential equations describing the dynamic behavior of the system must be 

included into the optimization problem. Hence, in this paper a new multi-objective evolutionary 

algorithm based on differential evolution for solving constrained multi-objective 

dynamic optimization problems is presented. The proposed approach adopts a secondary 

population in order to retain the non-dominated solutions found during the evolutionary 

process. The non-dominated solutions are found using the constrained domination 

principle. In addition, a self adaptive grid is considered for the secondary population 

to hold and distribute the found non-dominated solutions. In order to avoid overflow 

of the self adaptive grid, each element of the grid has a previous maximum number of 

non-dominated solutions (Pareto solutions) and the excess of these solutions are removed 

based on the crowding distance. The selection of the three individuals of the population 

for the mutation process of the differential evolution algorithm is changed to spread the 

exploration of non-dominated solutions in the elements of the self adaptive grid. The 

modification of the selection scheme consists on randomly generate the three individ-

uals from the element of the self adaptive grid of the secondary population instead of 

the entire parent population. This selection scheme has the main advantage that only 

non-dominated solutions in the element of the grid can be considered for the mutation 

process, such that, the non-dominated solutions of one element of the grid can not be 

mutated with the non-dominated solutions of others elements of the grid. The main contribution 

of this work is to present a new algorithm that spreads the search exploration 

for solving constrained multi-objective dynamic optimization problems. In addition, a 

mechatronic design approach is formulated as a nonlinear multi-objective dynamic optimization 

problem. The mechatronic design problem is used to validate the proposed 

algorithm. The results are compared with respect to another multi-objective evolutionary 

algorithm based on differential evolution and with respect to the approach that is 

representative of the state of the art in the area: the NSGA-II. 

57

58 

Session 2.4: Special Functions 

Chair: Patricia J.Y.Wong 

Place: Hall 4

On Koornwinder classical orthogonal polynomials 

Lidia Fernandez 

email: lidiafr@ugr.es 

Dpto. Matematica Aplicada. Universidad de Granada, 

Campus Universitario de Cartuja. E-18071. Granada 

Spain 

(Joint work with: T.E. Perez, M.A. Pinar) 

Abstract: In 1975, Tom Koornwinder studied examples of two variables analogues of the 

Jacobi polynomials in two variables. Those orthogonal polynomials are eigenfunctions 

of two commuting and algebraically independent partial differential operators. Some of 

these examples are well-known classical polynomials, such as orthogonal polynomials on 

the unit ball, on the simplex or the tensor product of Jacobi polynomials in one variable. 

The definition of classical orthogonal polynomials considered in this work, provides a 

different perspective on the subject. We analyze in detail the Koornwinder polynomials 

not considered classical by other authors. We pay special attention to differential and 

structural properties that they satisfy. 

References 

1. Fernndez, L., Prez, T. E., Piar, M. A., Classical orthogonal polynomials in two variables: 

a matrix approach, Numer. Algorithms 39 no. 1 3 (2005) 131142. 

2. Koornwinder, T., Two variable analogues of the classical orthogonal polynomials, Theory 

and application of special functions, Proceedings of Advanced Seminar, Mathematics 

Research Center, University Wisconsin, Madison, WI, 1975, Publ. No. 35, Academic 

Press, New York, 1975, 435495. 

3. Krall, H. L., Sheffer, I. M., Orthogonal polynomials in two variables, Ann. Mat. Pura 

Appl. Serie 4 76 (1967) 325376. 

59

60 

A note on a family of two variable polynomials 

Rabia Aktas 

email: raktas@science.ankara.edu.tr 

Ankara University 

Faculty of Science, Department of Mathematics 

06100 Tandogan-Ankara 

Turkey 

(Joint work with: A.Altin and F. Tasdelen Yesildal) 

Abstract: The main object of this paper is to construct a two-variable analogue of jacobi 

polynomials and give some properties of these polynomials. We show that these polynomials 

are orthogonal, then we obtain various differential formulas for these polynomials. 

Furthermore, we give some integral representations for these polynomials.

Some generalizations of multiple Hermite polynomials via 

Rodrigues formula 

Cem Kaanoglu 

email: kaanoglu@ciu.edu.tr 

Cyprus International University, Haspolat, North Cyprus 

Turkey 

(Joint work with: Mehmet Ali Ozarslan) 

Abstract: The object of this paper is to develope some properties of multiple Hermite 

polynomials. 1 For this, we consider a family of polynomials which defined by a Rodrigues 

formula and in particular case the polynomials include the multiple Hermite polynomials. 

1 The explicit forms, certain operational formulas involving these polynomials and 

linear generating function is obtained. 1 

References 

1. D. W. Lee, Properties of multiple Hermite and multiple Laguerre polynomials by the 

generating function, Integral Transforms and Special Functions, Vol.18, No.12, December 

2007, 855-869. 

61

62 

Extension of Gamma, Beta and Hypergeometric Functions 

Emine Ozergin 

email: emine.ozergin@emu.edu.tr 



(Joint work with: M.A. Ozarslan, A. Altin) 

Abstract: The main object of this paper is to present generalizations of gamma, beta 

and hypergeometric functions. Some recurrence relations, transformation formulas, operation 

formulas and integral representations are obtained for these new generalizations. 

Furthermore Tricomi type expansions are obtained for the generalized incomplete gamma 

function which was introduced by Chaudhry and Zubair. 1 

References 

1. M. A. Chaudhry and S. M. Zubair, Generalized incomplete gamma functions with 

applications, Journal of Computational and Applied Mathematics 55 (1994) 99-124.

Application of Padé approximation of differential transform 

method to the solution of prey and predator problem 

Onur Karaoglu 

email: karaogluonur@yahoo.com 

Selcuk University 

Department of Mathematics, Faculty of Science 

Campus, 42003, Konya 

TURKEY 

(Joint work with: Ayse Betul Koc, Haldun Alpaslan Peker, Yildiray Keskin, Yucel Cenesiz, Galip 

Oturanc, Sema Servi) 

Abstract: Mathematical model of the prey and predator problem is governed by system 

of nonlinear Volterra differential equations. In this study, solutions under the changing 

conditions of the problem are considered by Padé approximation of the differential transform 

method (DTM). Generally, Padé approximation provides a high accuracy of convergence 

to true solution on truncated series solutions. Some examples are presented to 

show alteration of the prey and predator rates in a population with respect to changing 

time. 

63

64 

Jensen divergence based on Fisher’s information 

Yoji Otani 

email: pablos@ugr.es 

Departamento de Matematica Aplicada Facultad de Ciencias Avenida de Fuentenueva, S/N 

18071 - Granada - SPAIN 

(Joint work with: A. Zarzo, J.S. Dehesa) 

Abstract: During the last years the Jensen-Shannon divergence between two or more 

arbitrary probability densities has been used in numerous mathematical and physical 

contexts. This relative information measure, in contrast to the Kullback-Leibler entropy 

or relative Shannon entropy, presents three important characteristics: symmetry under 

exchange of the involved densities, applicability to more than two densities, and finiteness 

even in the case that the involved densities have non-common zeros. In this paper we 

introduce a Jensen divergence based on the Fisher information. The Fisher information, 

in contrast to the Shannon entropy, is an information measure with a local character, 

providing a measure of the gradient and oscillatory content of the density. The new 

Jensen-Fisher divergence enjoys the same properties as the Jensen-Shannon divergence; 

namely, non-negativity, additivity when applied to an arbitrary number of probability 

densities, symmetry under exchange of these densities, vanishing if and only if all the 

densities are equal, and definiteness when these densities present non-common zeros. 

Moreover,the Jensen-Fisher divergence can be expressed in terms of the relative Fisher 

information as the Jensen-Shannon divergence does in terms of the Kullback-Leibler 

entropy. It is remarkable that the last property is only shared by these two divergences, 

in contrast with the recently introduced Jensen-Renyi and Jensen-Tsallis divergences. 

Here we present the theoretical grounds of the Jensen-Fisher divergence. We apply it to 

several families of probability densities (including the Rakhmanov densities associated to 

the classical families of orthogonal polynomials). Finally, a comparison with the Jensen- 

Shannon divergence and the relative Fisher information is performed.

Session 2.5: Statistics and Data Analysis I 

Chair: Ismihan Bayramoglu 

Place: Hall 5 

65

66 

Weibull-Negative Binomial Distribution 


email: mcagatay@artvin.edu.tr 

Artvin-Coruh University Science and Arts Faculty, Department of Statistics, Artvin - Turkey 

(Joint work with: Coskun Kus, Asir Genc) 

Abstract: Some probability distributions have been proposed to fit real life data with 

decreasing failure rates. In this article, a three-parameter distribution with decreasing 

failure rate is introduced by mixing Weibull and negative-binomial distributions. Various 

properties of the introduced distribution are discussed. An EM algorithm is used to 

determine the maximum likelihood estimates when one parameter is given or known. 

Illustrative examples based on real data are also given.

Comparison of a New Robust Test and Non-parametric 

Kruskal-Wallis Test in One-way Analysis Of Variance Model 

Yeliz Mert Kantar 

email: ymert@anadolu.edu.tr 

Anadolu University, Science Faculty 

Department of Statistics, Eskisehir 

Turkey 

(Joint work with: Birdal Senoglu, Omer L. Gebizlioglu) 

Abstract: Observations in many real life situations do not often follow a normal distribution. 

Moreover, outliers may exist in observed data. In these situations, normal theory 

tests based on least squares (LS) estimators have a low power and are not robust against 

plausible deviations from the assumed distribution. Therefore, we resort to nonparametric 

test procedures to analyze the non-normal data. In the context of one-way analysis 

of variance, the well-known nonparametric Kruskal-Wallis test based on ranks is used to 

compare the three or more groups of observations. In this paper, we compare the power 

and the robustness properties of the Kruskal-Wallis test with a new test, namely the 

test developed by enolu and Tiku (2004) when the distribution of error terms are type 

II censored generalized logistic. It is shown that the test is more powerful and robust 

in general. An application on a real data set is presented by using the test based on 

modified maximum likelihood (MML) estimators. 

67

68 

General Linear Model (GLM) Approach to Repeated 

Measurements Data Involving Univariate Analysis of 

Variance (ANOVA) and Multivariate Analysis of Variance 

(MANOVA) Techniques 

Neslihan Iyit 

email: niyit@selcuk.edu.tr 


Department of Statistics 

42031 Campus-Konya 

Turkey 

(Joint work with: Asir Genc) 

Abstract: A repeated measurements design is one in which at least one of the factors 

consists of repeated measurements on the same subjects or experimental units, under 

different conditions. Such a factor is commonly called a ”within-subjects” factor. A 

”between-subjects” factor is one in which each level of the factor contains different experimental 

units. The statistical analysis of such a repeated measurements design includes 

models for both the expected value of the observations and for their within-subject 

variance-covariance structure. General linear model (GLM) which is a traditional approach 

to repeated measurements data analysis for modeling the expected value of the 

observations as a linear function of explanatory variables is appropriate when it is assumed 

that the observations from different subjects are statistically independent and 

uncorrelated and that the variance-covariance structure is the same for each subject. 

From the violations of these assumptions, random intercept model (RIM) from linear 

mixed models (LMMs) is the preferred one for modeling flexible within-subject variancecovariance 

structure of the response variable instead of GLM approach to the repeated 

measurements data. In this paper, after defining the between-subjects factor as treatment 

and the within-subjects factor as time, GLM approach involving adjusted univariate tests 

and multivariate analysis of variance (MANOVA) technique and also RIM from LMMs 

approach to repeated measurements data is given in an application from a clinical trial.

Comparing Estimation Results in Nonparametric and 

Semiparametric 

Alper Sinan 

email: alpsin@selcuk.edu.tr 

Selcuk University, Faculty of Science, Department of Statistics 

42031 Campus-Konya / Turkey 


Abstract: In this study, estimation methods for nonparametric and semiparametric 

regression models are investigated. Nonparametric regression model is given by yi = 

q 

j=1 mj (xji) + εi, i = 1, 2, . . . , n where y is dependent variable, xji, i = 1, 2, . . . , n, 

j = 1, 2, . . . , q are independent variables, εi, i = 1, 2, . . . , n are the disturbance and 

mj (·) , j = 1, 2, . . . , q are regression functions. Kernel estimators and median method 

which is simple and commonly used method are evaluated in details. Choosing smoothing 

parameter h and the kernel function are also investigated. Semiparametric regression 

model is given by 

yi = β ′ 

Z + 

q 

mj (xji) + εi, i = 1, 2, . . . , n 

j=1 

where β is the parameters vector, Z is design matrix for parametric part of semiparametric 

model. The model determining process and mostly used estimation methods in 

semiparametric regression model are investigated. Results obtained by simulations in 

different sample sizes are compared. 

References 

1. Roy, N., 1997, “Nonparametric and Semiparametrc Analysis of Panel Data Models: 

An Application to Calorie-Income Relation for Rural South India”, University of California, 

Ph.D. Thesis, Riverside 

2. Liu, Z., 1998, “Nonparametric and Semiparametric Estimation and Testing of Econometric 

Models”, The University of Guelph, Ph.D. Thesis 

3. Pagan, A., Ullah, A., 1999, “Nonparametric Econometrics”, Cambridge University 

Press, Cambridge, U.K. 

4. Marlene, M., 2000, “Semiparametric Extensions to Generalized Linear Models”, Ph.D. 

Thesis Berlin. 

5. Yatchew, A., 2003, “Semiparametric Regression for the Applied Econometrician”, 

Cambridge Uni. press, UK 

6. Yapıcı Pehlivan, N., 2005, “Parametrik Olmayan Regresyonda Alternatif Tahmin Ediciler”, 

Selcuk University, Ph.D. Thesis, Institute of the Natural and Applied Sciences, 

Konya. 

69

70 

Confidence Intervals for Mean Time to Failure in 

Two-Parameter Weibull with Censored Data 

Noor Akma Ibrahim 

email: nakma@putra.upm.edu.my 

Institute for Mathematical Research, Universiti Putra Malaysia 


Malaysia 

(Joint work with: N. Poh Bee) 

Abstract: We consider a two-parameter Weibull distribution as the underlying distribution 

for a set of failure time data. For failure time distributions, the parameters are 

easily estimated by the maximum likelihood method. These estimators can then be used 

to estimate other quantity of interest such as the mean time to failure (MTTF) which 

plays an important role in reliability analysis. From the asymptotical normality of the 

maximum likelihood estimators, confidence intervals can be obtained. However, these 

results might not be very accurate for small sample sizes and/or large proportion of 

censored observations. For this purpose a simulation study with varying sample size and 

percentage of censoring was carried out to compare the accuracy of the asymptotical confidence 

intervals with confidence intervals based on bootstrap procedure. The alternative 

methodology of confidence intervals for the MTTF of Weibull distribution function is 

illustrated by using real data from engineering field. 

Key-Words: Two-parameter Weibull, failure time, MTTF, censored, maximum likelihood, 

bootstrap

Rough Set-based Functional Dependency Approach for 

Clustering Categorical Data 

Tutut Herawan 

email: tututherawan@yahoo.com 

Universiti Tun Hussein Onn Malaysia 

Parit Raja, Batu Pahat 86400, Johor 

Malaysia 

(Joint work with: Mustafa Mat Deris) 

Abstract: Clustering data is an integral part of data mining and has attracted much 

attention recently. However, few of these methods focus on categorical data. The main 

idea of the rough clustering for categorical data is a clustering data set is mapped as 

a decision table. This can be done by introducing a decision attribute. In this paper, a 

novel algorithm called MADE (Maximal Attributes Dependencies) which finds a decision 

attribute is presented. It is based on a maximal degree of attributes dependencies in 

categorical datasets. After selection, a divide and conquer method is used to cluster the 

data. Experimental results on three benchmark UCI datasets, i.e. Soybean, Zoo and 

Mushroom datasets show that MADE provides better performance with the baseline 

categorical data clustering algorithm with respect to computational complexity up to 

64%, 77% and 83%, response time up to 63%, 67% and 57% and cluster purity up to 

9%, 17% and 16%, respectively. 

71

30 September 2009, 16:15-18:30 

PARALLEL SESSIONS 3

Session 3.1: Mathematical Modelling, Analysis, Applications I 

Chair: Alejandro Zarzo 

Place: Hall 1 

75

76 

Parameter Estimation by ANFIS in Cases Where Outputs 

are Non-Symmetric Fuzzy Number 

Turkan Erbay Dalkilic 

email: tedalkilic@gmail.com 

Karadeniz Technical University 

Faculty of Arts and Sciences 

Department of Statistics and Computer Sciences 

61080, Trabzon - Turkey 

(Joint work with: Aysen Apaydin) 

Abstract: Regression analysis is an area of statistics that deals with the investigation 

of the dependence of a variable upon one or more variables. Recently, much research 

has studied fuzzy estimation. There are some approach exist in the literature for the 

estimation of the fuzzy regression model. The two of them are frequently used in parameter 

estimation, one of them is proposed by Tanaka et al. and it is known as linear 

programming approach and the other is fuzzy least square approach. 

The fuzzy inference system forms a useful computing framework based on the concepts 

of fuzzy set theory, fuzzy reasoning, and fuzzy if-then rules. The fuzzy inference system 

is a powerful function approximater. There are several different types of fuzzy inference 

systems developed for function approximation. The Adaptive-Network Based Fuzzy Inference 

System (ANFIS) is a neural network architecture that can solve any function 

approximation problem. In this study we will use the ANFIS for parameter estimation 

and propose an algorithm in cases where outputs are non-symmetric fuzzy number. In 

this algorithm the error measure is defined as the difference between the estimated outputs 

which are obtained by adaptive network and the target outputs. In order to obtain 

the difference between two fuzzy numbers, some fuzzy ranking method must used to define 

the operator -. There are many fuzzy ranking methods for measuring the difference 

between two fuzzy numbers in literature. In this work, the method of Chang and Lee, 

which is based on the concept of overall existence, will be used.

A Multizone Overset Algorithm for the Solution of Flow 

around Moving Bodies 

Fatemesadat Salehi 

email: fatemehsalehi62@yahoo.com 

Aerospace Engineering Department 

Amirkabir University of Technology 

Hafez Street, Tehran - Iran 

(Joint work with: S.M.H. Karimian, H. Alisadeghi) 

Abstract: A two-dimensional moving mesh algorithm is developed to simulate the general 

motion of two rotating bodies with relative translational motion. The grid includes a 

background grid and two sets of grids around the moving bodies. With this grid arrangement 

rotational and translational motions of two bodies are handled separately, with no 

complications. Inter-grid boundaries are determined based on their distances from two 

bodies. In this method, the overset concept is applied to hybrid grid, and flow variables 

are interpolated using a simple stencil. To evaluate this moving mesh algorithm unsteady 

Euler flow is solved for different cases using dual-time method of Jameson. Numerical 

results show excellent agreement with experimental data and other numerical results. 

To demonstrate the capability of present algorithm for accurate solution of flow fields 

around moving bodies, some benchmark problems have been defined in this paper. 

77

78 

Spectral Singularities of Sturm-Liouville Problems with 

Eigenvalue Dependent Boundary Conditions 

Nihal Yokus 

email: unluturk@science.ankara.edu.tr 




Turkey 

(Joint work with: E. Bairamov) 

Abstract: Let L denote the operator generated in L2(R+) by Sturm-Liouville equation 

−y ′′ 

+ q(x)y = λ 2 y, x ∈ R+ = [0, ∞) , 

y ′ 

(0) 

y(0) = α0 + α1λ + α2λ 2 , 

where q is a complex valued function and αi ∈ C, i = 0, 1, 2 with α2 = 0. In this article 

we investigate the eigenvalues and the spectral singularities of L and obtain analogs of 

Naimark and Pavlov conditions for L.

Vague DeMorgan Complemented Lattices 

Zeynep Eken 

email: zeynepeken@akdeniz.edu.tr 

Akdeniz University, Faculty of Science and Literature, Department of Mathematics, Antalya, 

Turkey 

(Joint work with: Sevda Sezer) 

Abstract: Vague partially ordered sets and vague lattices have been studied on the basis 

of many-valued equivalence relations. Then, the concept of DeMorgan complement was 

fuzzily defined on vague partially ordered sets. In this work, a new characterization of 

vague lattices will be given and the concept of DeMorgan complement on vague lattices 

will be defined. Furthermore, some examples on these concepts will be presented. 

79

80 

Approximating the singular integrals of Cauchy type with 

weight function on the interval 

Zainidin Karimovich Eshkuvatov 

email: ezaini@science.upm.edu.my 

Department of Mathematics, Faculty of Science, Universiti Putra Malaysia - Malaysia 

Abstract: It is known that the solutions of characteristic singular integral equations 

(SIEs) are expressed in terms of singular integrals of Cauchy type with weight functions 

of the form w(x) = (1 + x) ν (1 − x) µ , where ν = ± 1 

1 

, µ = ± . In this paper a new 

2 2 

quadrature formulas (QFs) are presented to approximate the singular integrals (SIs) 

of Cauchy type for all the solutions of characteristic SIE on the interval [-1,1]. Linear 

spline interpolation and modification discrete vortices method are used to construct QFs. 

Estimate of errors are obtained in the classes of functions Hα (A, [−1, 1]) and C1 ([−1, 1]). 

Numerical results are presented to show the validity of the QFs constructed.

Lobatto IIIA-IIIB Discretization for the Strongly Coupled 

Nonlinear Schrödinger Equation 


email: bulent@metu.edu.tr 



(Joint work with: Ayhan Aydin) 

Abstract: We construct second order symplectic and multisymplectic integrators for 

strongly coupled nonlinear Schrödinder equation using the Lobatto IIIA-IIIB partitioned 

Runge-Kutta method, which yield an semi-explicit scheme.Numerical dispersion properties 

and the stability of both integrators are investigated. Numerical results for different 

solitary wave solutions confirm the excellent long time behavior of symplectic and multisymplectic 

integrators by preserving local and global energy and momentum. 

81

82 

Session 3.2: Approximations and Interpolation II 

Chair: Miguel Angel Fortes 

Place: Hall 2

Rough Oscillatory Singular Integrals on R n 

Hussain Mohammed Al-Qassem 

email: husseink@qu.edu.qa 

Mathematics & Physics Department 

Qatar University P.O. Box 2713 

Doha - Qatar 

(Joint work with: L. Cheng, Y. Pan) 

Abstract: We obtain appropriate sharp estimates for rough oscillatory integrals. By 

using these estimates and employing an extrapolation argument we obtain some new 

and previously known results for oscillatory integrals under various sharp size conditions 

on the kernel functions. 

83

84 

Exponentially fitted two–step hybrid methods for y ′′ = f(x, y) 

Raffaele D’Ambrosio 

email: rdambrosio@unisa.it 

University of Salerno 

Via Ponte Don Melillo, 84084 Fisciano (SA) 

Italy 

(Joint work with: E. Esposito, B. Paternoster) 

Abstract: It is the purpose of this talk to derive two-step hybrid methods for second 

order ordinary differential equations with oscillatory or periodic solutions, having 

frequency-dependent parameters. We show the constructive technique to derive exponentially 

fitted methods, together with a regularization technique useful to express the 

coefficients in a suitable form to reduce the effects of numerical cancellation. We analyse 

the properties of the resulting methods, carrying out the linear stability analysis also 

in the case of parameters depending on two frequencies. We then perform some numerical 

experiments underlining the properties of the derived methods and confirming the 

theoretical expectations.

Improving the Gradient based search Direction to Enhance 

Training Efficiency of Back Propagation based Neural 

Network algorithms 

Nazri Mohd Nawi 

email: nazri@uthm.edu.my 


PO Box 101, 86400, Parit Raja, Batu Pahat, Johor 

Malaysia 

(Joint work with: Rozaida Ghazali, Mohd Najib Mohd Salleh) 

Abstract: Most of the gradient based optimisation algorithms employed during training 

process of back propagation networks use negative gradient of error as a gradient based 

search direction. A novel approach is presented in this paper for improving the training 

efficiency of back propagation neural network algorithms by adaptively modifying this 

gradient based search direction. The proposed algorithm uses the value of gain parameter 

in the activation function to modify the gradient based search direction. It has been 

shown that this modification can significantly enhance the computational efficiency of 

training process. The proposed algorithm is generic and can be implemented in almost 

all gradient based optimisation processes. The robustness of the proposed algorithm 

is shown by comparing convergence rates for gradient descent, conjugate gradient and 

quasi-Newton methods on many benchmark examples. 

85

86 

Approximation Properties of Q-Konhauser Polynomials 

Gurhan Icoz 

email: gurhanicoz@gazi.edu.tr 

Gazi University, Faculty of Science and Literature, Department of Mathematics, Besevler, 

Ankara, Turkey 

(Joint work with: F. Tasdelen Yesildal) 

Abstract: In this work, we introduce q−Konhauser polynomials. The main object of 

this paper is to investigate the approximation properties of linear positive operators 

including q−Konhauser polynomials with the help of Korovkin’s theorem. The rates of 

convergence of these operators are computed by means of modulus of continuity, Peetre’s 

K − functional and the elements of Lipschitz class. Also we introduce the r−th order 

generalization of these operators and we obtain approximation properties of them.

An Alternative Region-Based Active Contour Model Using 

Cauchy-Schwartz Divergence 

Veronica Biga 

email: v.biga@sheffield.ac.uk 

The University of Sheffield 

Department of Automatic Control and Systems Engineering Mappin Street , Sheffield S1 3JD 

United Kingdom 

(Joint work with: Daniel Coca, Visakan Kadirkamanathan, Stephen A. Billings) 

Abstract: In this paper, we explore the potential of a new geometric active contour 

model for image segmentation based on Cauchy-Schwartz divergence. In essence, the 

model assumes that the image features of the target region and background region are 

random variables independently sampled from two probability distribution functions 

(PDFs) and can be separated by maximising the divergence measure. By using shape 

gradient tools we rigorously formulate the corresponding criterion to be optimised over 

the evolving regions. A common problem in well established ratio-type models such 

as the ones based on entropy and Kullback-Leibler distance are numerical errors in the 

approximation of region-specific PDFs. Although kernel density estimation methods help 

in overcoming this disadvantage, the problem of evaluating the criterion becomes critical 

as the size of the feature space shrinks. In contrast, Cauchy-Schwartz divergence is a 

product-type measure and can be evaluated even in the case of only a few feature samples 

available. By using texture descriptors to extract relevant regions, we demonstrate the 

applicability of our model on a range of synthetic and real cell imaging examples and 

compare the results against the alternative Kullback-Leibler distance approach. Finally, 

we focus the conclusions on robustness and versatility of our model in dealing with 

segmentation problems in phase-contrast microscopy images. 

87

88 

On Chlodovsky variant of multivariate beta operator 

Gulen Bascanbaz Tunca 

email: tunca@science.ankara.edu.tr 

Ankara University, Faculty of Science 


06100, Tandogan-Ankara 

Turkey 

(Joint work with: Yalcin Tuncer) 

Abstract: In this work, we state Chlodovsky variant of multivariate beta operator, say 

multivariate beta-Chlodovsky operator. We show that the multivariate beta-Chlodovsky 

operator can preserve the properties of the general function of modulus of continuity and 

also Lipschitz constant of a Lipschitz continuous function. Furthermore we set an Hω (∆) 

class by the function of modulus of continuity ω and taking its concave (convex) majorant 

ω ∗ into account, we give some general results for functions belonging to Hω (∆).

Session 3.3: Nonlinear Equations and Mathematical Modelling 

Chair: Ersan Akyildiz 

Place: Hall 3 

89

90 

Stability analysis of recurrent neural networks with deviated 

argument of mixed type 

Enes Yilmaz 

email: enes@metu.edu.tr 

Middle East Technical University 

Department of Mathematics and Institute of Applied Mathematics 

Inonu Bulvari 06531 Ankara - Turkey 

(Joint work with: M.U. Akhmet, D. Arugaslan) 

Abstract: In this talk, we apply the method of Lyapunov functions for differential 

equations with piecewise constant argument of generalized type to a model of recurrent 

neural networks (RNNs). The main novelty of the model is that it involves both advanced 

and delayed arguments. Sufficient conditions are obtained for global exponential stability 

of the equilibrium point. Examples with numerical simulations are presented to illustrate 

the results.

The Periodicity of Solutions of the Rational Difference 

Equation xn+1 = pnxn−k+xn−(k+1) 

qn+xn−(k+1) 

Turgut Tollu 




Abstract: In this study, we investigated to generaliziation of the solutions of the difference 

equation x(n + 1) = [p(n).x(n − k) + x(n − (k + 1))]/[q(n) + x(n − (k + 1))] with 

(k +1)-th periodic coefficients, where every k, x(−k), x(−k +1), ..., x(0) are real numbers 

and p(n) is not equal to q(n). Also, we obtained that the solutions were periodic with 

period (k + 1). 

91

92 

On the behavior of solutions of a rational system 

x(n + 1) = 1/[y(n − 1)], y(n + 1) = x(n − 1)/[x(n).y(n − 2)] 

Emine Hekimoglu 

email: o.hekimoglumat@hotmail.com 




Abstract: In this study, we analysed to the solutions of a rational system x(n + 1) = 

1/[y(n−1)], y(n+1) = x(n−1)/[x(n).y(n−2)], where x(−1), x(0), y(−2), y(−1), y(0) are 

positive real numbers. Also, we obtained that the solutions of this system were periodic 

with period eight.

A modification on some improved Newton’s method without 

direct function evaluations 

Behzad Ghanbary 

email: b.ghanbary@yahoo.com 

Guilan University 

Faculty of Sciences, Department of Mathematics 

Rasht - Iran 

(Joint work with: Jafar Biazar) 

Abstract: In this paper, we are concerned with the further study for system of nonlinear 

equations. Due to the fact that systems with inaccurate function values or problems 

with high computational cost arise frequently in science and engineering, recently such 

systems have attracted researchers interest. In this work we present a new method which 

is independent of function evolutions and has a quadratic convergence. This method 

can be viewed as a extension of some recent methods for solving mentioned systems of 

nonlinear equations. Numerical results of applying this method to some test problems 

show the efficiently and reliability of method. 

93

94 

Error Inequalities for Discrete Hermite Interpolation 

Patricia J. Y. Wong 

email: ejywong@ntu.edu.sg 

School of Electrical and Electronic Engineering 

Nanyang Technological University 

50 Nanyang Avenue, Singapore 639798, Singapore 

(Joint work with: Fengmin Chen) 

Abstract: In this paper we shall develop a class of discrete Hermite interpolates Hρf 

for a function f defined on the discrete interval N[a, b + 2] = {a, a + 1, · · · , b + 2}. Let 

ρ : a = k1 < k2 < · · · < km = b, ki ∈ Z, 1 ≤ i ≤ m 

be a uniform partition of N[a, b]. We say Hρf is the discrete Hermite interpolate of f if 

Hρf(t) is a quintic polynomial in each subinterval [ki, ki+1], 1 ≤ i ≤ m − 1 with 

Hρf(ki) = f(ki), ∆Hρf(ki) = ∆f(ki), ∆ 2 Hρf(ki) = ∆ 2 f(ki), 1 ≤ i ≤ m. 

Further, we shall offer explicit error bounds for the discrete Hermite interpolate, i.e., 

f − Hρf ≤ aj 

max 

t∈N[a,b+2−j] |∆jf(t)|, 2 ≤ j ≤ 6 

where the constants aj, 2 ≤ j ≤ 6 are explicitly given.

Parallel Newton-like methods for solving systems of 

nonlinear equations 

Josep Arnal 

email: arnal@ua.es 

University of Alicante, Carretera San Vicente del Raspeig 

s/n - 03690 San Vicente del Raspeig - Alicante 

Spain 

Abstract: A class of Newton-like iterative methods for the parallel solution of systems of 

nonlinear algebraic equations is investigated. The methods permit that the Jacobian be 

singular at some points. Theorems are obtained demonstrating convergence for the cases 

when the jacobian matrix is monotone and when the jacobian matrix is an H-matrix. 

Numerical experiments of these methods on a parallel computing system are discussed. 

Experiments show the e?ectiveness and feasibility of the new methods. 

95

96 


Sciences II 

Chair: Jose M.Matias 

Place: Hall 4

Deriving Elastic Fields in an Anisotropic Bi-material 

Demet Ersoy 

email: sinemsezer@akdeniz.edu.tr 


Izmir University of Economics 

Balcova, 35330, Izmir 

Turkey 

(Joint work with: V. Yakhno) 

Abstract: In this paper we consider a bi-material consisting of two elastic anisotropic 

plates with the same thickness. One layer of this bi-material is located between two 

planes 

P1 = {x = (x1, x2, x3) : −∞ < x1 < ∞, −∞ < x2 < ∞, x3 = 0} , 

 

P2 = x = (x1, x2, x3) : −∞ < x1 < ∞, −∞ < x2 < ∞, x3 = ℓ 

 

2 

and characterized by elastic moduli C − 

jkℓm and density ρ− . 

The second layer of bi-material is situated between two planes 

 

P2 = x = (x1, x2, x3) : −∞ < x1 < ∞, −∞ < x2 < ∞, x3 = ℓ 

 

, 

2 

P3 = {x = (x1, x2, x3) : −∞ < x1 < ∞, −∞ < x2 < ∞, x3 = ℓ} 

and characterized by elastic moduli C + 

jkℓm and density ρ+ . 

A plane wave with normal vector e3 = (0, 0, 1) drops on one side of bi-material at 

time t = 0. We consider the vibration problem which consists of finding the displacement 

vector 

u(x, t) = (u1(x, t), u2(x, t), u3(x, t)) 

for each point x of bi-material for the time t from [0, T ], where T is a given number. 

The mathematical model of the vibration in this bi-material is given by the following 

anisotropic system of elasticity [1,2,3]: 

with initial data 

ρ ∂2 3 uj ∂σjk 

= , (x1, x2) ∈ R 

∂t2 ∂xk 

k=1 

2 , x3 ∈ (0, ℓ ℓ 

) ∪ ( , ℓ), t ∈ R, (1) 

2 2 

uj(x, t)|t

98 

σj3| 

x3= ℓ 2 −0 = σj3| 

x3= ℓ +0, t ∈ R, (5) 

2 

where j = 1, 2, 3; σjk = 3 

ℓ,m=1 Cjkℓm(x3) ∂u j 

∂xm for all j, k = 1, 2, 3; Cjkℓm(x3) and 

ρ(x3) have the following forms: 

Cjkℓm(x3) = 

ρ(x3) = 

C − 

jkℓm , if 0 < x3 < ℓ 

2 , 

ℓ 

, if 2 < x3 < ℓ; 

 

ρ− , if 0 < x3 < ℓ 

2 , 

ρ + , if ℓ 

2 < x3 < ℓ, 

C + 

jkℓm 

where C − 

jkℓm , C+ 

jkℓm , ρ− > 0, ρ + > 0 are given constants for all j, k, ℓ, m = 1, 2, 3; T is 

a given positive number; δ3j is Kronecker symbol, δ(t) is Dirac delta function depending 

on t and u(x, t) = (u1(x, t), u2(x, t), u3(x, t)) is unknown vector function depending on 

x, t. 

An explicit formula for a solution of the vibration problem (1) − (5) has been found. 

Using this formula the simulation of elastic fields have been obtained. 

Keywords: System of anisotropic elasticity, bi-materials, elastic wave, boundary conditions, 

matching conditions, simulation. 

References 

1. Dieulesaint E. and D.Royer, ”Elastic Waves in Solids I” Springer-2000. 

2. Fedorov F.I., ”Theory of elastic waves in crystals” Plenum Press-1968. 

3. Ting T.C.T.,”Anisotropic elasticity: Theory and applications” Oxford University 

Press-1996. 

(6)

A Boundary Value Problem of the Frequency-Dependent 

Maxwell’s System for Layered Materials 

Sengul Kecelli 

email: sengul.kecelli@hotmail.com 


Dokuz Eylul University 

Tinaztepe Kampusu 35160, Buca -Izmir 

Turkey 

(Joint work with: V. Yakhno) 

Abstract: The main object of the paper is a boundary value problem of the frequencydependent 

Maxwell’s system for a layered material. The frequency-dependent Maxwell’s 

system has the following form (Eom,2004) 

curlxH(x, ω) = (−iω)εE(x, ω) + J(x, ω), (1) 

curlxE(x, ω) = (iω)µH(x, ω), (2) 

99 

divx(εE(x, ω)) = ρ(x, ω), (3) 

divx(µH(x, ω)) = 0, (4) 

where x = (x1, x2, x3) ∈ R 3 , i 2 = −1; ω is a given number (frequency). 

We assume that vector functions H, E, J and the scalar function ρ are independent 

of x3, that is, they depend on variables x1, x2 and the frequency ω. 

Let 

D = {x = (x1, x2) : 0 < x1 < b1, 0 < x2 < b2} , 

Dk = {x = (x1, x2) : 0 < x1 < b1, rk−1 < x2 < rk, } , 

where b1 > 0, b2 > 0, r0 = 0, rN = b2, rk k = 1, 2, . . . , N are given numbers. Let Γ 

be the boundary of the domain D. 

We assume also that the magnetic permeability µ(x) and the electric permittivity 

ε(x) are given in the form 

⎧ 

⎧ 

ε1, x ∈ D1, 

µ1, x ∈ D1, 

⎪⎨ ε2, x ∈ D2, 

⎪⎨ µ2, x ∈ D2, 

ε(x) = . . ; µ(x) = . . 

. 

⎪⎩ 

. 

. 

. 

⎪⎩ 

. 

. 

εN , x ∈ DN . 

µN , x ∈ DN . 

The Conservation law of charge is satisfied: 

divxJ(x, ω) + (−iω)ρ(x, ω) = 0. (5) 

Let J(x, ω) be a given vector function for x ∈ D, ω = 0 be a fixed number, ρ(x, ω) 

be a function satisfying (5). The main problem of this paper is to find H(x, ω), E(x, ω)

100 

satisfying (1)-(4) and the following boundary and matching conditions (Eom, 2004) 

(E × n) Γ = 0, (H × n) Γ = 0, (6) 

(D · n) Γ = 0, (B · n) Γ = 0, (7) 

(E × ν) Sk = 0 ⇒ (E S + 

k 

(H × ν) Sk = 0 ⇒ (H S + 

k 

(D · ν) = 0 ⇒ (µE 

Sk + 

S 

k 

(B · ν) = 0 ⇒ (µH 

Sk + 

S 

k 

− E − ) × ν = 0; 

S 

k 

− H S − 

k 

− εE S − 

k 

− µH S − 

k 

) × ν = 0; 

) · ν = 0; 

) · ν = 0, 

where k = 1, . . . , (N − 1); n is an external normal vector to Γ and ν = (0, 1, 0); 

D = εE and B = µH denotes electric and magnetic flux densities, respectively. Sk 

denotes the surface x2 = rk, between domains Dk and Dk+1 k = 1, 2, . . . , N − 1. This 

situation means that there is no electric and magnetic fields outside of the domain D. 

We have showed that the frequency-dependent Maxwell’s system (1)-(4) is reduced 

to two Helmholtz equations. Using boundary conditions (6)-(7) and matching conditions 

(8) we set up two subproblems for these Helmholtz equations. The separation of variables 

and the Fourier series expansion method are used for solving subproblems. 

As a result, the explicit formula for a solution of the original problem has been 

obtained for cases N = 1, 2, 3. These explicit formulae are presented in the form of 

Fourier series expansion. 

Keywords: Maxwell equations, layered medium, exact solution, the Fourier series 

expansion method. 

References 

Eom, 2004. Eom, H.J. (2004). Electromagnetic wave theory for boundary-value problems. 

Springer, Berlin. 

(8)

A Study on the Multiple Logistic Regression Analysis to 

Determine Risk Factors for the Smoking Behavior 

Sevgi Yurt Oncel 

email: syoncel@gmail.com 

Kirikkale University 


71100 Yahsihan - Kirikkale 

Turkey 

(Joint work with: Omer L. Gebizlioglu, Fazil Aliev) 

Abstract: To determine the risk factor of smoking using a multiple binary logistic regression 

method and to assess the risk variable for smoking, which is a major and growing 

health problem in many countries. We presented a questionnaire study, consisting of 1737 

students (869 males and 866 females, smokers or non-smokers). The data were collected 

using a standard questionnaire that contains 34 questions. The study was carried out in 

the Kirikkale University, Kirikkale, Turkey in 2008. A multiple logistic regression model 

was used to evaluate the data and to find the best model. The receiver operating characteristic 

curve was found successful to predict person with risk factor for smoking. Data 

were analyzed using the SPSS/PC package 15.0. 

We classified 68.8 % of the participants using the logistic regression model. This study 

suggests that gender, smoking status of mother, smoking status of sibling, education of 

mother and income are independent predictors of the risk of smoking status in our population. 

In addition, the findings of the present study indicate that the use of multivariate 

statistical method as a multiple logistic regression in smoking, which may be influenced 

by many variables, is better than univariate statistical evaluation. 

101

102 

Numerical simulation of tsunami generated in North Pacific 

Ocean near Japan 

Yoji Otani 

email: gev421104@s.okayama-u.ac.jp 

Graduate School of Environmental Science, Okayama University 

1-1, Naka 3-chome, Tsushima, Kita-ku, Okayama 700-8530 

Japan 

(Joint work with: M. Watanabe, L. Ying, K. Yamamoto, Hashentuya) 

Abstract: 

Propagation of a tsunami wave generated in Nankai Trough area in the North Pacific 

Ocean is simulated, and numerical techniques are described and some numerical 

results are presented. The simulation is based on a system of partial differential equations 

derived from momentum equations and a continuity equation. The Gauss-Kruger 

projection method is used to convert depth data given in terms of longitude and latitude 

to rectangular coordinates. Finite element approximation applied to spatial derivatives 

leads to a system of ordinary differential equations, which can be solved numerically 

by standard ODE solvers. Numerical results show the behavior of tsunami propagating 

towards coasts of Japan and changes in tsunami wave height and propagation speed. 

Furthermore, numerical results will be compared with observed data. Our numerical 

techniques will also be verified by testing some numerical solutions against analytical 

solutions

A new numerical method for solving 2D Electrical 

Impedance Tomography Inverse Problem 

Ata Olah Abbasi 

email: ata.abbasi@yahoo.com 

Sharif University of Technology 

Department of Electrical Engineering 

P.O. Box: 11365-8639 

Iran 

(Joint work with: B. Vosoughi Vahdat) 

Abstract: In this paper, we present a new numerical method for solving electrical 

impedance tomography inverse problem in 2D. Electrical Impedance Tomography (EIT) 

is a simple and economic technique to capture images from the interior of the subject. 

EIT is based on measurements made from electrodes on the surface of the subject. EIT 

inverse problem (image reconstruction algorithm) is an ill-posed and nonlinear problem. 

Recently, an inverse solution for EIT has been developed based on block method, however 

this method is using nonlinear algorithm. The present article provides a direct numerical 

method solution. This new approach provides fast solver algorithm and has ability to 

solve complicated problems. Numerical examples prove the reliability of our method. We 

have assumed that the subject has a 2D rectangular shape and is made of similar blocks. 

Also the presented algorithm demonstrates a reduction of both computation time and 

storage requirements without sacrificing the numerical stability. 

103

104 

Control strategy of avian influenza based on modeling and 

simulation 

Tertia Delia Nova 

email: delianovatertia@yahoo.com 

Faculty of Animal Husbandry, Andalas University, West Sumatera 

Limau Manis, Padang 

INDONESIA 

(Joint work with: H. Mawengkang, M. Watanabe) 

Abstract: Since outbreaks of bird flu (avian influenza) spread widely in 2003, poultry 

farms have been under constant threat by loss due to the disease characteristic of domestic 

birds. Source of the disease is the influenza virus H5N1 endogenous to wild birds. 

Unlike wild birds, infection of virus to domestic birds brings serious symptoms leading 

to death. In a production process of a poultry farm, the entire population of domestic 

birds is balanced with the capacity of the farm by supply of new healthy birds and by 

shipping of healthy birds to be products. Some of infected birds die of the disease while 

others stay alive. However regardless of being alive or dead, infected birds remain as a 

source of infection unless they are completely disposed of. These factors have been taken 

into account to construct a model consisting of nonlinear ordinary differential equations. 

Populations of susceptible birds and infected birds are unknown variables of those differential 

equations. Analysis of the model has led to the conclusion that the most effective 

measure against outbreak of bird flu within poultry farm is constant removal of infected 

birds, and that removal of infected birds can solely prevent an outbreak of bird flu. 

The analysis has also shown that vaccination is effective in conjunction with removal 

of infected birds, and that vaccination cannot prevent an outbreak without removal of 

infected birds. Study of mechanism for outbreak of bird flu is continued from the previous 

study, and a control strategy of avian influenza based on modeling and simulation 

is proposed. In particular, spatial effects are taken into accounts in modeling and simulation. 

In practice, so-called rapid test is conducted to detect infection of bird flu. It is 

a spot-check in which samples are taken randomly from the bird population of a farm. 

If one bird is found positive for infection, all the birds in the farm are disposed of. The 

result of previous study shows that it is necessary to dispose of infected birds only, not 

all the birds in the farm. 1 This conclusion is examined with spatial effects taken into 

consideration in modling and simulation. 

References 

1. Tertia Delia Nova, Herman Mawengkang, Masaji Watanabe, Modeling and analysis of 

bird flu outbreak within a poultry farm, Submitted.

Session 3.5: Mathematical Programming II 

Chair: Venancio Tomeo 

Place: Hall 5 

105

106 

Fuzzy Optimization of A Multi Stage Multi Item 

Closed-Loop Flexible Supply Chain Network Under Fuzzy 

Material Requirement Constraints 

Eren Ozceylan 



Turkey 

(Joint work with: T. Paksoy, N.Y. Pehlivan) 

Abstract: This work applies fuzzy sets to integrating the distribution problem of a 

multi product, multi tiered closed loop flexible supply chain network (involves suppliers, 

factories, warehouses, distribution centers, retailers, end customers and collection, 

recovery, recycling centers) under fuzzy material requirement constraints. The proposed 

fuzzy multi-objective linear programming (FMOLP) model attempts to simultaneously 

minimize total transportation costs between all echelons and total fixed costs of manufacturers 

and distribution centers. The model has been formulated as a mixed-integer 

linear programming model where data are modelled by triangular fuzzy numbers. Finally, 

a numerical example is solved by a professional package program, compiled the 

results and discussed.

Identification, Optimization and Dynamics of Regulatory 

Networks under Uncertainty 


email: gweber@metu.edu.tr 



(Joint work with: E. Kropat, C.S. Pedamallu) 

Abstract: The mathematical analysis of gene-environment networks is of significant importance 

in computational biology and life sciences. Time-discrete and time-continuous 

dynamical systems can be applied for a modeling of the complex interactions and regulating 

effects between the genetic and environmental variables. In order to include 

the effects of random noise and uncertainty, various regression models based on interval 

arithmetics but also on spline regression and stochastic differential equations have 

been developed. In this talk, we survey recent advances on gene-environment networks 

based on interval arithmetics and ellipsoidal uncertainty which correspond to the degree 

of correlation between system variables and related errors. For an identification 

of parameters of a gene-environment network based on interval arithmetics, Chebychev 

approximation and generalized semi-infinite optimization are applied. In addition, the 

time-discrete counterparts of the nonlinear equations are introduced and their parametrical 

stability is investigated. In addition, we analyze the topological landscape of 

the gene-environment networks in terms of structural stability. For an analysis of geneenvironment 

networks under ellipsoidal uncertainty, the uncertain states of clusters of 

data variables are represented in terms of ellipsoids and the interactions between the 

various clusters are defined by affine-linear coupling rules. Explicit representations of 

the uncertain multivariate states of the system are determined with ellipsoidal calculus. 

In addition, we introduce various regression models that allow us to determine the unknown 

system parameters from uncertain (ellipsoidal) measurement data by applying 

semidefinite programming and interior point methods. We analyze the structure of the 

optimization problems obtained, especially, in view of their solvability, we discuss the 

structural frontiers and research challenges, and we conclude with an outlook. 

107

108 

Using Dirichlet-to-Neumann operators and Conformal 

Mappings with Approximate Curve Factors in Waveguide 

Problems 

Erkki Laitinen 

email: anders.andersson@vxu.se 

University of Oulu, Dep. of Math. Sci. 90014 University of Oulu 

Finland 

(Joint work with: I. Konnov, O. Kashina) 

Abstract: We consider a problem of optimal allocation of a homogeneous resource in 

spatially distributed systems such as communication networks, where both utilities of 

consumers and network expenses must be taken into account. This approach leads to 

a two-objective optimization problem, which involves non-differentiable functions whose 

values are computed algorithmically. We propose several approaches to define a solution 

and to construct corresponding solution methods for such problems. In particular, new 

subgradient methods for non-differentiable Pareto optimization problems are suggested. 

Their work is illustrated by computational results on test problems.

Finding Efficient and Inefficient Outlier Layers by Using 

Skewness Coefficient 


email: mirbolouki.mahnaz@gmail.com 




Tehran, Iran 

(Joint work with: F.Hosseinzadeh Lotfi, G.R. Jahanshahloo, M.H. Behzadi) 

Abstract:Data Envelopment Analysis (DEA) is a mathematical programming for evaluating 

the efficiency of a set of Decision Making Units (DMUs). One of the significant 

problems which is under consideration in the field of DEA, is distinguishing the outlier 

DMUs. Such DMUs have a different behavior in contrast to the general prevailing 

behavior of the population; which is caused by the incorrect way of collecting data or 

other unknown factors which can be social, political and etc. These DMUs can affect the 

efficiency of other DMUs. Thus recognizing and excluding them from the population; or 

reducing their effect and proportioning their status with the population can influence 

the improvement of total efficiency of population. Therefore incorrect deduction about 

the population can be prevented. In this paper, on basis of the assumption that the efficiency 

of population must have a unimodal symmetric distribution, a method based on 

the skewness of efficiency and inefficiency has been presented. By utilizing this method 

all the outlier DMUs; in different layers; can be recognized. 

keywords: Data Envelopment Analysis, Normal distribution, Outlier, Skewness. 

109

110 

Multi-Objective Optimization Model for Solving Risk-Based 

Environmental Production Planning Problem in Crude Palm 

Oil Industry 

Hendaru Sadyadharma 

email: hendarusadyadharma@yahoo.com 

Doctoral Program of Natural Resources and Environment, 

the University of Sumatera Utara 

Kampus USU, Medan 

Indonesia 

(Joint work with: Z. Nasution, H. Mawengkang) 

Abstract: The crude palm oil industry could give significant impact to the economic 

development of a country. Despite obvious benefits of this industrial development, it 

contributes to environmental degredation from both input and output sides of its activities. 

On the input side, crude palm oil mill uses much water in production process 

and consumes high energy. On the output side, manufacturing process generates large 

quantity of wastewater, solid waste/by-product and air pollution. In environmental production 

planning and risk management decision process in crude palm oil industry, there 

are several alternatives need to be analyzed in terms of multiple noncommonsurate criteria, 

and many different stakeholders with conflicting preferences are involved. In this 

paper we propose a multi-objective optimization model for tackling such environmental 

risk production planning problem. In order to solve the model we develop an interactive 

method which involves analytical hierarchy process (AHP) strategy.

Staff scheduling with priority constraints 

Sacha Varone 

email: sacha.varone@hesge.ch 

Haute Ecole de Gestion de Geneve 

Route de Drize 7 1227 Carouge 

SWITZERLAND 

(Joint work with: David Schindl) 

Abstract:Staff scheduling, also known as timetabling, is a task to be done in any organisation. 

In this paper we model this problem as a minimal cost at maximal flow network 

problem, therefore with a polynomial time complexity. Besides the usual availability 

and skills constraints, we consider additional constraints: targeted workload, satisfaction 

of employees seen as a rotation constraint, some tasks require several employees, some 

employee can not be assigned to a same task. We consider cost specifications as those 

associated to the types of employee, overtime, task delayed, profit associated with the 

execution of a task. We also analyse the limits of our model, showing types of constraints 

that transform the problem into a NP-hard problem. 

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112

1 October 2009, 10:30-12:45 

PARALLEL SESSIONS 4

Session 4.1: Mathematical Modelling, Analysis, Applications II 

Chair: Alireza Ashrafi 

Place: Hall 1 

115

116 

Some Properties of Q-Biorthogonal Polynomials 

Fatma Tasdelen Yesildal 

email: yardimci@science.ankara.edu.tr 




Turkey 

Abstract: Almost four decades ago, Konhauser introduced and studied a pair of 

biorthogonal polynomials which are suggested by the classical Laguerre polynomials. 

The so-called Konhauser biorthogonal polynomials of the second kind were indeed considered 

earlier by Toscano without their biorthogonality property which was emphasized 

upon in Konhausers investigation. Many properties and results for each of these biorthogonal 

polynomials (such as generating functions, Rodrigues formulas, recurrence relations, 

and so on) have since been obtained in several works by others. The main object of this 

paper is to present a systematic investigation of the general family of q-biorthogonal 

polynomials. Several interesting properties and results for the q-Konhauser polynomials 

are also derived.

Positive solutions for nonlinear first-order m-point boundary 

value problem on time scale 

Ismail Yaslan 

email: iyaslan@pau.edu.tr 

Pamukkale University 


20070, Denizli 

Turkey 

Abstract: In this study, we investigate the existence of positive solutions for nonlinear 

first-order m-point boundary value problem on time scales by means of fixed point 

theorems. 

117

118 

Error Estimates for Discrete Spline Interpolation 

Fengmin Chen 

email: chen0519@ntu.edu.sg 

School of Electrical and Electronic Engineering 

Nanyang Technological University 

50 Nanyang Avenue, Singapore 639798, Singapore 

(Joint work with: Patricia J. Y. Wong) 

Abstract: We shall develop a class of discrete spline interpolates Sρf for a function f 

defined on the discrete interval N[a, b + 2] = {a, a + 1, · · · , b + 2}. Let 

ρ : a = k1 < k2 < · · · < km = b, ki ∈ Z, 1 ≤ i ≤ m 

be a uniform partition of N[a, b]. We say Sρf is the discrete spline interpolate of f 

provided that Sρf(t) is a quintic polynomial in each subinterval [ki, ki+1], 1 ≤ i ≤ m−1 

with 

Sρf(ki) = f(ki), 1 ≤ i ≤ m 

and 

∆Sρf(kj) = ∆f(kj), ∆ 2 Sρf(kj) = ∆ 2 f(kj), j = 1, m. 

We also establish explicit error estimates for the discrete spline interpolate, i.e., 

f − Sρf ≤ dj 

max 

t∈N[a,b+2−j] |∆jf(t)|, 2 ≤ j ≤ 6 

where the constants dj, 2 ≤ j ≤ 6 are explicitly derived.

Computational analysis for microbial depolymerization 

processes of xenobiotic polymers based on mathematical 

models and experimental results 

Masaji Watanabe 

email: watanabe@ems.okayama-u.ac.jp 

Graduate School of Environmental Science, Okayama University 

1-1, Naka 3-chome, Tsushima, Kita-ku, Okayama 700-8530 

Japan 

(Joint work with: F. Kawai) 

Abstract: Water-soluble polymers are not suitable for recycle or incineration, and 

biodegradation is an essential factor of environmental protection against undesirable 

accumulation of those polymers. Biodegradation is also essential for water-insoluble polymers, 

so-called plastics, because they are not completely recycled nor incinerated, and 

it is important to understand the mechanism of microbial depolymerization processes of 

xenobiotic polymers. In general, microbial depolymerization processes are classified into 

two types: exogenous type and endogenous type. In exogenous type depolymerization processes, 

molecules lose their weight by separation of monomer units from their terminals. 

Class of polymers subject to exogenous type depolymerization includes polyethylene and 

polyethylene glycol. In endogenous type depolymerization processes, molecules are separated 

at arbitrary parts. Class of polymers subject to endogenous type depolymerization 

includes polyvinyl alcohol and polylactic acid. Mathematical models for those microbial 

depolymerization processes have been proposed, and numerical techniques based 

on the models have been developed. In particular, experimental data have been taken 

into analysis to solve inverse problems numerically, and transitions of weight distribution 

have been simulated. In this study, mathematical analysis of microbial depolymerization 

processes of xenobiotic polymers is continued, and numerical results are presented. 

119

120 

Asymptotic Results for a Semi-Markovian Random Walk 

with a Normal Distributed Interference of Chance 

Tahir Khaniyev 

email: tahirkhaniyev@etu.edu.tr 

TOBB University of Economics and Technology, Faculty of Engineering 


Sogutozu Cad. 43, Sogutozu, 06560, Ankara, Turkey 

(Joint work with: I. Unver, Z. Mammadova) 

Abstract: In this study, a semi-Markovian random walk process with a discrete interference 

of chance (X(t)) is constructed and investigated. In this work, it is assumed that 

the random variables ζn, n ≥ 1 which describe the discrete interference of chance have 

a normal distribution with parameters (a, σ 2 ), a > 0, σ > 0, concentrated in the interval 

(0, ∞). Under this assumption, the ergodic distribution and its characteristic function 

are expressed by means of a boundary functional of the process X(t). Using E.Dynkin’s 

principle and taking into account the supplementary condition: σ/a → ∞ as a → ∞ , the 

moments of the boundary functional are expressed by the characteristics of the ladder 

heights of the random walk. Then, three-term asymptotic expansions for the first four 

moments of the ergodic distribution of the process X(t) are obtained. Moreover, using 

the Riemann zeta function and result on Lerch’s transcendent the explicit forms of the 

asymptotic expansions for the ergodic moments of the Gaussian random walk are derived, 

as an example. Finally, the weak convergence theorem for the ergodic distribution 

of the process Wa(t) ≡ X(t)/a is proved, when a → ∞. 

References 

(1) Feller W., Introduction to Probability Theory and Its Applications II, J. Wiley, New York, 

1971. 

(2) Gihman I. I., Skorohod A.V., Theory of Stochastic Processes II, Springer, Berlin, 1975. 

(3) Janssen A.J.E.M., Leeuwaarden J.S.H., On Lerch’s transcendent and the Gaussian random 

walk, The Annals of Applied Probability, 17, (2007) 421-439. 

(4) Khaniyev T.A., Mammadova Z., On the stationary characteristics of the extended model of 

type (s,S) with Gaussian distribution of summands, Journal of Statistical Computation and 

Simulation, 76, 10 (2006) 861-874. 

(5) Khaniyev T.A., Kesemen T., Aliyev R.T., Kokangul A., Asymptotic expansions for the moments 

of a semi-Markovian random walk with exponential distributed interference of chance, 

Statistics and Probability Letters, 78, 6 (2008) 785-793. 

(6) Lotov V.I., On some boundary crossing problems for Gaussian random walks, The Annals of 

Probability, 24, 4 (1996) 2154-2171.

A Model of Vascular Tumor Growth by Hybrid Systems 

Mustafa Kahraman 

email: kahraman.mustafa@gmail.com 

Atilim University, Software Engineering 

Kizilcasar Mahallesi, 06836 Incek Glbasi 

Ankara - Turkey 

(Joint work with: Nurgul Gokgoz, Hakan Oktem) 

Abstract: Tumor growth is a complex process which is dominated by some major interactions 

like division, migration and death of tumor cells according to the nutrients 

presented in the environment and angiogenesis. Angiogenesis is the formation of blood 

vessels from pre-existing vessels. Angiogenesis is the result of tumor growth and the interaction 

of tumor body with the nearby vessels. By formed new vessels, tumor body 

can gain access to rich nutrient sources. This is a fundamental step in the transition of 

tumors from a dormant to a malignant state. Mathematical models of both angiogenesis 

and tumor growth exist in the literature. However, a combined mathematical model of 

tumor growth involving the angiogenesis process has some implementational difficulities. 

In this paper we present a hybrid system model with partial differential equations of vascular 

tumor growth. Nutrient sources are dynamically changing with new formed vessels. 

Tumor growth is dependent to new nutrient sources. We suggest that we can represent 

the nutrient source by a switching varible determined by vascularization. Thus combine 

the tomor growth and angiogenesis processes within the same model by using the hybrid 

system formalism. The simulated vascular tumor growth is in agreement with biological 

data. 

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122 

Session 4.2: Applied Probability and Stochastic Processes II 

Chair: Roger B. Nelsen 

Place: Hall 2

Probability Failure Analysis for Cracked Structure 

M.R. Akramin 

email: akramin@ump.edu.my 

FKM, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Kuantan, Pahang 

Malaysia 

(Joint work with: M. Mazwan Mahat, A. Juliawati, A.H. Ahmad, A.R.M. Rosdzimin) 

Abstract: This research work presents a probabilistic approach for fracture mechanics 

analysis of cracked structures. The main focus is on uncertainties aspect which relates 

the nature of crack in materials. The objective of this work is to calculate the rigidity 

of cracked structures based on failure probability by using simulation technique. The 

methodology consists of cracked structures modelling, finite element calculation, generation 

of adaptive mesh, sampling of cracked structure including uncertainties factors 

and probabilistic analysis using Monte Carlo method. Probabilistic analysis represents 

the priority of proceeding either suitable to repair the structures or it can be justified 

that the structures are still in safe condition. Therefore, the hybrid finite element and 

probabilistic analysis represents the failure probability of the structures by operating 

the sampling of cracked structures process. The uncertainty in the crack size can have a 

significant effect on the probability of failure, particularly for the crack size with large 

coefficient of variation. The probability of failure caused by uncertainties relates to loads 

and material properties of the structure are estimated using Monte Carlo simulation 

technique. Numerical example is presented to show that probabilistic analysis based on 

Monte Carlo simulation provides accurate estimates of failure probability. Verification 

of the predicted failure probability is validated with analytical solutions and relevant 

numerical results obtained from other previous works. The comparisons show that the 

combination between finite element analysis and probabilistic analysis based on Monte 

Carlo simulation provides accurate estimation of failure probability for use in fracture 

mechanics. 

123

124 

On exceedances based on the list of top m scores after l-th 

change 

Burak Uyar 


Department of Statistics, Faculty of Science, Ege University 

35100 Bornova, Izmir 

Turkey 

(Joint work with: H. Tanil) 

Abstract: Consider an infinite sequence of scores which are indicated as independent 

and identically distributed (iid) continuous random variables. Let the first m scores of 

the sequence be the initial top m scores. The current top m scores will be able to change 

with the future observed scores in the sequence. Tanil (2009) derived the probability 

density functions of top m scores after l-th change from the beginning. In this study, 

distributions of exceedance statistics based on top m scores after l-th change are obtained 

for a random threshold model.

Functional Approach Using New L ∗ a ∗ b ∗ color functions to 

evaluate colour changes in granites after desalination using 

different methods 

Jose M. Matias 

email: jmmatias@ya.com 

Dpt. of Statistics, Univ. of Vigo, ETSEM, Lagoas - Marcosende, 36310 Vigo, Spain 

(Joint work with: T. Rivas, C. Ordonez, J. Taboada) 

Abstract: We use a functional data approach to evaluate changes in color in granite 

after a desalination treatment applied using different methods. Specifically, we applied 

functional analysis of variance (ANOVA) to the colour curves calculated from the product 

of source reflectance, granite reflectance and the matching of colour functions by the 

standard observer. Results for this method were compared with those produced by traditional 

ANOVA based on the colorimetric coordinates L ∗ a ∗ b ∗ . The RGB and XY Z colour 

coordinates systems are obtained by integrating the rgb and xyz colour functions, respectively. 

The L ∗ a ∗ b ∗ coordinates, however, are obtained directly by transforming the XY Z 

coordinates, as no corresponding functions have been proposed to date. With a view to 

comparing results for both functional and scalar ANOVA for a homogeneous colour measurement 

method, these functions, whose integral will coincide with the L ∗ a ∗ b ∗ values, 

were deduced and are proposed for the first time. The results obtained demonstrate the 

usefulness of the additional information supplied by the functional approach. However, 

this information does not replace that produced by the ANOVA for the scalar coordinates, 

and so it is recommended to use both approaches together. The new functions 

associated with the L ∗ a ∗ b ∗ coordinates are perfectly interpretable in an analogous way 

to the coordinates themselves, in other words, as the degree of luminosity (L ∗ ) and 

the relative positions of green-red (a ∗ ) and of blue-yellow (b ∗ ), except that they are 

interpreted for each infinitesimal wavelength interval. 

125

126 

On LIBOR and swap market models: calibration to caps and 

swaption markets 

Ceren Eda Can 

email: cerencan@hacettepe.edu.tr 

Hacettepe University, Faculty of Science, Department of Statistics, 06800 Beytepe / Ankara 

Turkey 

(Joint work with: M. Rainer) 

Abstract: The rapidly growing interest rate derivative market necessitates a sophisticated 

model for sufficiently accurate and efficient pricing and hedging techniques for 

interest rate derivatives which are getting more complicated day after day. The (LIBOR) 

Market Model is presented as a tool to price and hedge interest rate derivatives which are 

functions of market-forward rates (a generic term market rate is used here to describe 

forward-LIBOR rates and forward-swap rates). It was developed by Miltersen, Sandmann 

& Sondermann (1997), Brace, Gatarek & Musiela (1997), Musiela & Rutkowski 

(1997) and Jamshidian (1997). By contrast with previous interest rate models which 

were based on the evolution of the continuously compounded short rates (Black (1976), 

Vasicek (1977), Cox, Ingersoll and Ross (CIR) (1985), Hull and White (1994) models) 

or instantaneous forward rates (Heath, Jarrow and Morton (HJM)(1992)), which are not 

directly observable in the market, the stochastic objects (forward-LIBOR rates, forwardswap 

rates) modelled by the Market Models are quantities which are (rather directly) 

observable in the market. Modelling the stochastic behavior of the unobservable financial 

quantities leads to difficulties in calibration process. The calibration of these models to a 

set of market quantities (here, cap and swaption data) requires a transformation of the 

dynamics of these unobservable quantities into dynamics of observable quantities. To do 

this, complicated numerical procedures are needed and the results are not always satisfactory. 

So, these models are fairly cumbersome to be calibrated to market quantities 

and price the complex interest rate derivatives. Hence, the Market Models can be calibrated 

more easily to the relevant (caps, swaption) markets than previous interest rate 

models. Furthermore the Market Model is consistent with the market standard approach 

for pricing interest rate derivatives using the Black (1976) model. Previous to the Market 

Models, there was no interest rate models compatible with Black model. Typical Market 

Models are the lognormal forward-LIBOR model (LFM), or LIBOR Market Model, and 

the lognormal forward-swap rate model (LSM), or Swap Market Model. LFM is based on 

evolving the forward-LIBOR rates and prices caps with Black’s cap formula. In a similar 

way, LSM is based on evolving the forward-swap rates and prices swaptions with Black’s 

swaption formula. In this study, Market Models theory will be presented to account for 

the forward-LIBOR rates and forward-swap rates dynamics. Moreover, the calibration 

of the LMM to caps prices, the calibration to swaption prices and the joint calibration 

to caps and swaption prices will be focused on.

Analytical Recursive Algorithm for Path-dependent Option 

Pricing with Stochastic Time 

Zhaoning Shang 

email: zhaoning.shang@econ.kuleuven.be 

Katholieke Universiteit Leuven 

Department of Accountancy, Finance and Insurance Naamsestraat 69 3000 Leuven 

Belgium 

(Joint work with: M. Goovaerts) 

Abstract: In this paper, we developed a recursion algorithm for calculating the moment 

generation function of certain functionals of Brownian motion when time T is independently 

randomly distributed, e.g. exponentially distributed. The integral of the exponential 

functionals of Brownian motion, which plays a seminal role in path-dependent 

derivatives pricing, can be obtained by carrying out the real Laplace inversion. We first 

present a new method to efficiently obtain the Laplace transform of the transition density 

function for arbitrary diffusion processes of the form 

X0 = x0, dXt = µ(Xt)dt + σ(Xt)dWt. 

Considering the Laplace transform of this transition density with respect to the time 

variable, the problem is reduced to the solution of the determination of an ordinary 

differential equation with certain boundary conditions. Using Feynman-Kac integration 

containing a potential and in addition a δ-function perturbation, we construct an exact 

recursion scheme for the Laplace transform of the transition density and the moment 

generating function of the Brownian motion functionals. Finally, we perform the real 

Laplace inversion based on Gaver functionals with certain nonlinear acceleration sequence 

transformations to generate approximations for the distributions of the Brownian motion 

functional with stochastic time. 

127

128 

On the Semi-Markovian Random Walk with Delay and 

Weibull Distributed Interference of Chance 

Rovshan Aliyev 

email: aliyevrovshan@yahoo.com 

Karadeniz Technical University, Faculty of Arts and Sciences 

Department of Statistics and Computer Sciences 

61080, Trabzon-Turkey 

(Joint work with: Tulay Kesemen, Tahir Khaniyev) 

Abstract: In this paper, the semi-Markovian random walk with delay and a discrete 

interference of chance process is considered. We assume that the sequence of random 

variables which describes the discrete interference of chance forms an ergodic Markov 

chain with Weibull stationary distribution with parameters . Under this assumption, 

the ergodicity of this process is proved and the asymptotic expansions for the first four 

moments of the ergodic distribution of the process are derived, as . Moreover, the asymptotic 

expansions for the skewness and kurtosis of the ergodic distribution of the process 

are established.


Sciences III 

Chair: Hassan Yousefi-Azari 

Place: Hall 3 

129

130 

A nonlinear preconditioner for Jacobian-free Newton-Krylov 

methods 

Jisheng Kou 

email: koujisheng@yahoo.com.cn 

Shanghai University 

Department of Mathematics, Shanghai University, Shanghai 200444 

China 

(Joint work with: Xiuhua Wang, Yitian Li) 

Abstract: The Jacobian-free Newton-Krylov (JFNK) methods are used popularly in 

many areas for computing efficiently the solution of large sparse systems of nonlinear 

equations. Successful application of the JFNK methods to any given problem is dependent 

on adequate preconditioning. In this paper, we present a new nonlinear preconditioner 

for JFNK methods. In our method, we solve a new nonlinear system which is 

equivalent to the original system but more balanced in nonlinearities. This new preconditioner 

is fully matrix-free. We apply this new preconditioner to the nonlinear system 

arising from the discretization of 2D shallow-water equations. Numerical results show 

that with this new preconditioner, Newton-GMRES method can be more efficient and 

robust.

A splitting semi-implicit scheme for large-scale atmospheric 

dynamics model 

Ludmila Bourchtein 

email: burstein@terra.com.br 

Pelotas State University 

Rua Anchieta 4715, bloco K, ap.304 Pelotas 96015-420 

Brazil 

(Joint work with: A. Bourchtein) 

Abstract: In this study we apply splitting techniques in the context of the semi- 

Lagrangian semi-implicit approach in order to construct computationally efficient and 

accurate numerical scheme for large-scale atmospheric dynamics model. Description of 

the designed numerical algorithm is provided and its properties of accuracy and stability 

are discussed. Performed numerical experiments with the actual atmospheric data 

showed that the developed scheme supplies accurate forecast fields for the increased time 

steps chosen in accordance with the physical requirements. 

131

132 

Multilevel Factor Modeling as an Alternative in Evaluating 

the Performance of Statistics Education in Turkey ∗ 

Dogan Yildiz 

email: dyildiz@yildiz.edu.tr 

Yildiz Technical University,Faculty of Arts and Science, Department of Statistics,Davutpasa 

34210, Esenler, Istanbul - Turkey 

(Joint work with: Atif Evren) 

Abstract: Multilevel models are especially used for the analysis of data whose nature 

are hierarchical or clustered . These models are employed in performance evaluation 

analysis and are based on the data coming from social organizations which are consisting 

of many units from (different levels) encountered especially in economy and in 

social research fields such as education and health sectors. Statistical data coming from 

the studies on educational processes in different types of schools, the studies carried on 

families with children as well as the studies on companies with many units from different 

levels can be investigated by multilevel modeling techniques. Social groups and units 

constitute a hierarchical entity and within this system data coming from the same groups 

are supposed to possess similar characteristics. Thus for a hierarchical data, the necessary 

assumption for observation values to be independent from each other is violated 

for standard statistical tests . In multilevel models at each different level of hierarchy ( 

starting from a single unit, continuing by groups formed by units and clusters formed by 

groups ) different mathematical models are formulated. Thus by combining these models, 

a unified model is supposed to be obtained. A hierarchical model is achieved by a set 

of hierarchical regression equations. Educational research often depends on multivariate 

techniques like confirmatory factor analysis and other covariance structure techniques to 

study dimensions of systematic variation in student data. In this study, we concentrate 

on the issue of assessing the factor structure of a construct at aggregate levels of analysis. 

We use a procedure for performing multilevel confirmatory factor analysis. This procedure 

is developed recently and described by Dyer(2005) The empirical part of this study 

is based on the data obtained for TUBITAK (The Scientific and Technological Research 

Council of Turkey) within the context of the survey on the statistics education in Turkey 

in 2007. Here, the universities, statistics departments, even some statistics courses correspond 

to different levels in multilevel modeling. Our sample contains approximately 

2000 students ( and their answers to the questionnaire about their appreciation on the 

statistics program they follow) present in the statistics departments in Turkey. There 

are 25 statistics programs and within each program there are four classes (levels) in 

which the judgements of students might show variability. Here our data show a nested 

or hierarchical structure of students within classes, within schools, in school districts. 

∗ This paper is dedicated to our advisors.

Stabilized FEM Solution of Steady Natural Convection Flow 

in a Square Cavity 

Selcuk Han Aydin 

email: saydin@metu.edu.tr 

Middle East Technical University, Institute of Applied Mathematics Inonu Bulvari 06531 

Ankara - Turkey 

(Joint work with: M. Tezer Sezgin) 

Abstract: The present numerical study deals with the stabilized finite element solution 

of the steady natural convection flow in a square cavity in terms of primitive variables. 

Linear triangular elements are used for the velocities, pressure and temperature, and 

the solutions are obtained for high values of Rayleigh number (Ra) (10 4 ≤ Ra ≤ 10 6 ). 

The finite element method of SUPG type enables to obtain stable solution and avoids 

oscillations especially in the pressure. 

133

134 

Investigation of Large Eddy Simulation and Eddy-Viscosity 

Turbulence Models Applicable to Film Cooling Technique 

Hanieh Khalili Param 

email: h khalili@mecheng.iust.ac.ir 

Department of Mechanical Engineering 

Iran University of Science and Technology 

Tehran 16846-13114, Iran 

(Joint work with: F. Bazdidi) 

Abstract: One of the most effective means of achieving a higher thermal efficiency in 

gas turbine engines is to increase the turbine inlet temperature provided that the turbine 

blades are protected from such elevated temperatures. One of the most efficient techniques 

to achieve this goal is film cooling, where the coolant air bled from the compressor 

is conducted into channels in the turbine blades and injected at an angle through rows 

of holes drilled on the blades. This provides a thin and cool protecting layer (film) along 

the external surface of the blade. The aim of the present work is to investigate the ability 

and accuracy of different turbulence models for the prediction of flow field and also 

to study the effect of blowing ratio (M=0.5 and 1) on the flow field. For this purpose, 

the interaction between a three dimensional inclined injected jet (angle, ?=30?) and the 

cross-flow is simulated employing different two-equation eddy-viscosity turbulence models 

(k-?/SST and k-?) based on time-averaging, and the large eddy simulation (LES) 

approach. In the latter, the governing equations include the filtered time dependent 

Navier-Stokes equations under the conditions of incompressible and constant properties. 

In the LES approach, the filtering of equations is obtained by using the convolution integration 

with the filter function. The filter function is considered as 1/V, where V is the 

volume of a computational cell. The present numerical simulation is based on the use of 

the finite volume method, applying the unsteady PISO algorithm to a multi-block and 

non-uniform computational grid. The spatial discretization consists of bounded central 

differencing scheme. The time integration is performed by a second-order fully implicit 

scheme. Present results show that the predictions of the LES approach are in better 

agreement with the available experimental data than those of the two-equation eddyviscosity 

turbulence models. Also, an increase in the blowing ratio leads to a stronger 

penetration of the jet into the cross flow, resulting in a more upstream located and 

stronger Counter-rotating Vortex Pairs (CVP).

Transonic problems in multi-dimensional conservation laws 

Eun Heui Kim 

email: ekim4@csulb.edu 

California State University Long Beach 

Department of Mathematics and Statistics, 1250 Bellflower Blvd, Long Beach 

CA 90840-1001, USA 

(Joint work with: C. Lee, B. Englert) 

Abstract: Many practical problems in science and engineering, for example in aerodynamics, 

multi-phase flow and hemodynamics, involve conserved quantities, and lead 

to partial differential equations in the form of conservation laws. Understanding the 

mathematical structure of these equations and their solutions is essential to obtain physical 

insight into such practical problems. There are special difficulties associated (e.g. 

shock formation) with these equations that are not seen elsewhere and must be dealt 

with carefully. Moreover, in multidimensional conservation laws, there is little theory at 

present. One approach, the study of self-similar solutions, leads to the study of equations 

that change their type, namely, equations that are hyperbolic far from the origin 

and mixed near the origin. Some results have been obtained recently in this area, but 

there are still many open problems. We present recent results in transonic problems in 

multidimensional conservation laws. 

135

136 

Session 4.4: Mathematical Programming III 

Chair: Herman Mawengkang 

Place: Hall 4

Modified iteration methods to solve system Ax = b 

Masoud Allame 

email: masoudallame@yahoo.com 



Khorasgan, Isfahan - Iran 

P.O.Box 81595-158 

(Joint work with: B. Vatankhahan, S. Abbasbandy) 

Abstract: A new method for solving linear systems is derived. It can be considered as a 

modification of the coefficient matrix,A, and then apply Jacobi or Gauss-Seidel iteration 

methods or any iteration methods. 

137

138 

A Multi-Objective Mixed Integer Programming Model for 

Multi Echelon Supply Chain Network Design and 

Optimization 

Eren Ozceylan 



Turkey 

(Joint work with: T. Paksoy) 

Abstract: Minimizing total costs is a traditional objective of a supply chain management 

to answer customers demand. These total costs especially consist of inbound-outbound 

transportation costs, production and distribution costs, facility investments costs, inventory 

holding and backorder costs, raw material or semi product costs and etc. This paper 

applies a mixed integer linear programming to designing a multi echelon supply chain 

network (SCN) via optimizing commodity transportation and distribution of SCN. Proposed 

model attempts to aim multi objectives of SCN by considering total transportation 

costs and capacities of all echelons. The model composed of three different objective functions. 

The first one is minimizing the total transportation costs between all echelons and 

fixed costs of potential suppliers, manufacturers, distribution centers (DCs) and retailers. 

Second one is maximizing DCs service level in allowable terms to meet retailers demand 

and the last objective function is minimizing the unnecessary and unused capacity of 

plants and DCs via decreasing variance of transported amounts between echelons. Finally, 

in order to prove the validity of the proposed model, a numerical example is solved 

and conclusions are discussed.

Effect of Floating Point Aritmetic on Monodromy Matrix 

Computation of Periodic Linear Difference Equation System 

Ali Osman Cibikdiken 

email: aocdiken@selcuk.edu.tr 

Selcuk University, Kadinhani Faik Icil MYO, Department of Computer Technologies and 

Programming Konya - Turkey 

(Joint work with: Kemal Aydin) 

Abstract: It is important to determine that problem is well-conditioned or illconditioned 

in scientific computing. The computations in computer are done with floating 

point arithmetics. The errors of computations in computer are unavoidable. Therefore, 

the floating point arithmetics effects to determine that the problem is well-conditioned 

or ill-conditioned. Let A(n) be a matrix of dimension N×N with period T and consider 

the difference equation system 

139 

x(n + 1) = A(n)x(n), n ∈ Z (1) 

With X(T ) being the monodromy matrix of the system (1), Schur stability of the system 

(1) is related to the results of computation errors on computation of the monodromy 

matrix X(T ). In this study, the effect of floating point on computation of the monodromy 

matrix X(T ) is investigated. The bounds are obtained for || X(T ) − Y (T ) || in which 

the matrix Y (T ) is the computed value of the monodromy matrix.

140 

Ranking Decision Making Units with Stochastic Data by 

Using Coefficient of Variation 

Mohammad Hassan Behzadi 

email: behzadi@srbiau.ac.ir 




Tehran, Iran 

(Joint work with: F. Hosseinzadeh Lotfi, N. Nematollahi, M. Mirbolouki ) 

Abstract:Data Envelopment Analysis (DEA) is a non-parametric technique which is 

based on mathematical programming for evaluating the efficiency of a set of Decision 

Making Units (DMUs). Throughout applications, managers encounter with stochastic 

data and the necessity of having a method that is able to evaluate efficiency and rank 

efficient units has been under consideration. In this paper considering the purport of 

coefficient of variation among efficient DMUs, two ranking methods has been proposed. 

Within these ranking methods, a DMU will have a higher rank if it’s coefficient of 

variation be smaller. These methods are suitable when managers are able to determine 

weights on coefficient of variations or on inputs and outputs. At the end we applied these 

methods on a numerical example. 

keywords: Coefficient of variation, Data envelopment analysis, Ranking.

Application of Advanced Machine Learning Methods For 

SNP Discovery in Complex Disease Association Studies 

Gurkan Ustunkar 

email: e145307@metu.edu.tr 

Middle East Technical University, Institute of Applied Mathematics 

Ankara-Turkey 

(Joint work with: S. Ozogur-Akyuz, U. Sezerman, G. W. Weber, N. Baykal) 

Abstract: Single nucleotide polymorphisms ( SNPs) are DNA sequence variations that 

occur when a single nucleotide (A,T,C,or G) in the genome sequence is altered. SNPs 

and other less common sequence variants are the ultimate basis for genetic differences 

among individuals, and thus the basis for most genetic contributions to disease. To make 

good use of SNPs for finding genes related to disease and studying their function, better 

and cheaper technological methods are needed for discovering SNPs. There is also a need 

for adequate algorithms and models for reducing biological and statistical redundancy 

from thousands of SNPs and ?nding an optimal set of SNPs associated with common 

complex diseases. However, the efficacy of searching for an optimal set of SNPs has not 

been as successful as expected in theory. One primary cause is the high dimensionality 

with highly correlated features/SNPs that can hinder the power of the identi?cation of 

small to moderate genetic effects in complex diseases. As in many other Bioinformatics 

applications (such as sequence analysis, microarray analysis, mass spectra analysis etc.), 

use of feature selection techniques is an apparent need to tackle this problem. Several 

computational methods for Feature Selection have been proposed in the literature and 

studies can be grouped into three categories: filtering, wrapper, and embedded. These 

three methods would perform differently when applied to categorical SNP data rather 

than continuous gene expression data, so there has been a need for categorical SNP 

data reduction methods. Among those methods, the most promising ones are supervised 

models. In this study, we apply various supervised feature selection methods to SNPdisease 

association data and compare the results. Among those methods are decision 

tree, multiple regression, subgroup discovery and a recently proposed novel method for 

classification of heterogeneous data called Infinite Kernel Learning (IKL), which makes 

use of infinite kernel combinations with the help of infinite and semi-infinite programming 

regarding all elements in kernel space. Finally, to evaluate the performance of the learning 

methods we calculated a special type of statistic called ROC AUC (Receiver Operating 

Characteristic Area Under Curve). 

141

142 

An Efficient Computational Method for Non-Stationary 

(R, S) Inventory Policy with Service Level Constraints 

Ulas Ozen 

email: uozen@alcatel-lucent.com 

Alcatel-Lucent, Blanchardstown Industrial Park, Dublin 15, Dublin - Ireland 

(Joint work with: S. A. Tarim, M. K. Dogru, R. Rossi) 

Abstract: This paper provides an efficient computational approach to solve the mixed 

integer programming (MIP) model developed by Tarim and Kingsman (2004) for calculating 

the parameters of an (R, S) policy in a finite horizon with non-stationary stochastic 

demand and service level constraints. Given the replenishment periods, we characterize 

the optimal order-up-to levels for the MIP model and use it to guide the development 

of a relaxed MIP model, which can be solved in polynomial time. The effectiveness of 

the proposed method hinges on three novelties: (i) the proposed relaxation is computationally 

efficient and yields an optimal solution most of the time, (ii) if the relaxation 

produces an infeasible solution, this solution can be used as a tight lower bound, and also 

(iii) this infeasible solution can be modified easily to obtain a feasible solution, which is 

an upper bound for the optimal solution. In case of infeasibility, the relaxation approach 

is implemented at each node of the search tree in a simple branch-and-bound procedure 

to efficiently search for an optimal solution. Extensive numerical tests show that our 

method dominates the MIP solution approach and can handle real-life size problems in 

trivial time.

Session 4.5: Statistics and Data Analysis II 

Chair: Fatih Tank 

Place: Hall 5 

143

144 

A Comprehensive Kansei Engineering Algorithm: An 

application of the university web page design 

Senol Erdogmus 


Eskihehir Osmangazi Universitesi 

Fen-Edebiyat Fakltesi F1 blok Istatistik Bolumu no:110 

Turkey 

(Joint work with: E. Koc, S. Ayhan) 

Abstract: In this study, a comprehensive Kansei engineering (KA) algorithm was proposed 

to solve the web page design problem. It reveals users’ perceptions and feelings 

and analyzes them using many statistical techniques. The algorithm was implemented 

to the university web page. The web page’s design components and their design goals 

influencing the quality feeling in users were analyzed with conjoint and ordinal regression 

analysis. Consequently, this study provides more customer-oriented methodology in web 

design

A JAVA Program for the Multivariate Zp and Cp Tests and 

Its Application 

Guvenc Arslan 

email: guvenca@baskent.edu.tr 

Baskent University, 

Balca Campus, Department of Statistics and Computer Sciences 

06810 Ankara - Turkey 

(Joint work with: I. Ozmen, B.O. Turkoglu) 

Abstract: The multivariate normality assumption is used in many multivariate statistical 

analyses. It is, therefore, important to assess the validity of this assumption. 

Unfortunately the application of multivariate normality tests is still limited in many 

software packages. The aim of this study is to develop a JAVA program for application 

of the and test statistics introduced by Src (2006). In addition, application of the 

program on some real data sets is presented. 

145

146 

Smoothing the Covariance Based on Functional Principal 

Component Analysis 

Ovgu Cidar 

email: ovgu.cidar@emu.edu.tr 



Turkey 

(Joint work with: Y. Tandogdu) 

Abstract: Functional Principal Component Analysis (FPCA) is an important field in the 

estimation problems. Determination of dominant elements of variation around an overall 

mean trend function is sought. Data comes from n random trajectories or subjects. 

They are mainly sparse in nature, time or space dependent. In this context computation 

of the covariance matrix from available sample data and its smoothing forms one of 

the major corner stones of a FPCA study. Sparse functional data from many different 

trajectories are assumed to be independent realizations of a smooth random function 

with mean function µ(t) and covariance function C(s, t). The orthogonal expansion of the 

covariance in L 2 is C(s, t) = 

k λkφk(s)φk(t). A trajectory can be expressed as Xi(t) = 

µ(t) + 

k ξikφk(t). Mean, covariance and eigenfunctions are required to be smooth. 

Functional principal component (FPC) scores ξik plays a major role in the estimation 

of a trajectory. They are uncorrelated random variables with a mean zero and their 

variances being the eigenvalues of C(s, t). Estimator of ξik is ξik = λk φT ik −1 

Y ( 

i Yi − µi), 

where 

Y = cov( 

i Yi, Yi) and Yi is the data matrix. Number of data values on the ith subject is Ni. Ni are assumed to be i.i.d. random variables. Observations will inherently 

include some measurement errors εi that are also assumed to be i.i.d. with E(εij) = 0 

and constant variance σ2 .Different methods are suggested by various researchers for 

smoothing the covariance matrix. The approach taken in this study is to check the 

covariance data for normality and apply c standard deviations interval to the covariance 

values by shrinking the those outside the interval to the limit values of the interval. 

References 

1. F. Yao, H. G. Müller, J. L. Wang; Functional Data Analysis for Sparse Longitudinal 

Data. J of Amarican Statistical Association. 100, pp. 577-590, 2005 

2. H. G. Müller; Functional Modelling and Classification of Longitudinal Data. Scandinavian 

Journa of Statistics, 32, pp.223-240, 2005 

3. P. Hall, H. G. Müller, J. L. Wang, Properties of Principal Component Methods for 

Functional and Longitudinal Data Analysis, The Annals of Statistics, 34, pp. 1493- 

1517, 2006.

Functional Predictor and Response Variables Under 

Non-Gaussian Conditions 

Yucel Tandogdu 

email: yucel.tandogdu@emu.edu.tr 



Turkey 

Abstract: Generalization of the classical linear regression model E(Y | X) = β0 + β1X 

by introducing the functional linear regression concept E[Y (t) | X] = µY (t) + 

 

ℑ β(s, t)Xc (s)ds enables the prediction of the response trajectory from the available 

sparse data. The slope parameter β1 in the linear multivariate regression, becomes the 

regression function β(s, t) in the functional case. Estimation of β(s, t) involves the estimation 

of the functional principal component scores ζ and ξ belonging to the predictor 

X and response Y functions respectively. Prediction of the response function through 

conditional expectation is obtained as 

E[Y ∗ (t) | X ∗ ∞ ∞ σkm 

] = µY (t) + 

ζ 

ρm 

k=1 m=1 

∗ mφk(t) 

Estimation of the functional principal component scores ζ ∗ m for the predictor X ∗ is crucial 

and necessitates the Gaussian assumption to be introduced. However, encountering 

the the non-Gaussian behavior in the process under study, renders the introduced theory 

inappropriate to the envisaged methodology. The study of the non-Gaussian case 

is considered. For the unimodal left or right skewed distributions an appropriate transformation 

to Gaussian case will suffice to use the theory under Gaussian assumption. 

Following the estimation process, the estimated values should be back transformed to 

the initial distribution of the predictor. It must be pointed out that the response function 

Y does not necessarily have to follow the same distribution as the predictor X. 

References 

1. S. Nadarajah, Some Truncated Distributions. Acta Appl. Math. 106, pp. 105-123, 2009. 

2. F. Yao, H. G. Müller, J. L. Wang, Functional Linear Regression Analysis for Longitudinal 

Data. The Annals of Statistics, 33,6, pp 2873-2903, 2005. 

3. G. He, H. G. Müller, J. L. Wang, Extending Correlation and Regression from Multivariate 

to Functional Data. Asymp. in Stat & Prob. M.L. Puri Ed. pp. 1-14, 2000. 

147

148 

Exponential-Negative Binomial Distribution 


email: mcagatay@artvin.edu.tr 

Artvin-Coruh University Science and Arts Faculty, Department of Statistics, Artvin - Turkey 

(Joint work with: Coskun Kus, Asir Genc) 

Abstract: Some probability distributions have been proposed to fit real life data with 

decreasing failure rates. In this article, a three-parameter distribution with decreasing 

failure rate is introduced by mixing exponential and negative-binomial distributions. 

Various properties of the introduced distribution are discussed. An EM algorithm is 

used to determine the maximum likelihood estimates when one parameter is given or 

known. Illustrative examples based on real data are also given.

Soft Set Theory for Maximal Association Rules Mining 

Tutut Herawan 

email: tututherawan@yahoo.com 


Parit Raja, Batu Pahat 86400, Johor 

Malaysia 

(Joint work with: Mustafa Mat Deris) 

Abstract: Maximal association rule introduced by Feldman in 1997 is to inspired from 

the fact that many interesting rules in datasets cannot captured by regular rules. It is 

based on frequent maximal itemsets which appear maximally in many records. In this 

paper, a new approach for maximal association rules mining from a transactional dataset 

under soft set theory is proposed. The proposed approach is based on representation of a 

transactional dataset as ”standard” soft set. Using the notion of items co-occurrence, a 

notion of soft maximal frequent itemsets can be defined. Furthermore, definitions of soft 

maximal association rules, maximal support and maximal confidence are presented. For 

comparison tests, firstly, the proposed approach is elaborated through a benchmark data 

set for text categorization from Reuters-21578. The results show that the captured maximal 

rules are identical with traditional and rough maximal association rules. Secondly, 

from a data set of air pollution in Kuala Lumpur Malaysia on July 2002, the results 

show that soft maximal association rule approach outperformed the previous approaches 

in capturing rules up to 87% and 50%, respectively. 

149

150

2 October 2009, 09:00-10:30 

PARALLEL SESSIONS 5

Session 5.1: Mathematical and Computational Finance 

Chair: Jan Dhaene 

Place: Hall 1 

153

154 

Approximations for Optimal Portfolio Selection Problems 

Koen Van Weert 

email: koen.vanweert@econ.kuleuven.be 

Katholieke Universiteit Leuven 

Department of Accountancy, Finance and Insurance Naamsestraat 69 3000 Leuven 

Belgium 

(Joint work with: J. Dhaene, M. Goovaerts) 

Abstract: In Dhaene et al. (2005), multiperiod portfolio selection problems are discussed, 

using an analytical approach to find optimal constant mix investment strategies 

in a provisioning or savings context. In this paper we extend some of these results, investigating 

some specific, real-life situations. First, we generalize portfolio selection problems 

to the case where a minimal return requirement is imposed. We derive an intuitive formula 

that can be used as a constraint on the admissible investment portfolios, in order to 

guarantee a minimal annualized return. Determining the distribution function of a sum 

of random variables, describing a series of future payments, is important when solving 

several problems in a general insurance or finance context. In this paper we extend the 

solution of Vanduffel et al. (2005) allowing for more arbitrary cash flows patterns. In the 

final section we investigate the so-called flashing light reserve. In our analytical framework, 

we derive convex bounds that can be used to estimate this additional provision, 

and related probability levels. We always apply our results to optimal portfolio selection.

A Classification Problem of Credit Risk Rating Investigated 

and Solved by Optimization of the ROC Curve 


email: gweber@metu.edu.tr 



(Joint work with: Kasirga Yildirak, Efsun Kurum) 

Abstract: The estimation of probability of default has considerable importance in risk 

management applications where default risk usually is referred to as credit risk. For 

this reason, Basel II (Committee on Banking Supervision) proposes a revision to the 

international capital accord that implies a more prominent role for internal credit risk 

assessments based on the determination of the probability of default of a borrower or 

group of borrowers. In our study, we try to classify borrower firms, which are in the credit 

institutes credit pool, into rating classes with respect to their probability of default. 

The task of classification of firms into rating classes necessitates the finding of cut-off 

values, which separate each rating class from the others. In other words, we actually 

aim at solving two problems. The first one is to distinguish the defaults from nondefaults, 

and the second problem is to put non-default firms in an order based on their 

credit quality and classify them into sub-rating classes. For using a model to obtain the 

probability of default of each firm, ROC (Receiver Operating Characteristics) analysis 

is employed to assess the distinction power of our model about the default and the 

non-default population. In our research, we optimize the ROC curve and to make a 

balanced choice of the thresholds. We also discuss and include accuracy of the model 

into our optimization problem. Therefore, a constrained optimization problem on the 

area under the curve (or its complement) is carefully modelled, discretized and turned 

to a penalized sum-of-squares problem of nonlinear regression. For this purpose, the 

algorithms of Gauss-Newton and Levenberg-Marquardt become presented and applied 

with a stepwise solving of a regularized linear problem in order to find the iteration steps. 

Here, Tikhonov regularization and Conic Quadratic Programming will be proposed, too. 

We shall introduce to the data use, present numerical computations and interpret them. 

We conclude with a discussion of the structural frontiers and an outlook. 

155

156 

Structuring Pension Funds Optimally 

Muhammed-Shahid Ebrahim 

email: m.shahid.ebrahim@nottingham.ac.uk 

Financial Economics Nottingham University Business School 

Jubilee Campus, Wollaton Road Nottingham NG8 1BB 

United Kingdom 

(Joint work with: Ike Mathur) 

Abstract: This paper studies pension fund design in the context of investment in the 

debt and equity of a firm. We employ a general equilibrium framework to demonstrate 

that (i) the asset location puzzle is purely a risk neutral phenomenon that disappears with 

the introduction of sufficient risk aversion, (ii) the inability of policy makers to manage 

an economy with multiple firms yields a mixed equilibrium, where bonds are observed 

in both taxable and tax-deferred accounts, and (iii) the pareto-efficiency of Defined 

Benefit plans over Defined Contribution plans is contingent on the relative administrative 

expenses and the ability to optimally define payout policy.

Multi-class classification algorithms based on polyhedral 

conic functions and application to companies listed on the 

Istanbul Stock Exchange 

Refail Kasimbeyli 

email: refail.kasimbeyli@ieu.edu.tr 

Department of Industrial Systems Engineering 

Izmir University of Economics 

Balcova - Izmir 

Turkey 

(Joint work with: G. Ozturk, O. Ustun) 

Abstract: The problems of supervised data classification arise in many areas including 

financial sector, management sciences, medicine, chemistry and so on. The aim of supervised 

data classification is to establish rules for the classification of some observations 

assuming that the classes of data are known. To find these rules, known training subsets 

of the given classes are used. During the last decades, many algorithms have been 

proposed and studied to solve data classification problems. These algorithms are mainly 

based on mathematical programming, statistical, machine learning, and neural network 

approaches. One of the promising approaches to data classification problems is based on 

mathematical programming techniques. There are two main approaches to apply mathematical 

programming techniques for solving supervised data classification problems. The 

first approach is an outer approach which is based on the separation of the given training 

sets by means of a certain function. The second approach is an inner approach. In this 

approach, the given training sets are approximated by cluster centers. The new data 

vectors are assigned to the closest cluster and correspondingly to the set that contains 

this cluster. In this paper we use the polyhedral conic functions and develop new classification 

methods based on an outer approach for the problem of discriminating real-world 

datasets with several classes. Given examples of points known to come from two or more 

classes, we construct a function (or functions) to discriminate between the classes. These 

classification techniques are used to classify companies from Istanbul Stock Exchange 

with respect to their credibility ratings. The feature vectors of companies are obtained 

using information from balance-sheets such as financial ratios, asset returns and so on, 

for the time period between 2001 and 2007 years. All these features are collected to a 

general data set. The decision support system developed, allows users to form different 

data sets, by selecting different financial ratios from the general set and thus to obtain, 

solve and analyze different classification problems. 

157

158 

Session 5.2: Cryptography 

Chair: Ersan Akyildiz 

Place: Hall 2

Efficient Multiplications in F55n and F77n Ferruh Ozbudak 

email: ozbudak@metu.edu.tr 



(Joint work with: M. Cenk) 

Abstract: Finite field multiplication plays an important role in the implementation of 

elliptic curve cryptography and pairing based cryptography. Recently efficient multiplications 

in F55n and F77n are used for computing the Eta paring over divisor class groups 

of the hyperelliptic curves y2 = xp − x + d where p is an odd prime1 in which Karatsuba 

type multiplications2,3 are used. Let µq(m) denote the minimum number of Fq 

multiplications in order to multiply two arbitrary elements of Fqm. Karatsuba type multiplications 

imply only µ5n(5) ≤ 15 and µ7n(7) ≤ 24. However there are more efficient 

methods improving the bounds on µq(m). For example, recently we have shown that 

one can obtain an explicit formula for multiplication in F55n with µ5n(5) ≤ 11 in.4,5 In 

this paper, using the recent methods for multiplication in Fqm (see,6–10 ) giving the best 

known bounds on µq(m) for certain values of q and m, we obtain improved values for 

the explicit formulas for multiplication in F55n and F77n. For example we get explicit 

formulas giving µ5n(5) ≤ 10 and µ7n (7) ≤ 15, which also improve the corresponding 

result in. 4,5 In particular these give much more efficient eta pairing computations than 

the ones in. 1 We also give timing results of implementations of Karatsuba type formulas 

and proposed formulas for multiplication in F55n and F77n for comparison. 

References 

1. E. Lee, H. Lee, and Y. Lee. Eta pairing computation on general divisors over hyperelliptic 

curves y 2 = x p − x + d. Journal of Symbolic Computation, (43), 452 - 474, 

(2008). 

2. A. Karatsuba, and Y. Ofman. Multiplication of multidigit numbers by automata. Soviet 

Physics-Doklady, (7). 595-596, 1963. 

3. A. Weimerskirch, and C. Paar. Generalizations of the Karatsuba algorithm for polynomial 

multiplication. Avaliable: http://eprint.iacr.org/2006/224. 

4. M. Cenk, and F. Özbudak. Efficient multiplication in finite fields of characteristic 3 and 

5 for pairing based cryptography. 3rd Information Security and Cryptology Conference, 

2008, Ankara, pp. 111-114. 

5. M. Cenk, Ç. K. Koç, and F. Özbudak. Polynomial multiplication over finite fields using 

field extensions and interpolation. Proceedings, 19th IEEE Symposium on Computer 

Arithmetic, Portland, Oregon, June 8-10, 2009, to appear. 

6. N. Arnaud, Evaluation Dérivée, Multiplication dans les Corps finis et codes correcteurs, 

Ph.D. dissertation, Université de la Méditerranée, France, 2006. 

159

160 

7. S. Ballet, On the tensor rank of the multiplication in the finite fields, Journal of Number 

Theory 128 (2008), 1795-1806. 

8. M. Cenk, and F. Özbudak. Efficient multiplication in F3ℓm, m ≥ 1 and 5 ≤ ℓ ≤ 18. In 

Africacrypt 2008 volume 5023 of Lecture Notes in Computer Science, 406-414, Springer 

- Verlag. 

9. M. Cenk, and F. Özbudak. Improved polynomial multiplication formulae over F2 using 

Chinese Remainder Theorem. IEEE Transactions on Computers, 58(4), 572 -576, 

(2009). 

10. M. Cenk, and F. Özbudak. On Multiplication in Finite Fields, submitted, 2009.

On the elliptic curves y 2 = x 3 − c with embedding degree one 

Baris Bulent Kirlar 

email: kirlar@metu.edu.tr 



Abstract: In recent years, there has been many works dealing with pairing-based cryptography. 

In particular, elliptic curves with small embedding degree and large primeorder 

subgroup have a great interest to implement pairing-based cryptographic systems. 

Although many papers have proposed families of elliptic curves with embedding degree 

k ≥ 2, there are few papers related to the families with embedding degree k = 1. Koblitz 

and Menezes give a detailed work for some family of curves of the form y2 = x3 − dx 

with embedding degree k = 1. 

In this paper, we give further examples of elliptic curves in the form y2 = x3 −c with 

embedding degree k = 1. This was done by first computing the number of points Np of 

the elliptic curve y2 = x3 − c over the finite field Fp. We note that it was already known 

Np = p + 1 + χ2(−c) χ3(c)J(χ2, χ3) + χ3(c) 2J(χ2, χ2 3 ) , where χ2, χ3 are quadratic 

and cubic multiplicative characters of Fp, respectively, and J(χ2, χi 3 ) is the Jacobi sum 

for i = 1, 2. Our contribution here is to compute the right hand side of this identity 

to obtain an explicit formula for Np. Then, using this description we give examples of 

curves y2 = x3 − c over Fp with Np = p − 1. 

161

162 

On the basis number of the lexicographic product of two 

graphs and some related problems 

Mohammed Mahmoud Jaradat 

email: mmjst4@qu.edu.qa 

Qatar University 

Department of Mathematics, Statistics and Physics 

P.O.Box 2713 Doha-Qatar 

Abstract: For a given graph G, the set E of all subsets of E(G) forms an |E(G)|dimensional 

vector space over Z2 with vector addition XY = (XnY )[(Y nX) and scalar 

multiplication 1:X = X and 0:X = ; for all X; Y 2 E. The cycle space, C(G), of a graph 

G is the vector subspace of (E; ; :) spanned by the cycles of G: Traditionally there have 

been two notions of minimality among bases of C(G). First, a basis B of G is called a 

d-fold if each edge of G occurs in at most d cycles of the basis B. The basis number, b(G), 

of G is the least non-negative integer d such that C(G) has a d-fold basis; a required 

basis of C(G) is a basis for which each edge of G belongs to at most b(G) elements of 

B. Second, a basis B is called a minimum cycle basis (MCB) if its total length PB2B 

jBj is minimum among all bases of C(G). The lexicographic product G[H] has the vertex 

set V (G H) = V (G) V (H) and the edge set E(G[H]) = f(u1; v1)(u2; v2)ju1 = u2 and 

v1v2 2 H; or u1u2 2 Gg. In this work, we give an upper bound of the basis number for 

the lexicographic product of two graphs. Moreover, in a related problem, we construct a 

minimum cycle bases for lexicographic product of the same.

Global Optimization In Practice 


email: janos.pinter@ozyegin.edu.tr 


Ozyegin University 

Istanbul - Turkey 

(Joint work with: Frank J. Kampas) 

Abstract: Mathematica (www.wolfram.com) is a well-recognized integrated scientific 

and technical computing system. The MathOptimizer software package, developed by 

the authors, serves to solve numerically a wide range of nonlinear optimization problems. 

In principle, all continuous Mathematica functions can become a model component (objective 

or constraint) function. We discuss MathOptimizer’s key features and illustrate 

its use to handle simple, more advanced, and non-standard optimization problems. 

163

164 

Session 5.3: Differential equations II 

Chair: Josep Arnal 

Place: Hall 3

Exponential Runge–Kutta methods for option pricing in 

jump-diffusion models 

Muhammad Asif Gondal 

email: gondalfast@gmail.com 

University of Innsbruck 

Department of Mathematics, Technikerstr. 13/7, A-6020, Innsbruck 

AUSTRIA 

(Joint work with: A. Ostermann) 

Abstract: In this paper, we consider exponential Runge–Kutta methods for the numerical 

pricing of options. The methods are shown to be an alternative to other existing 

procedures for the numerical valuation of jump-diffusion models. We show that exponential 

Runge–Kutta methods give unconditional second order accuracy for up-and-out 

Barrier options under Black–Scholes geometric Brownian motion model and Merton’s 

jump-diffusion model with constant coefficients. Exponential integrators have good stability 

properties. These integrators are fully explicit and do not require the numerical 

solution of linear systems as in contrast to standard integrators. On the other hand, 

exponential integrators require the evaluation of the exponential and related functions 

of the Jacobian matrix. Finally, the performance of the proposed methods is illustrated 

through some numerical experiments. 

165

166 

Discrete First-Order Four-Point Boundary Value Problem 


email: mesliza@perlis.uitm.edu.my 

Jabatan Matematik, Universiti Teknologi MARA, Kampus Arau 02600 Arau, Perlis 

Malaysia 

(Joint work with: M. Jusoh) 

Abstract: We establish existence results for solutions to four-point boundary value 

problems for systems of first-order difference equations associated with systems of firstorder 

ordinary differential equations.

The Solution of the Bagley-Torvik Equation with the 

Generalized Taylor Collocation Method 

Yucel Cenesiz 

ycenesiz@selcuk.edu.tr 

Selcuk University, Science Faculty, Math Department, Kampus/Konya - TURKEY 

(Joint work with: Y. Keskin, A. Kurnaz) 

Abstract:In this paper, the Bagley-Torvik equation which has an important role in 

fractional calculus is solved by generalizing the Taylor Collocation Method. The proposed 

method has a new algorithm for solving fractional differential equations. This new 

method has many advantages over variety of numerical approximations for solving fractional 

differential equations. To assess the effectiveness and preciseness of the method, 

results are compared with other numerical approaches. 

167

168 

Jensen divergence based on Fisher’s information 

Yoji Otani 

email: pablos@ugr.es 

Departamento de Matematica Aplicada Facultad de Ciencias Avenida de Fuentenueva, S/N 

18071 - Granada - SPAIN 

(Joint work with: A. Zarzo, J.S. Dehesa) 

Abstract: During the last years the Jensen-Shannon divergence between two or more 

arbitrary probability densities has been used in numerous mathematical and physical 

contexts. This relative information measure, in contrast to the Kullback-Leibler entropy 

or relative Shannon entropy, presents three important characteristics: symmetry under 

exchange of the involved densities, applicability to more than two densities, and finiteness 

even in the case that the involved densities have non-common zeros. In this paper we 

introduce a Jensen divergence based on the Fisher information. The Fisher information, 

in contrast to the Shannon entropy, is an information measure with a local character, 

providing a measure of the gradient and oscillatory content of the density. The new 

Jensen-Fisher divergence enjoys the same properties as the Jensen-Shannon divergence; 

namely, non-negativity, additivity when applied to an arbitrary number of probability 

densities, symmetry under exchange of these densities, vanishing if and only if all the 

densities are equal, and definiteness when these densities present non-common zeros. 

Moreover,the Jensen-Fisher divergence can be expressed in terms of the relative Fisher 

information as the Jensen-Shannon divergence does in terms of the Kullback-Leibler 

entropy. It is remarkable that the last property is only shared by these two divergences, 

in contrast with the recently introduced Jensen-Renyi and Jensen-Tsallis divergences. 

Here we present the theoretical grounds of the Jensen-Fisher divergence. We apply it to 

several families of probability densities (including the Rakhmanov densities associated to 

the classical families of orthogonal polynomials). Finally, a comparison with the Jensen- 

Shannon divergence and the relative Fisher information is performed.

Session 5.4: Numerical Linear Algebra II 

Chair: Serkan Eryilmaz 

Place: Hall 4 

169

170 

On the Modification of an Eigenvalue Problem that 

Preserves an Eigenspace 

Maxim Naumov 

email: naumov@purdue.edu 

Department of Computer Science 305 N. University Street West Lafayette, IN 47907-2107 

USA 

(Joint work with: A. Bourchtein) 

Abstract: Eigenvalue problems arise in many application areas ranging from computational 

fluid dynamics to information retrieval. In these fields we are often interested in 

only a few eigenvalues and corresponding eigenvectors of a sparse matrix. In this talk, we 

comment on the modifications of the eigenvalue problem that can simplify the computation 

of those eigenpairs. These transformations allow us to avoid difficulties associated 

with non-Hermitian eigenvalue problems, such as the lack of reliable non-Hermitian eigenvalue 

solvers, by mapping them into generalized Hermitian eigenvalue problems. Also, 

they allow us to expose and explore parallelism. They require knowledge of a selected 

eigenvalue and preserve its eigenspace. The positive definiteness of the Hermitian part 

is inherited by the matrices in the generalized Hermitian eigenvalue problem. The position 

of the selected eigenspace in the ordering of the eigenvalues is also preserved under 

certain conditions. The effect of using approximate eigenvalues in the transformation is 

analyzed and numerical experiments are presented.

A Variational Algorithm of the GPBi-CG Method for 

Solving Linear Systems 

Kuniyoshi Abe 

email: abe@gifu.shotoku.a.jp 

Faculty of Economics and Information, Gifu Shotoku University 

1-38, Nakauzura, Gifu 500-8288 

JAPAN 

(Joint work with: G. L. G. Sleijpen) 

Abstract: We treat Krylov subspace methods for solving a large sparse linear system 

Ax = b, where A stand for an n-by-n matrix, and x and b are n-vectors, respectively. 

The Bi-Conjugate Gradient (Bi-CG) method is a well-known Krylov subspace method for 

solving this problem, and several hybrid BiCG methods such as the Bi-CG STABilized 

(BiCGSTAB) method, the BiCGStab2 method, the Generalized Product-type method 

derived from Bi-CG (GPBi-CG) and the BiCGstab(l) method have been developed to 

improve the convergence. The residual polynomials of the hybrid BiCG methods are 

expressed by the product of the Lanczos polynomial and another polynomial Pn of degree 

n with Pn(0) = 1. The polynomial Pn of GPBi-CG has been built up by a pair of coupled 

two-term recurrence formulas. According to our studies, the residual norm of GPBi-CG 

does not converge on a problem, where those of BiCGStab2 and BiCGstab(2) converge. 

In other words, it appears that the recurrence formulas of the original GPBi-CG may be 

unstable. 

Therefore, we propose an alternative algorithm of GPBi-CG to improve the convergence 

of the classical GPBi-CG method. The recurrence formulas of the variant of 

GPBi-CG can be redesigned by coupling those of Bi-CG and the three-term recurrence 

formula which is similar to the Lanczos polynomial but has different recurrence coefficients 

from one. That is, the approximate solution and the residual vector in the 

alternative algorithm are updated by the different recurrence formulas from those of the 

original GPBi-CG method. Numerical experiments show that our proposed GPBi-CG 

variant is more effective and less affected by rounding errors than the classical GPBi-CG 

method. 

171

172 

Fully fuzzy linear system: New point of view 

Soheil Salahshour 

email: soheilsalahshour@yahoo.com 

Department of Mathematics, Science and Research Branch 


Tehran, Iran 

(Joint work with: Tofigh Allahviranloo) 

Abstract: Several problems in various areas such as economics, finance, engineering 

and physics boil down to the solution of a linear system of equations. In this paper, we 

proposed a new method to obtain a symmetric solution of fully fuzzy liner system, which 

is called FFLS. To this end, we resolve 1-cut of FFLS, then some unknown symmetric 

spreads are allocated to each rows of 1-cut of FFLS. So, after some manipulations, original 

FFLS is transformed to solving 2n linear equations to find symmetric spreads. However, 

our method always give us a fuzzy number vector solution. Moreover, we propose the 

first method to obtain solution of FFLS where the decision maker can be effected on 

the solution such that decision maker could select the fuzzy symmetric solution of FFLS 

which is placed in the Tolerable Solution Set(TSS) or Controllable Solution Set(CSS) or 

United Set Solution(USS). Finally, some numerical examples are given to compare our 

proposed solution of FFLS than the others.

Fuzzy Linear System: Satisfactory Level of Solution 

Tofigh Allahviranloo 

email: soheilsalahshour@yahoo.com 

Department of Mathematics, Science and Research Branch 


Tehran, Iran 

(Joint work with: Soheil Salahshour) 

Abstract: In this paper, we propose a simple and practical method to solve fuzzy linear 

system A ˜ X = ˜ b where, ˜ X and ˜ b are fuzzy triangular vectors with non-zero spreads 

and the matrix A is nonsingular matrix with real coefficients. The aim of this paper is 

twofold. First, we try to obtain the crisp solution of fuzzy linear system. To this end, we 

solve the 1-cut of fuzzy linear system. Second, we allocate a unknown symmetric spread 

to any row of fuzzy linear system in 1-cut position. Thus, fuzzy linear system in 1-cut, 

will be transformed to a system of interval equations. The symmetric spread of each 

elements of fuzzy vector solution is derived by solving such interval system. Moreover, to 

investigate the satisfactory level of obtained solution, we propose some new assay, such 

that by putting obtained solution in the original fuzzy linear system and compare with 

right hand side, satisfactory level of solution by proposed assay could be obtain 

173

174 

Session 5.5: Approximation and Interpolation III 

Chair: Dmitri V. Alexandrov 

Place: Hall 5

On q-Szász–Durrmeyer Operators 

Havva Kaffaoglu 

email: havva.kaffaoglu@emu.edu.tr 

Matematik Bolumu Dogu Akdeniz Universitesi Gazimagusa KKTC 

Turkey 

(Joint work with: N. Mahmudov) 

Abstract: In the present paper, we introduce the q-Szász-Durrmeyer operators and 

prove approximation results for continuous functions in terms of modulus of continuity. 

Furthermore we study Voronovskaja type result for the q-Szász-Durrmeyer operators. 

175

176 

Ostrowskis Fourth-order Iterative Method Solves Cubic 

Equations of State 

M. Cetin Kocak 


Ankara University, Engineering Faculty 

Chemical Engineering Department 

Tandogan 06100 Ankara 

Turkey 

Abstract: Successful design and operation of chemical plant require in depth knowledge 

of the pertinent processes. Simulation with a mathematical model can contribute 

to understanding how the plant behaves under widely different conditions. Large dimensionality, 

non-linearity, and interaction among process variables notoriously characterise 

chemical plant models and necessitate the use of a computer in this activity. Numerical 

solution techniques are harnessed very often because an analytical answer is either unavailable 

or intractable. Numerical integration proceeds in a piecewise fashion unless an 

approximate solution is wanted at a single point. Moreover, the majority of the accompanying 

algebraic equations are solved iteratively. Pressure-volume-temperature (P-V-T) 

data are required in simulating chemical plants because the latter usually involve production, 

separation, transportation, and storage of fluids. In the absence of actual experimental 

data, the model must rely on phase behavior prediction by so-called equations 

of state (EOS). The van der Waals EOS is a cubic EOS as are all the transformations 

and modifications that it has undergone since its publication in 1873. Ostrowski iterative 

technique is a partial-substitution variant of Newtons popular second-order method. Although 

simple and powerful, this two-point, fourth-order scheme has been utilized very 

little since its publication over forty years ago. This paper presents its application to 

solve cubic equations of state which have an important role in chemical plant simulation.

On Bivariate Bernstein-Chlodovsky Operator 

Hatice Gul Ince 

email: ince@gazi.edu.tr 

Gazi University, Faculty of Sciences and Arts 

Department of Mathematics , Teknikokullar 

06500-Ankara -Turkey 

(Joint work with: G. Bascanbaz Tunca, A. Erencin) 

Abstract: This work relates to bivariate Bernstein-Chlodovsky operator which is not 

a tensor product construction. We show that the operator preserves some properties of 

the original function, for example; function of modulus of continuity, Lipschitz constant, 

and a kind of monotony. 

177

178 

Implicit Fully Mesh-Less Method for Compressible Viscous 

Flow Calculations 

Yoseph Hashemi 

email: yoseph84@aut.ac.ir 

Center of Excellence in Computational Aerospace 

Amirkabir University of Technology, 424 Hafez Avenue 

Tehran, Iran 

(Joint work with: A. Jahangirian) 

Abstract: Difficulties in generating quality meshes, particularly for viscous flow simulations 

has recently attracted much interest towards the so-called mesh-less methods. 

These methods only use clouds of nodes in the influence domain of every node. Thus, 

they dont require the nodes to be connected to form a mesh. The flow derivatives are 

calculated using different approximation methods like least squares. The main purpose of 

this paper is; 1) to develop an efficient central difference mesh-less procedure for viscous 

flow calculations and 2) to enhance the computational efficiency of the method by adopting 

accelerating techniques and implicit time discretization. Thus, a pseudo-time implicit 

time discretization scheme is applied for mesh-less calculation of the compressible viscous 

flow equations. The Taylor series least square method is used for approximation of 

derivatives at each node which leads to a central difference spatial discretization. Several 

convergence acceleration techniques such as local time stepping and residual smoothing 

are adopted in this approach. The capabilities of the method are demonstrated by flow 

computations around single and multi-element airfoils at subsonic and transonic flow 

conditions. Results are presented which indicate good agreements with the reliable numerical 

finite volume and experimental data. The computational time is considerably 

reduced when using the proposed mesh-less method compared with the similar explicit 

mesh-less and finite-volume schemes using same point distribution. 

References 

1. Jahangirian A., Hashemi Y., Hybrid Unstructured Cartesian Grid with Meshless Zones 

for Compressible Flow calculations, 11th ISGG Numerical Grid Conference, May 25- 

28, 2009, Montral, Canada. 

2. Jahangirian A., Hadidoolabi M., Unstructured moving grids for implicit calculation 

of unsteady compressible viscous flows, International Journal for Numerical Methods 

in Fluids, Vol. 47, pp. 11071113, 2005.

2 October 2009, 11:00-12:30 

PARALLEL SESSIONS 6

Session 6.1: Applied Probability and Stochastic Processes III 

Chair: Kasiraga Yildirak 

Place: Hall 1 

181

182 

Newsvendor Characterizations for One-Warehouse 

Multi-Retailer Inventory Systems with Discrete Demand 

under the Balance Assumption 

Mustafa Kemal Dogru 

email: dogru@alcatel-lucent.com 

Alcatel-Lucent Bell Labs Blanchardstown Industrial Park Blanchardstown, Dublin 15 

Ireland 

(Joint work with: G.J. van Houtum, A.G. de Kok) 

Abstract: This paper considers a one-warehouse multi-retailer inventory system that 

faces discrete stochastic demand of the customers. Under the so-called balance assumption 

(also known as the allocation assumption), we extend the optimality of base stock 

policies known for continuous demand model to the discrete demand case. Our main 

contribution is we show that the optimal base stock levels satisfy newsvendor characterizations, 

which are in terms of inequalities, and extend the newsvendor equalities known 

for the continuous demand model. These characterizations are appealing because they 

(i) are easy to explain to non-mathematical oriented people like managers and MBA 

students, (ii) contribute to the understanding of optimal control, (iii) help intuition development 

by providing direct relation between cost and optimal policy parameters.

Modified Maximum Likelihood Estimators for Logistic 

Distribution under Type-II Progressively Hybrid Censored 

Data 

Ismail Kinaci 

email: ikinaci@selcuk.edu.tr 




Turkey 

(Joint work with: Bugra Saracoglu) 

Abstract: In this study, statistical inferences for Logistic parameters under progressively 

hybrid and adaptive progressively hybrid censoring are presented. In order to estimate 

the unknown parameters, the maximum likelihood estimators and the modified maximum 

likelihood estimators are developed. Finally, the performances of the point estimation of 

the parameters based on the two censoring methods are compared. 

183

184 

Modeling Coordination Relationships of School Communities 

to Achieve Environmental Behavior Using Influence Diagram 

Azizah Hanim Nasution 

email: adeanasti@yahoo.com 

Doctoral Program of Natural Resources and Environment, 

the University of Sumatera Utara 

PSL - Kampus USU, Medan 

Indonesia 

(Joint work with: A. Syahrin, H. Mawengkang) 

Abstract: The most effective way to promote environmental behavior is through education. 

The communities involved in the educational system of a school can be regarded 

as agents. In this situation a multi agent-based approach can be used due to the environment 

of the sustainable school we are modeling is complex and dynamics. Therefore 

it is necessarily to manage relationships among agents to achieve coordinated behavior. 

In the educational system each agent is allowed to choose its action based on them. 

In this paper we address an approach to represent coordination relationships assuming 

that agents inhabit an uncertain condition. We use influence diagram to model the coordination 

relationships such that agents are able to both represent and infer how their 

activities affect other agents activities in a way to achieve the environmental behavior 

objective.

Testing unit root and comparison of estimates 

Vilda Purutcuoglu 

email: vpurutcu@metu.edu.tr 

Middle East Technical University, Department of Statistics,06531 Ankara-TURKEY 

(Joint work with: Moti L. Tiku) 

Abstract:The problem of the unit root is one of the main challenges in nonstationary 

time series data. Therefore there are a number of testing procedures in the literature to 

check this situation. However the drawback of these tests is that as the exact distribution 

of the sample autocorrelation coefficient is intractable, the estimation is implemented under 

the asymptotic distribution of that value which is based on the normality of the error 

terms. Tiku and Wong (Communication in Statistics, 1998, 27(1), 185-198) propose a 

new test statistics for controlling unit root under simple AR(1) model when the errors 

have long-tailed symmetric density which covers values from cauchy to normal. In that 

work by using a simulated data the critical point for the significance is computed from 

three moment chi-square and four-moment F approximations. The results indicate that 

the power of the new test, whose parameter is estimated via the modified maximum 

likelihood method, is higher than those calculated under normality. In this study we 

extend this situation for skewed distributed errors like gamma and generalized logistic in 

AR(1) model with and without intercept terms and evaluate our results in a simulated 

data in terms of power and type I error. Then we compare the performance of this new 

test, whose errors are originated from both long-tailed symmetric and skewed distributions, 

with well-known unit root tests, namely, Dickey-Fuller and Phillips-Perron tests, 

by applying different real data sets. 

185

186 


Sciences IV 

Chair: Lucia Romani 

Place: Hall 2

Nonlinear Dynamics of Leads 

Dmitri V. Alexandrov 

email: dmitri.alexandrov@usu.ru 

Department of Mathematical Physics 

Urals state University 

Lenin ave., 51, Ekaterinburg, 620083 

Russian Federation 

(Joint work with: A.P. Malygin, I.V. Alexandrova) 

Abstract: We present new analytical results relating to the growth and evolution of 

sea ice. It is noteworthy that thin sea ice plays a central role in the surface heat and 

mass balance of the Arctic Ocean. In order to describe these balances, we analyze highly 

resolved temperature data taken through the air/sea/ice interface during the transition 

from an ice-free to an ice-covered Arctic Ocean surface. Our detailed analysis of the field 

data is based on the classical model of a mushy layer, which is modified in order to obtain 

analytical solutions in explicit form (so, for example, ice thickness and growth rate, temperature 

distributions, conductive and latent heat fluxes are determined). Furthermore, 

we find that the sea-ice growth is not simply a square-root function of time. It depends 

on the temperature variations in the atmosphere and lies between two square-root functions 

of time for the maximum and minimum temperatures found during observations. 

The theory under consideration is in good agreement with observations. 

187

188 

An Inverse Problem of Finding Control Parameter in a 

Parabolic Equation 

Reza Zolfaghari 

email: rzolfaghari@iust.ac.ir 

Department of Mathematic 


Tehran - Iran 

Abstract: In this article an inverse problem concering heat equation with time dependent 

unknown control parameter is considered which plays a very important role 

in many branches of science and engineering. A finite difference scheme based on the 

classical backward time centred space (BTCS) implicit scheme is presented and due to 

the boundary condition, the system of linear equations resulting from this scheme have 

a coefficient matrix that is a quasi-tridiagonal matrix. Then we estimate the unknown 

coefficient by using predictor-corrector method based on energy overspecified condition.

Analysis of Laminar Film Boiling on a Vertical Surface Using 

a Coupled Level-Set and Volume-of-Fluid Technique 

Mohammad Moalemi 

email: m moalemi@mecheng.iust.ac.ir 

Department of Mechanical Engineering 


Tehran 16846-13114, Iran 

(Joint work with: F. Bazdidi) 

Abstract: For modeling and analysis of laminar film boiling on a vertical Surface, the 

coupled level-set and volume-of-fluid (CLSVOF) technique is employed. This method 

combines some of the advantages of both the volume-of-fluid (VOF) method and the 

level-set (LS) method. The coupled algorithm conserves mass and captures the interfaces 

very accurately. In the present two-dimensional simulation, it is assumed that the plate 

is plane, smooth and vertical, at a constant temperature. Also, fluid properties in both 

of the two phases are constant. The governing equations are extended in cartesian coordinates. 

Flow is laminar and transient. First of all, equations ruling the thermodynamic 

behavior of laminar film boiling process on a vertical film flow have been extracted by 

the CLSVOF function, leading to extended conservative equations. Then, the discretization 

of the extended equations has been carried out by the finite volume technique. The 

Consistency of velocity and pressure field has been achieved using the transient SIMPLE 

algorithm. The Nusselt number and boiling heat transfer coefficient have been investigated. 

Finally, the results obtained by the present numerical method are compared with 

the other existing numerical and experimental data, showing reasonably good agreement. 

189

190 

Topological Indices of Graph Operations 

Hassan Yousefi-Azari 

email: hyousefi@ut.ac.ir 

School of Mathematics 

Statistics and Computer Science 

University of Tehran 

Iran 

(Joint work with: A.R. Ashrafi, M.H. Khalifeh) 

Abstract: A topological index is a numerical quantity invariant under graph isomorphisms. 

Such numbers are very important for studying molecular graphs of chemical 

compounds. In this talk four graph operations Cartesian product, join, composition and 

symmetric difference are considered. An exact expression for some new topological index 

for these operations are presented.

Session 6.3: Quadrature and Integral Equations 

Chair: Tahir Khaniyev 

Place: Hall 3 

191

192 

New approach for the construction of the solutions of 

Cauchy integral equation of the first kind 

Nik Mohd Asri Nik Long 

email: nmasri@math.upm.edu.my 

Department of Mathematics, Faculty of Science and Institute for Mathematical Research 

Universiti Putra Malaysia 

43400 Serdang, Selangor 

Malaysia 

(Joint work with: M. Yaghobifar, Z.K. Eshkuvatov) 

Abstract: In this paper, the four type of solutions of Cauchy integral equations (CIE) 

are obtained. The main tool is that the known function, which is of Holder class, are 

1 

written as a combination linear of the basis x+2 , 

1 

x+3 , 

1 

1 

, · · · , , · · · , which are 

x+4 x+n 

complete in L2 [−1, 1]. It is found that for the finite expansion of the known function, the 

exact solutions can be archived, else the approximate solutions are obtained. Numerical 

results demonstrate the efficiency and the accuracy of the present technique.

The Use of variational iteration method to Solve a nonlinear 

Volterra-Fredholm integro-differential equations 

Mohammad Ali Fariborzi Araghi 

email: mafa i@yahoo.com 

Islamic Azad University, Central Tehran Branch 

Department of Mathematics, Islamic Azad University, Central Tehran Branch, P.O.Box 

13185.768, Tehran, Iran 

Islamic Republic of Iran 

(Joint work with: Sh. Sadigh Behzadi) 

Abstract: In this paper, a nonlinear Volterra-Fredholm integro-differential equation is 

solved by using the He’s variational iteration method (VIM). The approximate solution 

of this equation is calculated in the form of a series which its components are computed 

easily. The accuracy of the proposed numerical scheme is examined by comparing with 

the modified Adomian decomposition method (MADM) and Taylor polynomials method 

(TPM). The existance, uniqueness and convergence of the proposed method are proved. 

193

194 

Modified Sinc-collocation methods for Volterra integral 

equations of the second kind and their theoretical analysis 

Tomoaki Okayama 

email: Tomoaki Okayama@mist.i.u-tokyo.ac.jp 

University of Tokyo, 7-3-1, Hongo, Bunkyoku, Tokyo- Japan 

(Joint work with: T. Matsuo, M. Sugihara) 

Abstract: In this talk we are concerned with the Sinc-collocation method that has been 

developed by Rashidinia–Zarebnia1 for Volterra integral equations of the second kind: 

t 

u(t) − k(t, s)u(s) ds = g(t), a ≤ t ≤ b, 

a 

where k and g are given functions, and u is the solution to be determined. Since naive 

Sinc-collocation method does not work properly when the solution u is non-zero at the 

endpoints (t = a and b), they have introduced auxiliary basis functions that are selected 

depending on the values of u(a) and u(b). Then they have proved that the order 

of the error of their method is O(A −1 

N 2 

√ 

exp(−c1 N)), where AN represents the coefficient 

matrix of the resulting linear equations. Their numerical experiments showed 

that A −1 

N 2 does not increase rapidly, and from which they have concluded the method 

√ 

converges at an exponential rate: O(exp(−c1 N)). One of the purposes of this work is 

to make their method more practical and reliable in the following two senses. First, it 

is not realistic to assume that the values of u(a) and u(b) can be known in prior to the 

computation. In order to remedy the difficulty, we employ modified auxiliary basis functions 

that do not depend on the values of u(a) and u(b) (the same approach has already 

been employed for Fredholm integral equations2 ). Second, the convergence rate of their 

method is still not proved because the term A −1 

N 2 is not theoretically estimated in their 

error analysis. In this project, it is rigorously 

√ 

proved theoretically that the convergence 

rate of the modified method is O(exp(−c1 N)). The other purpose of this work is to 

improve the rate of convergence. This is done by replacing the variable transformation 

employed in the methods above, the standard tanh transformation, with the so-called 

double-exponential transformation. 3 It is then shown theoretically and numerically that 

the convergence rate is improved to O(exp(−c2N/ log N)). 

References 

1. Rashidinia, J. and Zarebnia, M.: Solution of a Volterra integral equation by the 

Sinc-collocation method, J. Comput. Appl. Math., 206 (2007), 801–813. 

2. Okayama, T., Matsuo, T. and Sugihara, M.: Improvement of a Sinc-collocation 

method for Fredholm integral equations of the second kind, DWCAA09, Alba di 

Canazei, Trento, Italy (2009. 

3. Mori, M. and Sugihara, M.: The double-exponential transformation in numerical 

analysis, J. Comput. Appl. Math., 127 (2001), 287–296.

Differential Quadrature Solution of 2D Natural Convection 

in a Cavity Under a Magnetic Field 

Nagehan Akgun 

email: nalsoy@metu.edu.tr 

Middle East Technical University 


Inonu Bulvari 06531 Ankara - Turkey 

(Joint work with: M. Tezer Sezgin) 

Abstract: This study concerns with the problem of time dependent numerical simulation 

of 2D natural convection in a square cavity under a magnetic field. The differential 

quadrature method is used for solving the governing equations in terms of stream function, 

vorticity and temprature. Relaxation parameters are used for both the vorticity and 

the temprature to smooth the values between tvo consecutive time levels. This enables 

us to obtain inhomogenous modified Helmholtz equations for the time level concerned 

keeping all the terms at the previous time level as inhomogeneity. Thus, convergence 

to steady-state is accelerated by using proper values of the parameters. The results are 

obtained for several values of Rayleigh (Ra) and Hartmann (Ha) numbers. Differential 

Quadrature method gives quite accurate solutions by using considerably small number 

of grid points in space direction. As Ra or Ha increases one needs to take smaller time 

increments to achieve a preassigned accuracy. 

195

196 

Session 6.4: Mathematical Modeling, Analysis, Applications III 

Chair: Seiji Fujino 

Place: Hall 4

Approximation by div-rot variational splines 

Abdelouahed Kouibia 

email: kouibia@ugr.es 

University of Granada, Dept of Applied Mathematics, Faculty of Sciences 

C.P. 18071, Granada - Spain 

(Joint work with: M. Pasadas) 

Abstract: In Geology, Geophysic and other Earth Sciences, it is usual to find the construction 

problem of curves and surfaces from a Lagrange or Hermite data set. Vector 

field approximation is a problem arising in many Scientific applications, such as for example 

fluid mechanics, meteorology, optic flow analysis, electromagnetics. In the last 

years, different technics for the construction of a curve or surface are developed, for example 

the interpolation or fitting by spline functions, based on the minimization of a 

certain functional in a Sobolev space from some data as mentioned above. In this context, 

we present in this work an approximation problem by the new notion of div-rot 

variational splines. Some authors 2 have studied the div-curl approximation problem by 

weighted minimizing splines. The same authors have studied the splines under tension 

on a bounded domain in this work, 1 they have discussed error and convergence for interpolation 

by div-curl spline under tension of a vector field in the classical vectorial 

Sobolev space. In 3 the authors choose a seminorm based on the decomposition of vector 

fields into a rotational and a gradient part. They used the variational spline technique by 

determining the vectorial function which minimizes such seminorm over all the functions 

in a suitable semi-Hilbert space which interpolates the data. We study the existence and 

uniqueness of the solution of such problem. Then, we establish some convergence and 

error estimations results, as soon as, we compare our method with other existing ones 

on the literature. We show that the theory of the mimimizing functional splines may 

also be used for the approximation or for the interpolation of a vector field controlled 

by the divergence and the rotation of the vector field. This means that such minimizing 

functional contains various terms which are a mixed between a semi-norms of Sobolev 

with a divergence and rotational expressions. Such terms are controlled by some parameters. 

We study some geometrical effects of such divergence and rotational expressions 

and their influence on the minimized functional. 

References 

1. M. N. Benbourhim and A. Bouhamidi, Error estimates for interpolating div-curl splines 

under tension on a bounded domain, J. Approximation Theory 152 (2008), pp. 66-81. 

2. M. N. Benbourhim and A. Bouhamidi, Div-curl weighted minimizing splines, Analysis 

and Applications 5 No. 2 (2007), pp. 95-122. 

3. F. Dodu and C. Rabut, Vectorial interpolation using radial-basis-like functions, Computers 

and Mathematics with Applications 43 (2002), pp. 393-411. 

197

198 

Solving Distributed Optimal Control Problems for the 

Unsteady Burgers Equation in COMSOL Multiphysics 


email: bulent@metu.edu.tr 



(Joint work with: Fikriye Yilmaz) 

Abstract: We use COMSOL Multiphysics for solving optimal control of unsteady 

Burger’s equation without constraints, with mixed control-state constraints. Using the 

first order optimality conditions, we apply projection and semi-smooth Newton methods 

for solving the optimality system. We present results for the standard approach by integrating 

the state equation forward in time and the adjoint equation backward in time. 

We also consider the optimality system in the space-time cylinder as an elliptic equation 

and solve it adaptively. Numerical examples show the advantages and limits of the usage 

COMSOL Multiphysics.

Formalizing Dynamic Assignment of Rights and 

Responsibilities to Agents 

Farnaz Derakhshan 

email: farnazd@liv.ac.uk 

University of Tabriz 

29th Bahman Avn. Tabriz 

Iran 

Abstract: Recently, the design and development of multiagent systems (MASs) has 

become increasingly concerned with the recognition that they will be used in a dynamic 

and open environment. In such environments, it is a very difficult task to anticipate all 

possible runtime situations at design time. Therefore, in order to respond to changes 

in this environment it is necessary to allow the system to provide dynamic solutions 

at runtime. This paper is concerned with one particular aspect of such solutions. We 

explicitly address the problem of dynamic assignment of rights, responsibilities (R&Rs) 

and sanctions to external agents in normative MASs. We propose a novel method based 

on conditional norms for dynamic assignment of R&Rs and sanctions to external agents, 

and propose a formalism to represent a commonsense understanding of our solution. 

199

200 

Topology of two separation bubbles with opposite rotations 

in a double-lid-driven rectangular cavity 

Ali Deliceoglu 

email: adelice@erciyes.edu.tr 

Erciyes University 

Faculty of Science and Literature 


38039 Melikgazi - Kayseri 

Turkey 

(Joint work with: F. Gurcan) 

Abstract: The flow structures close to a stationary wall are investigated using both 

analytic solutions and methods from nonlinear dynamical systems. A particular region 

of S (speed ratio of the lid velocities), A (height to width) parameter space has been 

considered to construct a bifurcation diagram for the flow structure of two separation 

bubbles with opposite rotations in a double-lid-driven rectangular cavity.

Session 6.5: Numerical Analysis and Optimization 

Chair: Janos D. Pinter 

Place: Hall 5 

201

202 

The Block-Grid Method for Solving Laplace’s Boundary 

Value Problem with Singularities 

Adigozal Dosiyev 

email: adiguzel.dosiyev@emu.edu.tr 



Abstract: Block grid method is one of high accurate combined methods for the solution 

of Laplace’s equation on polygons proposed and justified in [1] [2]. In this method in 

a finite neighborhood, on the block sectors, of each singular point a special integral 

representation of the solution is approximated. Outside of these block sectors the Laplace 

equation is approximated by a finite difference scheme on a finite number of overlapping 

rectangles. The uniform estimate for the error of approximate solution is of order of 

O(h ν ), when the given boundary functions on the sides that not cause the singularity, 

belong to the Hölder classes C ν,λ , where , 0 < λ < 1, ν = 2 for 5-point, ν = 4, 6 for 

9-point schemes. Moreover, in the block sectors the derivatives of the exact solution of 

order p, p = 1, 2, ...are defined by simple differentiation of the approximate solution, and 

they converge as h ν with the constants depending on the index of the derivative and the 

distance from the current point to the singular vertex. In this presentation we analyse 

the errors when the class C ν,λ is replaced by C ν−1,1 . It is proved that the error of the 

approximate solution in uniform metric is O(h υ (|ln h| + 1)) and can not be improved. 

To remove |ln h| term in error of estimation, when ν = 2 or ν = 4, a combined “5 and 

9” point scheme [3] is used in overlapping rectangles of which at least one of its sides lie 

on the boundary of the polygon.

Analytical and numerical evaluation of finite-part integrals 

Johan Hendrik DeKlerk 

email: johan.deklerk@nwu.ac.za 

Mathematics and Applied Mathematics 

North West University (Potchefstroom Campus) 

Potchefstroom 2520, South Africa 

Abstract: As with a new development in any subject (in this case finite-part integrals) a 

large number of articles have been written on the specific topic, resulting in, what seems 

to be, a web of results. This makes it difficult to keep up with the development and usage 

of the new field. What is perhaps necessary is an ordering of results in the form of a good 

textbook. To my view, such a book should address at least the following: (a) a historical 

presentation of the development of hypersingular integrals, (b) a summary of different 

definitions of hypersingular integrals, (c) a discussion of available integration techniques 

for hypersingular integrals, (d) a list of relevant tables with constants for the quadrature 

formulae (nodes and weights), (e) a theoretical example illustrating every method given, 

(f) a practical example from reality which gives more flesh to the bone than a mere 

illustrating example, (g) a discussion of extensions that could be made in this field, and 

(h) a comprehensive list of bibliographic information. As far as my knowledge goes, a 

book of this kind has not been published yet. In this talk attention will be paid to some 

of these matters, especially, integration techniques and quadrature formulae (points (c) 

and (d)). 

203

204 

Automatic Zone Decomposition in Iterative Solution of 

Differential Equations over Unstructured Grids 

Nematollah Fouladi 

email: nefouladi@yahoo.com 

Sharif University of Technology, Aerospace Dep., Azadi Avenue 

Tehran, Iran 

(Joint work with: M. Darbandi) 

Abstract:This paper contributes to an adaptive computational zone approach on unstructured 

grids. The idea behind this method comes from automatic controlling of the 

computational zone during iterative solutions of differential equations over unstructured 

grids. This method automatically tracks the disturbances which are caused in some small 

portions near the inner bodies and are diffused into the computational domain during 

the iterative solutions of differential equations. So, this method avoids unnecessary computations 

by automatically dividing the computational domain into active and inactive 

zones. In this regard, firstly, we modify the connectivity matrix in an ordering based 

manner without requiring the additional memory storage. In this step, the domain mesh 

nodes and elements are successively renumbered respect to their sensitivities to the inner 

boundary grid points. In other hand, the elements and nodes indices are improved in 

connectivity matrix to construct element and node layers inside the mesh data structure. 

This method with confinement of searching process in the data structure of an 

unstructured grid facilitates the grid substructures addressing. Secondly, we use a suitable 

algorithm that provides a suitable management of disturbances propagation inside 

the mesh domain.

An Extended Implicit Pis Scheme to Efficent Simulation of 

Turbulent Flow with Moving Boundaries 

Alireza Naderi 

email: naderi33@yahoo.com 

Sharif University of Technology, Tehran, Iran 

(Joint work with: M. Darbandi) 

Abstract: We extend an implicit second-order time accurate method to simulate turbulent 

flows in domains with moving boundary. The arbitrary Lagrangian-Eulerian ALE 

approach is used for grid movement purpose. To enhance the efficiency of an original 

finite-volume based finite-element method, we treat the convection terms using a 

physical influence scheme PIS. We use standard k-epsilon, RNG kepsilon, and Spalart- 

Allmaras eddy viscosity turbulence models to perform the efficiency of our formulations. 

We show that our numerical method is very accurate and efficient in simulating domains 

with nonstationary fluid flow, separated turbulent flow over bluff bodies, and deep stall 

phenomenon over NACA0012 airfoil 

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206

2 October 2009, 13:30-15:45 

PARALLEL SESSIONS 7

Session 7.1: Optimization II 

Chair: Gerhard W. Weber 

Place: Hall 1 

209

210 

Survey of Polynomials Transformations between 

NP-Complete problems 


email: jruizvanoye@yahoo.com.mx 

Centro Nacional de Investigacion y Desarrollo Tecnologico 

Interior internado palmira s/n Col. Lomas de Cuernavaca. Cuernavaca, Morelos 

Mexico 

(Joint work with: Joaquin Perez-Ortega, Rodolfo A. Pazos R., Ocotlan Diaz-Parra) 

Abstract: Exists diverse polynomial reductions/transformations between NP-complete 

problems, in this paper will be to show the differences between polynomial reductions and 

polynomial transformation, the methodologies of polynomial reduction/transformation 

of instances between NP-complete problems using: the theory of NP Completeness, 

the theory of graphs and the application of formal languages. It will show examples 

of the polynomial reductions/transformation, the restrictions to reduce/transform between 

NP-complete problems, the verification of the reduction/transformation, besides 

to show the reduction/transformations that exist between NP-Complete problems, the 

way to verify the reduction/transformations, and a digraph with the historical reductions/transformations 

between instances of NP-Complete problems.

Application of Formal Languages in the Polynomial 

Transformations of Instances Between Np-Complete 

Problems 


email: jruizvanoye@yahoo.com.mx 

Centro Nacional de Investigacion y Desarrollo Tecnologico 

Interior internado palmira s/n Col. Lomas de Cuernavaca. Cuernavaca, Morelos 

Mexico 

(Joint work with: Joaquin Perez-Ortega, Rodolfo A. Pazos R., Ocotlin Diaz-Parra) 

Abstract: In this paper, we propose to define formal languages to express instances of 

NP-complete problems to be used in the polynomial transformations. The new idea proposed 

of to use formal languages theory for polynomial transformations is more practical 

and fast to apply to real problems than the theoretical theory of polynomial transformations 

(it is a mechanism to determine if a problem belongs to a class of problems, 

but in addition to determine if a problem is more complex than another). We proposed 

a methodology of transformation of instances between NP-complete problems, the differences 

between the Johnson methodology and with our methodology, and examples of 

the polynomial transformations. 

211

212 

Some Inequalities for Increasing Positively Homogeneous 

Functions 

Serap Kemali 

email: skemali@akdeniz.edu.tr 

Akdeniz University Vocational School Of Technical Sciences 

Antalya-Turkey 

(Joint work with: Gabil R. Adilov) 

Abstract:In this paper we study Hermite-Hadamard type inequalities for increasing positively 

homogeneous functions. Some examples of such inequalities for functions defined 

on special domains are investigated and the concrete results are obtained.

A Comparative Study on Parameter Estimations in 

Multivariate Nonlinear Model 

Aydin Karakoca 

email: akarakoca@selcuk.edu.tr 




Turkey 


Abstract: The univariate nonlinear model can be given by, 

213 

yt = f xt, θ 0 + et, t = 1, 2, . . . , n. (1) 

Here we consider the case there are M such regressions called multivariate nonlinear 

model is given by 

 

yαt = fα xt, θ 0 

α + eαt, t = 1, 2, . . . , n, α = 1, 2, . . . , M (2) 

that are related in one of two ways (Gallant, 1987). The first arises most naturally 

when repeated measures on same subject, the second way these models can be related is 

through shared parameters. In this study, the parameter estimates for Eq(1) and Eq(2) 

will be obtained by modified Gauss-Newton algorithm and Genetic Algorithm. Results 

of parameter estimates will be compared. 

References 

1. Bates, D.M., Watts, D.G., (1988), Nonlinear Regression Analysis and Its Applications, 

John Wiley & Sons, Inc. 

2. Gallant, A. R., (1987), Nonlinear Statistical Models, John Wiley & Sons, Inc. 

3. Genç, A., (1997). Çok Degi¸skenli Lineer Olmayan Modeller: Parametre Tahmini ve 

Hipotez Testi, Ankara Universitesi, Fen Bilimleri Enstitüsü Doktora Tezi. 

4. Holland. J., (1975), Adaptation in Natural and Artificial Systems, The University of 

Michigan Press, Ann Arbor, MI, 1975. 

5. Goldberg, D.E., (1989) , Genetic Algorithms in Search, Optimization and Machine 

Learning, Addison Wesley, Readin, MA. 

6. Seber, G.A, Wild, J., (1989). Nonlinear Regression. John Wiley & Sons, New York

214 

Interior point filter line search strategies for large scale 

optimization: practical behavior 

M. Fernanda P. Costa 

email: mfc@mct.uminho.pt 

University of Minho, Department of Mathematics for Sciencie and Technology - Portugal 

(Joint work with: Edite M.G.P. Fernandes, A. Ismael F. Vaz) 

Abstract: We present two classes of primal-dual interior point methods that rely on a 

filter line search strategy for large scale nonlinear optimization. The first class approximately 

solves a sequence of associated barrier problems and each entry in the filter has 

three components. The feasibility and the centrality measures come directly from the 

KKT conditions of the barrier problem and the optimality measure is represented by 

the barrier objective function. The other class uses the Newtons method to solve the 

perturbed primal-dual system to generate iteratively the search directions. The filter in 

the line search strategy uses the same previously mentioned three components. We solve 

a well-known set of large scale optimization problems and a comparison with the Ipopt 

solver is provided. The results show that both classes of filter line search methods are 

effective in reaching the solutions, and are comparable in terms of number of iterations, 

number of function evaluations and CPU time.

Interval Malmquist productivity in DEA analysis and its 

application in determining the regress and progress of 

Islamic Azad university’s departments 


email: toloie@gmail.com 

Poonak-Hesarak-I.A.U.Science and Research Branch 

Iran 

(Joint work with: H. Nikoomaram, A. Toloie Eshlaghy, M.A. Kazemi, R. Sharifi, M. Ahadzadeh 

Namin) 

Abstract: In this paper, a method is proposed for obtaining productivity using 

Malmquist Productivity Index on interval data. Through using this index and also DEA 

models, the progress and regress of Decision Making Units (DMU) can be calculated. 

Although the data are not exact and definite, but they lie in an interval, then Malmquist 

Productivity Index is calculated within an interval. 

Keywords: Data Envelopment Analysis (DEA), Efficiency, Malmquist Productivity Index, 

Interval Data. 

215

216 

Session 7.2: Mathematical Modeling, Analysis, Applications IV 

Chair: Andrei Bourchtein 

Place: Hall 2

Parameter Interval Estimations through Chebyshev-Type 

Inequalities for Nonlinear Regression Models ∗ 

Atif Evren 

email: aevren@yildiz.edu.tr 

Yildiz Technical University,Faculty of Arts and Science, Department of Statistics,Davutpasa 

34210, Esenler, Istanbul - Turkey 

(Joint work with: Dogan Yildiz) 

Abstract: In linear regression models, parameter estimators are linear functions of independent 

variables. Therefore, under the assumption of normality, parameter interval 

estimation procedures can be based on normal distribution itself or other distributions 

which are derived from normality assumption like student-t distribution, chi-square distribution 

and Snedecor F distribution. On the other hand for nonlinear regression models, 

parameter estimates are not simply linear functions of variables. Therefore for nonlinear 

models , interval estimation procedures are realized by assuming asymptotic normality 

. This assumption is, of course, not realistic all the time. In these cases, multivariate 

versions of Chebyshev-type inequalities can be used since all these inequalities do not require 

strict restrictions on the distributions of variables. Sometimes the results obtained 

by using these inequalities are poor. Nevertheless, these interval estimates may be helpful 

especially for obtaining initial parameter estimates since nonlinear estimation techniques 

are based on iterative procedures. In this study , we propose an algorithm through which 

initial parameter estimates can be made by using Chebyshev-type inequalities. Then we 

compare all results (i.e. the results obtained by assuming normality, the bootstrap results 

and the results we have obtained through this algorithm. 

∗ This paper is dedicated to our advisors. 

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218 

Special functions, non-linearity and algebraic and differential 

properties: Computational aspects 

Alejandro Zarzo 

email: alejandro.zarzo@upm.es 

Departamento de Matematica APlicada, ETS Ingenieros Industriales, Universidad Politecnica 

de Madrid 

C/ Jose Gutierez Abascal 2, 28006 Madrid , Spain 

(Joint work with: L. Fernandez, P. Martinez-Gonzalez, B. Soler) 

Abstract: A method for the explicit construction of general non-linear sum rules involving 

hypergeometric type functions and their derivatives of any order is derived which only 

requires the knowledge of the coefficients of the differential equation that they satisfy, 

i.e. the simplest Lamé equation also known as hypergeometric type differential equation. 

Special attention is paid to the quadratic case for which, as illustration of the method, 

some particular sum rules are explicitly constructed in terms of the differential equation 

coefficients. Moreover, an extension of the method to the generalized hypergeometric 

type functions and some explicit applications are given.

Trace Inequalities for Matrices 

Ramazan Turkmen 

email: rturkmen@selcuk.edu.tr 

Selcuk University, Science Faculty, Department of Mathematics, Turkey 

(Joint work with: Zubeyde Ulukok) 

Abstract: Matrix trace inequalities are used in many areas such that analysis, statistics. 

In this talk, we present some inequalities on traces of the ordinary product and sum of 

positive semidefinite matrices and any matrices. 

219

220 

The Convergence of Family of Integral Operators with 

Positive Kernel 

Mine Menekse Yilmaz 

email: menekse@gantep.edu.tr 

University of Gaziantep Department of Mathematics, 27310 Gaziantep, Turkey 

(Joint work with: Sevilay Kirci Serenbay) 

Abstract: The aim of this study is to investigate the convergence of family of generalized 

integral operators with positive kernel in space Lp. Previously unused , A modulus of 

continuity is defined. This modulus of continuity was proven features. Using this modulus 

of continuity, convergence has been investigated.

Approximation of patches by C r -finite elements of 

Powell-Sabin type 

Miguel Angel Fortes 

email: mafortes@ugr.es 

Universidad de Granada 

Edificio Politcnico. Campus de Fuentenueva 

18071-Granada - Spain 

(Joint work with: P. Gonzalez, M. Pasadas) 

Abstract: Let D ⊂ R2 be a polygonal domain and m ∈ N. Let us consider, for each 

i = 1, . . . , m, a polygonal domain Hi ⊂ D in such a way that the H ′ is are disjoint, 

and a real function ϕi ∈ L2 (Hi). We present a method to obtain a Cr-spline surface 

approximating the functions {ϕi}1≤i≤m and minimizing the “energy functional” defined 

by 

m 

 

J (v) = (v(x) − ϕi(x)) 2 r+1 

dx + τj|v| 2 j , 

i=1 

H i 

where τi ≥ 0 for i = 1, . . . , r, τr+1 > 0, v belongs to a finite element space V constructed 

from a triangulation of D of Powell-Sabin type, and | · |j denotes the usual semi-norm on 

the Sobolev space H r+1 (D) for j = 1, . . . , r + 1. We prove that there exists a unique element 

σ ∈ V such that J (σ) ≤ J (v) for all v ∈ V . We give a variational characterization 

of σ, a convergence result, and we present some numerical and graphical examples. 

j=1 

221

222 

Project Scheduling Problem 

Alejandro Fuentes-Penna 

email: alexfp10@hotmail.com 

Universidad Popular Autonoma del Estado de Puebla 

Otilio Montano No. 115 B-103, Colony Altavista, Cuernavaca, Morelos. CP 62010 

Mexico 

(Joint work with: Jorge A. Ruiz-Vanoye and Ocotlán Díaz-Parra) 

Abstract: The project management is the application of knowledge, abilities, tools 

and techniques to activities of projects so that they fulfill or exceed the needs and 

expectations of a project, such as: reach, time, cost and quality, requirements identified 

(needs) and requirements non-identified (expectations). The application areas usually are 

defined in terms of: technical elements (development of software, pharmaceutical drugs 

or civil engineering), elements of the administration (contracts with the government 

or development of new products), and groups of industry (automobiles, chemicals or 

financial services). In this paper, we propose a new NP-hard combinatorial problem 

optimization problem called Project Scheduling Problem, which search to minimize the 

total time of software project development by means of the optimal management of 

the project resources. In addition, we described the mathematical model for the new 

problem, the definition of the instances and demonstrated that problem is NP-hard 

by means of the instances polynomial transformation(Project Scheduling Problem to 

TimeTable Problem).

Interval Malmquist productivity in DEA analysis and its 

application in determining the regress and progress of 

Islamic Azad university’s departments 



Poonak-Hesarak-I.A.U.Science and Research Branch 

Iran 

(Joint work with: H. Nikoomaram, A. Toloie Eshlaghy, M.A. Kazemi, R. Sharifi, M. Ahadzadeh 

Namin) 

Abstract: In this paper, a method is proposed for obtaining productivity using 

Malmquist Productivity Index on interval data. Through using this index and also DEA 

models, the progress and regress of Decision Making Units (DMU) can be calculated. 

Although the data are not exact and definite, but they lie in an interval, then Malmquist 

Productivity Index is calculated within an interval. 

Keywords: Data Envelopment Analysis (DEA), Efficiency, Malmquist Productivity Index, 

Interval Data. 

223

224 

Session 7.3: Probability, Stochastic Processes and Computational 

Methods 

Chair: Birdal Senoglu 

Place: Hall 3

Super efficiency in stochastic data envelopment analysis: An 

input relaxation approach 

Mohammad Khodabakhshi 

email: mkhbakhshi@yahoo.com 

Operations Research Department of Mathematics 

Faculty of Science, Lorestan University, Khorram Abad 

Iran 

Abstract: This paper addresses super-efficiency issue based on input relaxation model, 

e.g. Khodabakhshi and Asgharian(2008) , in stochastic data envelopment analysis. The 

proposed model is not limited to use the input amounts of evaluating DMU, and one can 

obtain a total ordering of units by using this method. The input relaxation super efficiency 

model is developed in stochastic data envelopment analysis, and its deterministic 

equivalent, also, is derived which is a nonlinear program. Moreover, it is shown that the 

deterministic equivalent of the stochastic super efficiency model can be converted to a 

quadratic program. As an empirical example, the proposed method is applied to data of 

textile industry of China to rank efficient units. Finally, when allowable limits of data 

variations for evaluating DMU are permitted, sensitivity analysis of the proposed model 

is discussed. 

Keywords: DEA; Employment; Super-efficiency; Input relaxation; Chance constraints 

225

226 

Two Level Fractional Factorials with Long-Tailed Symmetric 

Error Distributions 

Sukru Acitas 

email: sacitas@anadolu.edu.tr 

Anadolu University, Science Faculty 


26470 Eskisehir - Turkey 

(Joint work with: Birdal Senoglu) 

Abstract: In this study, we obtain the explicit estimators for the parameters in 2 k factorial 

design by using the methodology known as modified maximum likelihood (MML). 

We also develop a test statistic based on MML estimators for testing main effects and 

interactions in the one-half fraction of the 2 k design. We show that our solutions are more 

efficient and robust then the classical least squares (LS) solutions. We give an example.

X-ray Fluorescence Computed Tomography: Inversion 

Methods 

Alvaro Rodolfo De Pierro 

email: alvaro@ime.unicamp.br 

University of Campinas, IMECC-UNICAMP 

Applied Mathematics Department, CP 6065, CEP 13083-030, Campinas, SP 

Brazil 

(Joint work with: E.X. Miqueles) 

Abstract: X-ray Fluorescence Computed Tomography (XFCT) is a novel synchrotron 

based imaging modality aiming at reconstructing the distribution of an element inside 

the body. In XFCT, high intensity monochromatic synchrotron X-rays, with energy 

greater than the K-shell binding energy of the elements of interest, stimulates fluorescence 

emissions, isotropically distributed, which are detected by a detector placed parallel to 

the direction of the incident beam. Mapping fluorescence emission could have many 

important biomedical applications (iodine distributions in thyroid tissue, platinum in 

clusters of cancer cells treated with cisplatin, etc). A continuous mathematical model for 

XFCT is given by the Generalized Attenuated Radon Transform (GART). In this article, 

we present an analytic inversion formula for the GART as well as some approximated 

ones based on the inversion of the Radon Transform. A comparison between the different 

inversion approaches is also shown by means of simulated and real data. 

227

228 

Using Dirichlet-to-Neumann operators and Conformal 

Mappings with Approximate Curve Factors in Waveguide 

Problems 

Anders Andersson 

email: anders.andersson@vxu.se 

Vaxjo University 

MSI, SE-35195 Vaxjö Sweden 

Sweden 

(Joint work with: B. Nilsson) 

Abstract: We consider wave scattering in waveguides with comparatively arbitrary geometry 

and boundary conditions. The setting is acoustic, but the same techniques can 

be used for electro-magnetic or quantum scattering problems. When applying the so 

called Building Block Method, see, 4 such problems can be solved by solving a sequence 

of two-dimensional wave scattering problems in infinite waveguides where all variations 

in geometry and boundary conditions are smooth. Furthermore, these waveguides are 

straight and with constant width outside some bounded region. To solve these subproblems, 

we 

• use a global conformal mapping to transform the geometry to a straight horizontal waveguide, 

• represent the field and scattering operators by matrices based on expansions in Fourier series, 

• introduce Dirichlet to Neumann operators and solve equations for their matrix representations 

using standard numerical ODE solvers, see, 1–3 and can hence determine a matrix representation 

for the wave field. 

For the conformal mapping, we use a variant of the Schwarz-Christoffel mapping. The 

mapping is modified using so called approximate curve factors, which means that polygonal 

regions with rounded corners are produced in such a way that the mapping function 

is C ∞ on the boundary. 

References 

1. L. Fishman, A. K. Gautesen, and Z. Sun, Wave Motion 26, 127–161 (1997), ISSN 

0165-2125. 

2. Y. Y. Lu, Math. Comput. Simulation 50, 377–391 (1999), ISSN 0378-4754, wave splitting 

and inverse problems (Berlin, 1997). 

3. Y. Y. Lu, J. Comput. Appl. Math. 173, 247–258 (2005), ISSN 0377-0427. 

4. Börje Nilsson and Olle Brander. IMA J. Appl. Math., 27(3):263–289 (1981).

Imprecise probability and application in finance 

Mila Milan Stojakovic 

email: shamsul.qamar@comsats.edu.pk 

Faculty of Engineering, University of Novi Sad, 21000 Novi Sad Serbia 

Serbia and Montenegro 

Abstract: Fuzzy probability is a generic name used to represent the concept in which 

the fuzzy theory is used for analyzing and modeling highly uncertain probability systems. 

In this paper the fuzzy probability is defined over the measurable space. It is 

derived from a fuzzy valued measure using restricted arithmetics. The range of fuzzy 

probability is the set of real valued upper semicontinuous fuzzy sets. The expectation 

with respect to fuzzy probability is defined and some properties are discussed. Since L. 

Zadeh published his now classic paper more then forty years ago, fuzzy set theory has 

attention from researches in a wide range of scientific areas, especially in recent years. 

Theoretical advances and applications have been made in many directions. The theory 

of fuzzy sets, as its name implies, is a theory of graded concepts, a theory in which everything 

is a matter of degree. This theory was developed to give techniques for dealing 

with models for natural phenomena which do not lend themselves to analysis by classical 

methods based on probability theory and bivalent logic. Applications of this theory can 

be found in artificial intelligence, computer sciences, expert systems, logic, operations 

research, pattern recognition, decision theory, robotics and others. In the classical set 

theory if A ⊆ X , then this relation can be described by indicator (or characteristic) 

function IA : X → {0, 1}, where IA(x) = 1 if x ∈ A and IA(x) = 0 if x ∈ X \A. One 

can interpret the function IA as the degree of membership of x in X . There are only two 

possibilities: 0 or 1. In fuzzy concept the set A is identified with the membership function 

uA : X → [0, 1] where the interpretation uA(x) is the degree to which “x is in A”, or x is 

compatible with A. Fuzzy set A of X we identify with its membership function uA. The 

set of all functions u : X → [0, 1] we denote by F(X ) and we say that F(X ) is the set 

of all fuzzy sets defined on X . Uncertainty regarding some experiment may essentially 

have two origins. It may arise from randomness due to natural variability of observation 

or it may be caused by imprecision due to partial informations, e.g. expert opinions or 

sparse data sets. Highly imprecise probabilistic system could be formalized using the 

theory of fuzzy random variables or using the theory of fuzzy probability. An incomplete 

data set delivers an imprecise assessment of the probability of an event which should be 

expressed by a [0,1]-fuzzy set instead by a number. In other words, probability theory 

is complemented with extra dimension of uncertainty provided by fuzzy set theory. This 

concept has received the generic name of fuzzy probability. However, this generic term 

has been interpreted and mathematically formalized in various ways. One of the most 

attractive interpretations of fuzzy probability is where probability of a crisp event, due 

to the imprecision of background knowledge or sparsity of data sample, is expressed in 

terms of fuzzy numbers. In our paper, the method of restricted fuzzy arithmetics is used 

to treat the probabilities which are fuzzy valued but in spite of that the sum of all the 

individual probabilities is one. One can consider this concept as the extension and generalization 

of the classical model of probability theory. We introduce the fuzzy probability 

229

230 

as the function derived from a finite complete fuzzy valued measure. That kind of fuzzy 

probability still has some nice properties - it is normed and *additive, where *additivity 

is the additivity with respect to addition in restricted arithmetics. It turns out that our 

model is suitable to define the expectation which generalize the single and interval valued 

model. The range of fuzzy valued measure and the derived fuzzy probability is the set 

of real valued upper semicontinuous fuzzy sets. Since there is no any assumption about 

convexity, this theory can be used to model and analyse probabilistic systems where the 

values of probability are highly imprecise but discrete. This mathematical model is used 

to treat some financial problem- such as stock prices process - with imprecise data.

Session 7.4: Mathematical Programming and Data Analysis 

Chair: Pablo Sanchez-Moreno 

Place: Hall 4 

231

232 

A new hybrid algorithm for quadratic knapsack problem 

Tugba Sarac 

email: tsarac@ogu.edu.tr 

Eskisehir Osmangazi University, Industrial Enginnering Department 

Meselik, 26480 Eskisehir 

Turkey 

Abstract: Quadratic knapsack problem (QKP) with quadratic objective function and a 

capacity constraint is one of the well-known combinatorial optimization problems. Many 

solution methods have been proposed for this problem in the literature. One of them 

is Modified Subgradient (MSG) Algorithm. The performance of the MSG algorithm on 

solving the QKP was examined by Sipahioglu and Sarac in 2009. They showed that the 

quality of the MSG solutions depends on choosing proper values of the algorithm parameters. 

In this study, a new hybrid solution approach that a tabu search algorithm to 

find the proper MSG parameter values and the MSG algorithm run together. The performance 

of the developed algorithm is evaluated and the obtained results are compared 

to the previous studies in the literature.

Criteria Function Efficiency Against Outliers in Nonlinear 

Regression 

Ahmet Pekgor 

email: ikinaci@selcuk.edu.tr 




Turkey 


Abstract: In this work, it is compared the efficiency of confirmation outliers of criteria 

functions, using S scale estimators and M location estimators different criteria functions 

which are not affected by outliers in nonlinear regression. It is used six scripts which 

Serbert and friends exerted and twenty four different situations. And, based on errors 

that are came by different confusion in Richards sigmoid model, It is used Monte Carlo 

simulation for determining efficiency of these criteria functions in confirming outliers. 

Keywords: Nonlinear Regression, Criterion Function, S-Estimator, M-Estimator, 

Outlier 

References 

1. Barrera, M.S. ve Yohai V.J. (2006), A Fast Algorithm for S-Regression Estimates, 

Journal of Computational and Graphical Statistics, vol. 15, no.2, pp 1-14. 

2. Huber, P.J, Robust Statistics, John Willey & Sons, Inc., USA, 1981. 

3. Rousseeuw, P. J. and Yohai, V. J. (1984), Robust Ragression by Means of S-Estimator, 

in Robust and Nonlinear Time Series Analysis, eds. J. Franke, W. Hardle and R. D. 

Martin, (Lecture Notes in Statistics), Springer - Verlag, New York, pp. 256-272. 

4. Serbert, D.M., Montgomery, D.C. and Rollier, D. (1998), A Clustering Algorithm for 

Identifying Multiple Outliers in Linear Regression, Computational Statistics & Data 

Analysis, vol. 27, pp. 461-484. 

5. Stromberg, A.J., Computation of High Breakdown Nonlinear Regression Parameters,J. 

Am. Stat. Assoc. 88 (1993) 237. 

6. Wu, J.W. ve Lee, W.C. (2006), Computational Algorithm of Least Absolute Deviation 

Method for Determining Number of Outliers Under Normality, Applied Mathematics 

and Computation, vol. 175, pp. 609-617. 

233

234 

A two-objective integer programming mathematical model 

for a one-dimensional assortment problem 

Nergiz Kasimbeyli 

email: n.ismail@ogu.edu.tr 

Industrial Engineering Department 

Engineering and Architecture Faculty 

Eskisehir Osmangazi University 

Meselik, Eskisehir 

Turkey 

(Joint work with: Tugba Sarac) 

Abstract: This paper considers the one-dimensional assortment problem which includes 

the determination of the number of different sizes of standard lengths to be maintained 

as inventory and to be used to fulfill a set of customer orders. One of the main difficulties 

in formulating and solving this kind of problems is the use of cutting orders in the mathematical 

model. Many mathematical programming approaches for solving the assortment 

problems assume the existence of the set of cutting orders. The corresponding mathematical 

models use the cutting orders as model parameters. Because of a huge number 

of cutting orders to be obtained for such kind of models, this leads to computational 

difficulties in solving these problems. The purpose of this paper is therefore to develop 

a mathematical model without the use of cutting orders. In this paper, a two objective 

integer programming mathematical model is developed for solving a one-dimensional 

assortment problem with two or more types of stock lengths. Our model involves nonlinearity 

in the demand satisfaction constraints. Because of this nonlinearity we suggest 

the special solution method presented in this paper. The mathematical model and the 

solution approach are demonstrated on test problems.

Estimation of reliability P (Y < X) for the proportional 

reversed hazard models using lower record data 

A. Asgharzadeh 

email: a.asgharzadeh@umz.ac.ir 

Dept of Statistics, University of Mazandaran 

Babolsar-Iran 

(Joint work with: R. Valiollahi) 

Abstract: This paper deals with the estimation of P [Y < X] when X and Y are two 

independent random variables from a proportional reversed hazard models. Based on 

lower record values, the maximum likelihood estimator, Bayes estimator and approximate 

Bayes estimator of P [Y < X] are obtained. Different confidence intervals are proposed. 

Monte Carlo simulations are performed to compare the different proposed methods. 

Analysis of a simulated data set has also been presented for illustrative purposes. 

235

236 

Libor Market Model as a Special Case of Parameter 

Estimation in Nonlinear Stochastic Differential Equations 

(SDEs) 

Ceren Eda Can 

email: cerencan@hacettepe.edu.tr 

Hacettepe University, Faculty of Science, Department of Statistics, 06800 Beytepe / Ankara 

Turkey 

(Joint work with: N. Erbil, G. W. Weber) 

Abstract: This paper is concerned with the problem of parameter estimation in nonlinear 

stochastic differential equations based on three statistical modelling techniques, 

Generalized Additive Models, Multivariate Adaptive Regression Splines (MARS), Nonlinear 

Regression Methods. These techniques will be applied to SDEs by optimization. 

In this study, the general structure of optimization will be described in the context of 

interest rate derivatives. Optimization in finance finds its particular application within 

the context of calibration problems. In particular, the LIBOR Market Model, based on 

evolving the forward-LIBOR rates, will be studied under this topic as a special case. Calibration 

of LIBOR Market Model to some target state determined by available relevant 

market data implies a continuous optimization of the model parameters, volatility and 

correlations of the forward- LIBOR rates, such that the deviation between the target 

state and the model state variables becomes minimal. In addition, we also include regularization 

terms in order to control the complexity of the model and the stability of the 

solution with respect to noise in the data. Finally, model performance will be evaluated 

using these statistical modelling techniques and the similarities and dissimilarities will 

be given among these methods. We conclude by an outlook on possible future studies.

Alternative Long-Run Analysis of Services and Goods 

Sectors Inflation in Turkey by Fractional and Asymmetric 

Cointegration Methods 

Koray Kalafatcilar 

email: koray.kalafatcilar@tcmb.gov.tr 

Monetary Policy and Research Department 

The Central Bank of Turkey, 

06100, Ulus-Ankara 

Turkey 

(Joint work with: Yilmaz Akdi, Kivilcim Metin-Ozcan) 

Abstract: In this study we analyze the long-run relationship between goods and services 

sectors inflation rates in Turkey. Deterioration in relative prices over the last decade encouraged 

us to study the inflation dynamics of the two sectors. Problems we encountered 

in standard time series long - run analysis tools led us to conduct the empirical work in 

asymmetric and fractional cointegration methods. Estimation results of fractional cointegration 

suggest, just as conventional time-series tools, that the inflation rates of the two 

sectors are not cointegrated, even fractionally. Application of asymmetric cointegration 

method sheds more light on the issue and suggests that series are not cointegrated along 

downward movements either. 

237

238 

Some Relations Between Functionals On Bounded Real 

Sequences 

Seyhmus Yardimci 

email: yardimci@science.ankara.edu.tr 




Turkey 

Abstract: In this study, we mainly concern with the functionals L∗∗ and l∗∗ , respectively, 

defined by L∗∗ r 

1 

(x) = lim sup |xk+i|, l r 

k 

i=0 

∗∗ r 

(x) = lim infsup 

|xk+i|. on 

r k 

i=0 

bounded real sequences and give some inequalities between these functionals.

Session 7.5: Mathematical Modeling and Computational 

Approaches 

Chair: Guvenc Aslan 

Place: Hall 5 

239

240 

Efficient numerical techniques for solving batch 

crystallization models 

Shamsul Qamar 

email: shamsul.qamar@comsats.edu.pk 

Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 

Magdeburg - Germany 

(Joint work with: S. Mukhtar, S. Noor, A. Seidel-Morgenstern) 

Abstract: Crystallization is the process of forming a solid phase from a homogeneous 

supersaturated solution and therefore is a solid-liquid separation technique. It is an 

important separation and purification process used in chemical, pharmaceutical, semiconductor, 

and food industries. An understanding and optimization of crystallization 

processes are important for improving the product quality and for the minimization of 

production costs. Achieving the desired goal can be significantly supported by modeling 

the underlying processes and by developing advanced control algorithms that can be 

used for optimization of the resulting crystal size distribution (CSD). However, an accurate 

simulation of the CSD is challenging since the distribution can extend over many 

orders of magnitude in size and time. This work focuses on the numerical investigation 

of one- and two-dimensional batch crystallization models with size-dependent or sizeindependent 

growth rates. On the one hand, we implement the existing high resolution 

finite volume scheme, which were originally derived for the gas dynamics, for solving 

multi-dimensional batch crystallization models. On the other hand, we derive our own 

numerical techniques which we found to more efficient and accurate for solving the batch 

crystallization models. Especially, our proposed numerical method is very suitable for 

solving multi-dimensional batch crystallization models. The proposed numerical method 

has two parts. In the first part, a coupled ODE system of moments and solute mass 

is solved at the discrete points of the given computational time domain. In the second 

part this discrete data is used to construct the final CSD from an algebraic equation obtained 

either by employing the method of characteristics and Duhamel’s principle or the 

Laplace transformation on the given model. To overcome the closure problem of moment 

system in the case of size-dependent growth rate, a Gaussian quadrature method based 

on orthogonal polynomials is used for approximating integrals appearing in the moment 

system. Moreover, we have also implemented moving mesh techniques for improving the 

results of the numerical schemes further. For validation, the numerical results of the proposed 

technique are compared with those from the high resolution finite volume schemes. 

The numerical results demonstrate the high order accuracy, efficiency and potential of 

our numerical method for solving the batch crystallization models.

Equations of anisotropic elastodynamics as a symmetric 

hyperbolic system:deriving the time-dependent Green’s 

function 

Handan Cerdik Yaslan 

handan.yaslan@deu.edu.tr 

Dokuz Eylul Universitesi Fen Edebiyat Fak. Matematik Bolumu 

(Joint work with: Valery G. Yakhno) 

Abstract:Let x = (x1, x2, x3) is a space variable from R3 , t is a time variable from R. Let 

us consider a homogeneous three-dimensional space characterized by the density ρ > 0 

and the four order elastic moduli tensor {cijkl} 3 i,j,k,l=1 which components subject to the 

following symmetry properties cijkl = cjikl = cijlk = clkij, and the positive definiteness 

property 3 j,k,l,m=1 cjklmξjkξlm > 0, where ξjk are components of arbitrary second 

order nonzero tensor ξ satisfying ξjk = ξkj. It is convenient and customary to describe 

the elastic moduli in terms of a 6 × 6 matrix according to the following conventions 

relating a pair (i, j) of indices i, j = 1, 2, 3 to a single index α = 1, ..., 6 : 

(1, 1) ↔ 1, (2, 2) ↔ 2, (3, 3) ↔ 3, 

(2, 3), (3, 2) ↔ 4, (1, 3), (3, 1) ↔ 5, (1, 2), (2, 1) ↔ 6, 

Using the symmetry properties this correspondence is possible due. Moreover the matrix 

C = (cαβ)6×6, where α = (ij), β = (kl), is symmetric and positive definite. The 

mathematical model of elastic wave propagation in this homogeneous, anisotropic space 

is described by the linear system of elastodynamics ( Dieulesaint and Royer (1980) ) 

ρ ∂2ui = 

∂t2 241 

3 ∂Tij 

+ fi(x, t), i = 1, 2, 3, (1) 

∂xj j=1 

where u = (u1, u2, u3) is the displacement vector with components ui = ui(x, t); f = 

(f1, f2, f3) is the vector density of the external forces with components fi(x, t); Tij = 

Tij(x, t) are stresses defined as 

3 ∂uk 

Tij = cijkl , i, j = 1, 2, 3. (2) 

∂xl 

k,l=1 

We show that relations (1) and (2) are written in the form of a first-order symmetric 

hyperbolic system. 

here 

A0 = 

∂V 

A0 

∂t + 

3 ∂V 

Aj = F, (3) 

∂xj 

j=1 

 

ρI3 03×6 

06×3 C−1 

03,3 Bj 

, Aj = 

B∗ j 06×6 

 

,

242 

where C −1 is the inverse matrix to C, I3 is the identity matrix of the order 3 × 3 and 

0l×m is the zero matrix of the order l × m; 

⎛ 

−1 0 0 0 0 0 

⎞ ⎛ 

0 0 0 0 

⎞ 

0 −1 

B1 = ⎝ 0 0 0 0 0 −1 ⎠ , B2 = ⎝ 0 −1 0 0 0 0 ⎠ , 

0 0 0 0 −1 0 

0 0 0 −1 0 0 

⎛ 

0 0 0 0 

⎞ 

−1 0 

B3 = ⎝ 0 0 0 −1 0 0 ⎠ ; 

0 0 −1 0 0 0 

V = (U1, U2, U3, T1, T2, T3, T4, T5, T6) ∗ , F = (f1, f2, f3, 06×1) ∗ , 

Ui = ∂ui/∂t, i = 1, 2, 3; Tα, α = 1, 2, 3, 4, 5, 6 are stresses defined by 

∂u1 

Tα = cα1 

∂x1 

∂u3 

+ cα5 

∂x1 

∂u1 

+ cα6 

∂x2 

∂u3 

+ cα4 

∂x2 

∂u1 

+ cα5 

∂x3 

∂u2 

+ cα6 

∂x1 

∂u2 

+ cα2 

∂x2 

∂u2 

+ cα4 

∂x3 

∂u3 

+ cα3 , α = 1, 2, 3, 4, 5, 6. (4) 

∂x3 

In the last relations we denote a pair (i, j) of indices i, j = 1, 2, 3 as a single α, α = 1, ..., 6 

and use the above mentioned rule of the re-numeration the relations (2). In the time domain 

for the considered homogeneous anisotropic elastic three-dimensional space , the 

Green’s function G(x−x 0 , t−t 0 ) = (G k j (x−x0 , t−t 0 ))3×9 is defined as a 3×9 matrix whose 

k-th column Gk (x−x0 , t−t0 ) = (Gk 1 (x−x0 , t−t0 ), Gk 2 (x−x0 , t−t0 ), ..., Gk 9 (x−x0 , t−t0 )) 

is a solution of the system (3) for F = Ekδ(x − x0 )δ(t − t0 ) and vanishing for 

t − t0 < 0 as well as |x| → ∞ for all t. Here x = (x1, x2, x3) is 3-D space variable, 

x0 = (x0 1 , x0 2 , x0 3 ) is 3-D parameter, t is the time variable, t0 is the time parameter; 

δ(x − x0 ) = δ(x1 − x0 1 )δ(x2 − x0 2 )δ(x3 − x0 3 ), δ(xj − x0 j ) is the Dirac delta 

function considered at xj = x0 j , j = 1, 2, 3; δ(t − t0 ) is the Dirac delta function considered 

at t = t0 ; E1 = (1, 0, 0, 01×6), E2 = (0, 1, 0, 01×6), E3 = (0, 0, 1, 01×6). Using 

theory of the symmetric hyperbolic systems of the first order partial differential 

equations ( Mizohata (1973) ), ( Courant and Hilbert (1962) ) we find that there exists a generalized 

vector function with components from C1 ([0, T ]; S ′ (R3 )) satisfying (3) with 

F = Ekδ(x−x 0 )δ(t−t 0 ). Here T is an arbitrary positive real number; C1 ([0, T ]; S ′ (R3 )) 

is the class of all continuously differentiable mappings from [0, T ] into S ′ (R3 ); S ′ (R3 ) 

is the space of tempered distributions (generalized functions of slow growth)(see, for 

example, ( Vladimirov (1971) )). Moreover the components of this solution V (x, t) have 

finite supports for any fixed t from [0, T ]. Using the Paley-Wiener theorem (see, for 

example,( Reed and Simon (1975) ) ) the image of the Fourier transform of Vj(x, t) with 

respect to x = (x1, x2, x3) ∈ R3 is entire analytic function of the Fourier parameters 

ν = (ν1, ν2, ν3) ∈ R3 , i.e. if ˜ Vj(ν, t) = Fx[Vj](ν, t), where the Fourier operator Fx is 

defined by (see, for example, ( Vladimirov (1971) ) ) 

+∞ +∞ +∞ 

Fx[Vj](ν, t) = 

Vj(x, t)e 

−∞ −∞ −∞ 

iνx dx1dx2dx3, j = 1, 2, 3, 

ν = (ν1, ν2, ν3) ∈ R 3 ; xν = x1ν1 + x2ν2 + x3ν3, i 2 = −1, 

then ˜ Vj(ν, t) may be presented in the form of the convergent power series. The coefficients 

of this power series are functions depending on t only. In our paper we find explicit 

formulae for the coefficients of this power series, i.e. formulae for the columns of the 

Green’s matrices are derived explicitly. Using these formulae the simulation of elastic 

waves (components of G(x − x 0 , t − t 0 )) has been obtained for the different anisotropic 

crystals.

References 

Courant and Hilbert (1962). R. Courant and D. Hilbert, Methods of Mathematical 

Physics, Interscience, Newyork, 1962. 

Dieulesaint and Royer (1980). E. Dieulesaint, D. Royer, Elastic waves in solids, John Wiley 

and Sons, Chichester, 1980. 

Mizohata (1973). S. Mizohata, The theory of partial differential equations. Cambridge 

University Press, 1973. 

Reed and Simon (1975). M. Reed and B. Simon, Methods of modern mathematical 

physics. II. Fourier analysis, self-adjointness, Academic Press, New York, 1975. 

Vladimirov (1971). JV. S. Viladimirov, Equations of Mathematical Physics, Marcel 

Dekker, New York, 1971. 

243

244 

Measuring the importance and the weight of decision makers 



Poonak-Hesarak-I.A.U.Science and Research Brnach 

Faculty of Management and Economics 

Iran 

(Joint work with: Mohammadali Afshar Kazemi, Ebrahim Nazari Farokhi, Bahareh Sagheb) 

Abstract: Criterion weights change in decision-making process, especially in multiple 

criteria decision making methods, have very large effects on decision-making results and 

to the rank of alternatives. Many methods for criteria weighting exists, such as LINMAP, 

SMART, Eigenvector. Often seen that decision makers, in all methods of group decisionmaking 

(even in voting methods), participates with a same weight of importance and in 

the decision making process this has its logical drawbacks. 

This paper introduces a simple method to find the weight of importance of humans in the 

index decision making process. In fact, this article following response to this question; 

what is the importance of decision makers in group decision making process? The present 

article, introduced an idea for a degree to realize the importance of decision makers using 

Eigenvector method, base on pair wise comparison techniques. Considering the number 

of iteration of decision making matrix, using the above method, will be determined that, 

if the number of iteration of decision making matrix for a decision maker to reach convergence 

is low ,then DM must be have a greater importance. 

At the end, a case study for indicate the importance of decision makers, in decisionmaking 

process by 3 DM decision has been carried out for identifying the importance of 

decision makers is considered. 

Keywords: Multiple criteria decision making, weighting methods, Eigenvector, Pair 

wise comparison, importance and weight of decision makers.

Sensitivity analysis for criteria values in decision making 

matrix of SAW method 



Poonak-Hesarak-I.A.U.Science and Research Brnach 

Faculty of Management and Economics 

Iran 

(Joint work with: Rastkhiz Paydar, Khadijeh Joda, Neda Rastkhiz Paydar) 

Abstract: All of organizations around the world try to increase competitive ability regards 

to other similar companies, therefore, decision making processes are one of the 

most important activities for help them. 

The multiple criteria decision making methods create for help better decision making 

in multidimensional environment to monitor organizational resources and, generally, for 

ranking them. 

One of the simplest and applicable methods in multiple criteria decision making 

is SAW (simple additive weighting method).the general problem in MADM methods is 

lack of complementary information for final decision making. In optimizations methods 

(for example linear programming) the sensitivity analysis use for produce complementary 

information and this reason helps for popularity of this methods. Although MADM 

methods don’t belong optimizations methods but in this paper tries to use sensitivity 

analysis approach for produce complementary information by determination of criteria 

value domain in decision making matrix. 

Key Words: Multiple criteria decision making method, Ranking Methods, SAW, 

sensitivity analysis. 

245

246 

Rational Eigenvalues of Fullerenes 

Modjtaba Ghorbani 

email: ag.paper@gmail.com 


Faculty of Science 

University of Kashan 

Kashan - Iran 

(Joint work with: A.R. Ashrafi, M. Saheli) 

Abstract: A fullerene graph F is a cubic 3-connected plane graph with exactly 12 

pentagons and other hexagons. The name is taken from the fullerene molecule. It is 

well-known that the molecular graph of a fullerene molecule is a fullerene graph. In this 

talk, we present our recent results on the problem of computing rational eigenvalues of 

fullerene graphs.

Bounds on Estrada Index of Fullerenes 

G.H. Fath-Tabar 

email: fathtabar@kashanu.ac.ir 

Department of Mathematics, Faculty of Science, University of Kashan, 

Kashan 87317-51167, Iran 

(Joint work with: A.R. Ashrafi) 

Abstract: A fullerene is a molecule consisting entirely of carbon atoms. Each carbon 

is three-connected to other carbon atoms by one double bond and two single bonds. A 

fullerene graph is a cubic planar graph with all faces cycles or 6−cycles. The aim of this 

paper is to bound the Estrada index of fullerenes. 

247

248 

A characterization of the Riesz potentials space with the aid 

of a composite wavelet transform 

Sinem Sezer 

email: sinemsezer@akdeniz.edu.tr 

Akdeniz University, Faculty of Education 

Department of Mathematics Education 

07058 Antalya - Turkey 

(Joint work with: Ilham A. Aliev) 

Abstract: The space I α (Lp) of Riesz potentials is defined by 

where α > 0, 1 

α and 

I α ϕ(x) = 

1 

 

γn(α) 

I α (Lp) = {f : f = I α ϕ, ϕ ∈ Lp(R n )} , 

R n 

ϕ(y) 

|x − y| n−α dy , γn(α) = 2απn/2Γ(α/2) Γ((n − α)/2) . 

Most of known characterizations of the space I α (Lp) are given in terms of finite differences, 

see[1-3]. 

In this work we give a new characterization of the space I α (Lp) in terms of a 

composite wavelet-like transform, associated with some semigroup. 

For f ∈ Lp(R n ), 1 

W (β) ∞ 

f(x, t) = B (β) 

tη f(x)dµ(η), (0 < β < ∞), 

R n 

0 

where µ is a finite Borel measure on [0, ∞), µ([0, ∞)) = 0 and 

B (β) 

 

τ f(x) = ω (β) (y, τ)f(x − y)dy, ω (β) (y, τ) = F −1 

 

−τ|ξ|β 

ξ↦→y e . 

Using the wavelet-like transform W (β) f we define the following “truncated” integrals: 

D (β) 

∞ 

ε f(x) = W (β) f(x, t)t −1−α/β dt, (ε > 0). 

The main result of this work is as follows. 

ε 

Theorem: Let 0 < α < n, 1 α. Then f ∈ Iα 

(Lp) if and 

 

only if f ∈ Lq, q = np/(n − αq), and sup D 

ε>0 

(β) 

 

 

ε f 

< ∞. 

p

Abbasbandy, S., 137 

Abbasi, A.O., 103 

Abderraman, J., 44 

Abe, K., 171 

Abu Hassan, M., 30, 40 

Acitas, S., 226 

Adilov, G.R., 212 

Ahmad, A.H., 123 

Aishima, K., 49 

Akbulak, M., 45, 46 

Akdi, Y., 237 

Akgun, N., 195 

Akhmediev, N., 15 

Akhmet, M.U., 90 

Akramin, M.R., 123 

Aktas, R., 60 

Aktuglu, H., 36, 39 

Akyuz, S.O., 24, 141 

Al-Qassem, H.M., 83 

Al-Shemas, E.A., 55 

Alexandrov, D.V., 187 

Alexandrova, I.V., 187 

Aliev, F., 101 

Aliev, I.A., 248 

Alisadeghi, H., 77 

Aliyev, R., 128 

Allahviranloo, T., 172, 173 

Allame, M., 137 

Altin, A., 60, 62 

Andersson, A., 228 

Ankiewicz, A., 15 

Apaydin, A., 76 

Araghi, M.A.F., 31, 193 

Arnal, J., 95 

Arslan, G., 11, 145 

Arugaslan, D., 90 

Asgharzadeh, A., 235 

Ashrafi, A.R., 16, 190, 246, 247 

Asri, N.M., 192 

Aydin, K., 21, 139 

Aydin, S.H., 133 

AUTHOR INDEX 

Aydin,A., 81 

Ayhan, S., 144 

Bairamov, E., 78 

Baykal, N., 141 

Bayramoglu, I., 3 

Bazdidi, F., 134, 189 

Beccari, C., 2 

Behzadi, M.H., 53, 109, 140 

Behzadi, S.S., 193 

Bekar, S., 39 

Berriochoa, E., 37 

Biazar, J., 93 

Biga, V., 87 

Billings, S.A., 87 

Bourchtein, A., 8, 131, 170 

Bourchtein, L., 8, 131 

Bozkaya, C., 13, 14 

Bozkurt, D., 45, 46 

Buranay, S.C., 28 

Cachafeiro, A., 37 

Can, C.E., 126, 236 

Casciola, G., 2 

Cenesiz, Y., 63, 167 

Cenk, M., 159 

Cervantes, M.G.V., 56 

Chen, F., 94, 118 

Cheng, L., 83 

Cibikdiken, A.O., 139 

Cidar, O., 146 

Coca, D., 87 

Costa, L., 51 

Costa, M.F.P., 214 

D’Ambrosio, R., 84 

Díaz-Parra, O., 210, 211, 222 

Dalkilic, T.E., 29, 76 

Darbandi, M., 204, 205 

Davoodi, A., 25 

de Kok, A.G., 182 

249

250 Author Index 

De Pierro, A.R., 227 

Dehesa, J.S., 64, 168 

DeKlerk, J.H., 203 

Deliceoglu, A., 200 

Derakhshan, F., 199 

Deris, M.M., 71, 149 

Dhaene, J., 154 

Dogru, M.K., 142, 182 

Dosiyev, A., 28, 202 

Ebrahim, M.S., 156 

Eken, Z., 79 

Eltayeb, H., 20 

Englert, B., 135 

Erbil, N., 236 

Erdogmus, S., 144 

Erencin, A., 177 

Ersoy, D., 97 

Eryilmaz, S., 9 

Eshkuvatov, Z.K., 80, 192 

Eshlaghy, A.T., 215, 223, 244, 245 

Esposito, E., 84 

Evren, A., 132, 217 

Farokhi, E.N., 244 

Fath-Tabar, G.H., 247 

Fernandes, E.M.G.P., 51, 54, 214 

Fernandez, L., 59, 218 

Fortes, M.A., 197, 221 

Fouladi, N., 204 

Fujino, S., 48 

Gallegos, J.A., 56 

Gebizlioglu, O.L., 67, 101 

Genc, A., 66, 68, 69, 148, 213, 233 

Gezer, H., 36 

Ghanbary, B., 93 

Ghazali, R., 85 

Ghorbani, M., 246 

Gokgoz, N., 121 

Gondal, M.A., 165 

Gonzalez, P., 221 

Gonzalez, P.M., 218 

Goovaerts, M., 127, 154 

Gulec, H.H., 47 

Gurcan, F., 200 

Gurses, I., 45, 46 

Hamdi, A., 55 

Harumatsu, M., 48 

Hashemi, Y., 178 

Hashentuya, 102 

Hassen, Y., 41 

Hekimoglu, E., 92 

Herawan, T., 71, 149 

Hosseinzadeh, L.F., 53, 109, 140, 215, 

223 

Ibrahim, N.A., 70 

Icoz, G., 86 

Ince, H.G., 177 

Iscioglu, F., 9 

Ismail, F., 30, 40 

Iyit, N., 68 

Jahangirian, A., 178 

Jahanshahloo, G.R., 109 

Jaradat, M.M., 162 

Joda, K., 245 

Juliawati, A., 123 

Jusoh, M., 18, 166 

Kaanoglu, C., 61 

Kadirkamanathan, V., 87 

Kaffaoglu,H., 175 

Kahraman, M., 121 

Kalafatcilar, K., 237 

Kampas, F.J., 163 

Kannov, I., 108 

Kantar, Y.M., 67 

Karakoca, A., 213 

Karaoglu, O., 63 

Karasozen, K., 81, 198 

Kariman, S.M.H., 77 

Karimi, A., 30, 40 

Kashina, O., 108 

Kasimbeyli, N., 234 

Kasimbeyli, R., 157 

Kawai, F., 119 

Kazemi, M.A., 215, 223, 244 

Kecelli, S., 99 

Kemali, S., 212 

Kesemen, T., 128 

Keskin, Y., 63, 167 

Khadem, F., 31 

Khalifeh, M.H., 190 

Khaniyev, T., 120, 128 

Khodabakhshi, M., 225 

Kilicman, A., 20 

Kim, E.H., 135

Kinaci, I., 183 

Kirlar, B.B., 161 

Kiyak, H., 45, 46 

Kizilkan, G.C., 21 

Koc, A.B., 63 

Koc, E., 144 

Kocabiyik, S., 13, 14 

Kocak, M.C., 176 

Koren, B., 41 

Korkmaz, M.C., 66, 148 

Kou, J., 130 

Kouibia, A., 197 

Kozan, A., 10 

Kropat, E., 107 

Krutitskii, P., 19 

Kula, K.S., 29 

Kurnaz, A., 167 

Kurum, E., 155 

Kus, C., 66, 148 

Kusakabe, Y., 48 

Laitinen, E., 108 

Lee, C., 135 

Li, Y., 130 

Mahat, M.M., 123 

Mahmudov, N., 175 

Malygin, A.P., 187 

Mammadova, Z., 120 

Martins, T.F.M.C., 54 

Mathur, I., 156 

Matias, J.M., 125 

Mawengkang, H., 104, 110, 184 

Mawengkang, H. , 52 

Md Ariffin, N., 30, 40 

Miqueles, E.X., 227 

Mirbolouki, M., 109, 140 

Moalemi, M., 189 

Mohamed, M., 18, 166 

Moreno, P.S., 64, 168 

Mozaffari, M.R., 53 

Mukhtar, S., 240 

Murota, K., 49 

Mutsuo, T., 49, 194 

Naderi, A., 205 

Namin, M.A., 215, 223 

Nasution, A.H., 184 

Nasution, Z., 110 

Naumov, M., 170 

Nawi, N.M., 85 

Nelsen, R.B., 1 

Nematollahi, N., 53, 140 

Nikoomaram, H., 215, 223 

Nilsson, B., 228 

Noor, S., 240 

Nova, T.D., 104 

Okayama, T., 194 

Oktem, H., 121 

Oncel, S.Y., 101 

Ordonez, C., 125 

Ortega, J.P., 210, 211 

Ostermann, A., 165 

Otani, Y., 102 

Oturanc, G., 63 

Ozarslan, M.A., 61, 62 

Ozbudak, F., 159 

Ozcan, K.M., 237 

Ozceylan, E., 23, 106, 138 

Ozen, U., 142 

Ozergin, E., 62 

Ozkurt, F.Y., 26 

Ozmen, A., 26 

Ozmen, I., 145 

Ozturk, G., 157 

Paksoy, T., 23, 106, 138 

Pan, Y., 83 

Param, H.K., 134 

Pasadas, M., 221 

Paternoster, B., 84 

Paydar, N.R., 245 

Paydar, R., 245 

Pazos, R.A.R., 210, 211 

Pedamallu, C.S., 107 

Pehlivan, N.Y., 106 

Peker, H.A., 63 

Pekgor, A., 233 

Penna, A.F., 222 

Perez, T.E., 59 

Pinar, M.A., 59 

Pinter, J.D., 4, 163 

Poh Bee, N., 70 

Purutcuoglu, V., 185 

Qamar, S., 240 

Rainer, M., 126 

Rivas, T., 125 

Author Index 251

252 Author Index 

Rocha, A.M.A.C., 54 

Romani, L., 2 

Rosdzimin, A.R.M., 123 

Rossi, R., 142 

Ruiz-Vanoye, J.A., 210, 211, 222 

Sadyadharma, H., 110 

Sagheb, B., 244 

Saheli, M., 16, 246 

Salahshour, S., 172, 173 

Salehi, F., 77 

Salleh, M.N.M., 85 

Santo, I.E., 51 

Sarac, T., 232, 234 

Saracoglu, B., 183 

Schindl, D., 111 

Seidel-Morgenstern, A., 240 

Senoglu, B., 67, 226 

Serenbay, S.K., 220 

Servi, S., 63 

Sezer, S., 79, 248 

Sezerman, U., 141 

Sezgin, M.T., 133, 195 

Shang, Z., 127 

Sharifi, R., 215, 223 

Sinan, A., 69 

Sleijpen, G.L.G., 171 

Soler, B., 218 

Soto-Crespo, J.M., 15 

Stojakovic, M.M., 229 

Sugihara, M., 49, 194 

Syahrin, A., 184 

Taboada, J., 125 

Tandogdu, Y., 146, 147 

Tanil, H., 10, 124 

Tank, F., 29 

Tarim, S.A., 142 

Taskara, N., 47, 91, 92 

Thompson, H.B., 18 

Tiku, M.L., 185 

Tollu, D.T., 91 

Tomeo, V., 44 

Tunca, G.B., 88, 177 

Tuncer, Y., 88 

Turkmen, R., 219 

Turkoglu, B.O., 145 

Ulukok, Z., 219 

Unver, I., 120 

Uslu, K., 47, 91, 92 

Ustun, O., 157 

Ustunkar, G., 24, 141 

Uyar, B., 124 

Vahdat, B.V., 103 

Valiollahi, R., 235 

van Houtum, G.J., 182 

Van Weert, K., 154 

Varone, S., 111 

Vatankhahan, B., 137 

Vaz, A.I.F., 214 

Villar, C.A.C., 56 

Wang, X., 130 

Watanabe, M., 102, 104, 119 

Weber, G.W., 24, 26, 107, 141, 155, 236 

Wong, P.J.Y., 94, 118 

Xie, X., 38 

Yaghobifar, M., 192 

Yakhno, V., 97, 99 

Yakhno, V.G., 241 

Yamamoto, K., 102 

Yang, L., 38 

Yardimci, S., 238 

Yaslan, H.C., 241 

Yaslan, I., 117 

Yesildal, F.T., 60, 86, 116 

Yildirak, K., 155 

Yildiz, D., 132, 217 

Yilmaz, E., 90 

Yilmaz, F., 45, 46, 198 

Yilmaz, M.M., 220 

Ying, L., 102 

Yokus, N., 78 

Yousefi-Azari, H., 190 

Zarzo, A., 64, 168, 218 

Zolfaghari, R., 188

ICCAM2009

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