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106 Ellaia et al.1. IntroductionThe objective of this work is the optimization of electrical energy relative to a complexof drinking water. Our work consists in formulating the problem of optimization,namely objective function and its constraints. On the basis of this formulation, we realizea computer application allowing to determine the combination of drillings to use so thatthe corresponding cost of electrical energy is minimal, that give nonlinear 0-1 programming.We think that using a penalty function to transform a nonlinear integer programmingproblem to global optimization problem is still a better way to solve such a problem ifan efficient global optimization algorithm exists. In fact, random perturbation of reducedgradient method (RPRGA) [3] has shown it’s efficiency for global optimization. Thus,we attempt to use a penalty function to solve nonlinear integer programming problemsparticularly combinatorial optimization [5].2. Model FormulationFunction cost C of electrical energy is proportional in consummate electrical energyE in Ref. [1]: C = K.E, with K is the price for the KW h consumed in DH (whereDH ∼ = 0.1$). Because electrical energy is dependent to the consummate power P bythe relation: E = P ∆t, with ∆t is the duration of functioning of drillings function costspells then: C = KP ∆t.On the other hand, power p i consumed by the group of pumping of a given drilling F ispells: p i = ρg.Q i.H i, with:η pi .η mi .η ciQ i is a repulsed debit (repressed) by the drilling F i in (m 3 /s)H i is the total manometric height of the drilling F i in (m)gis the acceleration of the gravity in (m/s 2 )ρis the mass volumetric of some water in (Kg/m 3 )η pi is the return on the pump.η mi is the return on the engine.η ci is the driving return on transmission - pumps.Let η gi be a global return: η gi = η pi η mi η ci , so p i = ρg.Q i.H iη gi- A flat period (noted ∆t 1 ), full period (∆t 2 )and rush hour (∆t 3 ). As a consequence, theexpression of the cost function corresponding in the functioning of the drilling F i duringa duration ∆t j is the following one:C i,j = K j . ρg.Q i.H iη gi.∆t j ,TAMTAM –Tunis– 2005
Global Optimization of Water Resources 107where K j is the price for the KW h consumed during the period ∆t j .The objective of our formulation of the objective function is to determine, at the givenmoment, the optimal combination of the drillings which have to work simultaneously tosatisfy the drinking water requirements of the population. Or (α i , Q i ) debit supplies bythe drilling F iIf one finds as result of our model of optimization: α i = 1, it means that drilling F i hasto work. If one finds α i = 0, then drilling F i does not have to work.Our objective function will be so the sum of costs functions of every drilling F i . Thatis [7]: Z = ∑ i,j C i,j, and because electric fixing of a price scale imposes the followingthree slices:Objective function will be so: Z = ∑ 3 ∑ nj=1 i=1 C i,j, where n is the number of drillings.By replacing function cost C i,j by its expression, one will have:Z = (3∑j=1( ∑nK j .∆t j ).i=1ρg.(α i .Q i ).(H i )).η giIt is so necessary to determine the theoretical capacity of a reservoir. The calculationof this capacity makes on the basis of the variation of the advanced debit schedule Q ph :V Reservoir = f(Q pj , Q ph ), with Q pj is a daily advanced debit see Ref. [2].Notice that the reservoir has to store the surplus of water during the hours of weak consumptionand fill the deficit if water V 1 during the rush hours.This condition is translated in practice, by the fact that the sum of the initial volume V 0of the reservoir, at the given moment, and the difference between entering volume andoutput of the reservoir has to be superior to the volume V 1 . What means mathematically:V 1 ≤ V 0 + (V put − V output ) (1)Now, the volume of water pumped in the reservoir does not have to exceed its maximalcapacity V max . So disparity (1) becomes: V 1 ≤ V 0 + (V put − V output ) ≤ V max .Besides, the volume of water pumped in the reservoir during the duration ∆t expressesitself as follows: V put = ∆t. ∑ ni=1 (α i.Q i ). Also for the outgoing volume of water:V output = ∆t.Q d (Q d is wanted debit).Mathematical formulation to minimize the cost of the electrical energy of the pumpingspells so:⎧⎪⎨ Minimize f(α) = ( ∑ 3j=1 K j.∆t j ).( ∑ n ρg.(α i .Q i ).(H gi + 1.1.∆H iL )i=1)η gi⎪⎩ subject to V 1 ≤ V 0 + ∆t.( ∑ ni=1 (α (2)i.Q i ) − Q d ) ≤ V maxα i ∈ {0, 1}2.1. Example in KenitraThe application of our model of optimization requires the data collection concerningthe parameters of definition of the objective function and its constraints. So, one is goingTAMTAM –Tunis– 2005
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PréfaceOrganiser la seconde éditi
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Comité d’organisationMohamed Abd
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SOMMAIRE / CONTENTSI Conférences I
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Equilibre dans un système dynamiqu
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Arlequin method: Practical impacts
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Application de la méthode de Gauss
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Conférences InvitéesInvited Prese
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4 Amara et al.1. IntroductionWe are
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6 Amara et al.2.2. The nonlinear Na
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8 Amara et al.4. Numerical resultsW
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10 Auger et al.1. Introduction :Dan
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12 Auger et al.La condition de stab
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14 Auger et al.3.1. Taux de migrati
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16 Auger et al.L’équilibre rapid
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18 Auger et al.[7] BRAVO DE LA PARR
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Quelques aspects mathématiques etn
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22 El Alaoui Talibi M.- Modèle d
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24 El Alaoui Talibi M.[3] M. Chamba
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26 Habbal1. IntroductionAngiogenesi
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28 HabbalThe pressure drop denoted
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30 Habbaltheorem 1 There exists a N
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32 HabbalFigure 2. Second Nash loop
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34 Hauray et al.1. IntroductionWe a
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36 Hauray et al.minimal time interv
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38 Hauray et al.From this last theo
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Approximation de l’opérateur d
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42 LemrabetLorsque δ → 0, l’é
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44 Lemrabetavec[∆ ∗ (δ)c = [I
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46 Lemrabet6. Bibliographie[1] N. B
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48 Jaafar-Belaid et al.1. Introduct
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50 Jaafar-Belaid et al.where f(ρ)
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52 Jaafar-Belaid et al.202040406060
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Page 76 and 77: 58 Arfaoui1. IntroductionCe travail
Page 78 and 79: 60 ArfaouiLe système adjoint assoc
Page 80 and 81: 62 Arfaoui[3] H. ARFAOUI , « Comma
Page 82 and 83: 64 Benzekri et al.1. Global control
Page 84 and 85: 66 Benzekri et al.ẏ = ∂H∂x =
Page 86 and 87: 0 1 2 3 4 5 668 Benzekri et al.32.5
Page 88 and 89: 70 Akian et al.1. IntroductionWe co
Page 90 and 91: 72 Akian et al.We prove that v t+δ
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Page 94 and 95: 76 Bokanowski et al.1. General fram
Page 96 and 97: 78 Bokanowski et al.One interesting
Page 98 and 99: 80 Bokanowski et al.4. Numerical ex
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Page 102 and 103: 84 Metouileur lorsque u est dans L
Page 104 and 105: 86 MetouiThéorème 2 Soit ū ε le
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Page 109 and 110: Système d’information intégré
Page 111 and 112: Gestion et modélisation des ressou
Page 123: Random perturbations of reduced gra
Page 127 and 128: Global Optimization of Water Resour
Page 129: IVEquations DifférentiellesDiffere
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Page 134 and 135: 116 B. AbdelkaderNotons que les con
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Page 138 and 139: 120 Bouzahir1. IntroductionWe consi
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Page 144 and 145: 126 A. Guezane-Lakoud et al.3. Func
Page 146 and 147: 128 A. Guezane-Lakoud et al.5. Exis
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Page 150 and 151: 132 Chitroubl’approximation de la
Page 152 and 153: 134 Chitroubcompression égal à 3.
Page 154 and 155: 136 Chitroub[4] J. P. Nougier, Mét
Page 156 and 157: 138 Ferchichi et al.1. Introduction
Page 158 and 159: 140 Ferchichi et al.soit T −1 = (
Page 160 and 161: 142 Ferchichi et al.[4] G.I. BISCHI
Page 162 and 163: 144 Hafidi1. IntroductionOn étudie
Page 164 and 165: 146 Hafidia ) ∫ Ωpdx → +∞ qu
Page 166 and 167: 148 HafidiLEMME 3.2. On a lim R(θ
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Page 170 and 171: 152 LefebvreOn peut aussi écrire q
Page 172 and 173: 154 Lefebvre5. BibliographieD.R. Co
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156 Meskine1. IntroductionDans le p
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158 Meskinefaibles σ( ∏ L M ,
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160 Meskine[12] E. YA. KHRUSLOV, L.
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162 K. Saoudi1. IntroductionL’ét
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164 K. Saoudice qui montre que la s
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166 K. Saoudieton aboutit au résul
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168 K. Saoudietc 1 + c 2 = 1 ∫(u
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170 K. SaoudiRemarque 3.1. Du lemme
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172 K. Saoudiet∫v(t, x) dxΩest c
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VEstimation d’ErreursError Estima
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178 Achchab et al.1. IntroductionDu
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180 Achchab et al.such that}Xh 2 ={
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182 Achchab et al.[2] B.ACHCHAB, M.
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184 Alla et al.1. IntroductionLes e
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186 Alla et al.3. Position du probl
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IsoValue-0.00070533-0.000604452-0.0
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190 Achchab et al.1. IntroductionLe
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192 Achchab et al.où T hi/2 est le
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IsoValue0.000933570.002800710.00840
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196 El Dabaghi et al.1. Motivation
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198 El Dabaghi et al.0 ≤ λ i ≤
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200 El Dabaghi et al.Figure 4. Mail
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Residual error estimators for the t
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204 Kharrat et al.The step (3) need
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206 Kharrat et al.following estimat
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VIMécanique des FluidesFluid Mecha
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212 Abdelwahed et al.1. Introductio
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214 Abdelwahed et al.Ainsi, suivre
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216 Abdelwahed et al.Figure 3. Isov
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Procédure spectrale avec diagonali
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220 El Guarmah et al.où Ra et P r
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222 El Guarmah et al.M 10 20 25 35
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Simulation de l’onde de crue via
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226 El Dabaghi et al.de R 2 , de fr
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228 El Dabaghi et al.INRIA-MODULEFm
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INRIA-MODULEF230 El Dabaghi et al.I
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232 Amoura et al.1. IntroductionFor
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234 Amoura et al.where u = rot r ψ
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236 Amoura et al.CURRENT FUNCTION5
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238 Frih et al.1. IntroductionLa mo
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240 Frih et al.et dans la fracture,
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242 Frih et al.6. Bibliographie[1]
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244 Hasnaoui et al.1. IntroductionL
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246 Hasnaoui et al.On obtient alors
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248 Hasnaoui et al.5. Conclusion et
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250 Hernane-Boukari1. IntroductionW
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252 Hernane-Boukarianda 3 =−11 +
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254 Kloucha et al.1. Motivation et
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256 Kloucha et al.Si le domaine Λ
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INRIA-MODULEF0INRIA-MODULEF.250INRI
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Dimensions fractales : attracteurs
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262 Lamrini Uahabi et al.4. Attract
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264 Lamrini Uahabi et al.l 0 = λ
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266 Lamrini Uahabi et al.En conséq
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Numerical analysis for the problem
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270 El-Kyal et al.d(u) = 1 2(∇u +
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272 El-Kyal et al.Theorem 3.1 There
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274 Marchand et al.1. IntroductionD
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276 Marchand et al.On remarque en p
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278 Marchand et al.dans la formulat
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280 Mezali et al.1. Motivation et m
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282 Mezali et al.s’annulant sur c
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284 Mezali et al.Temps CPUTemps Ela
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R. Touihri & S. Ghnimi *Méthode de
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288 Touihri et al.Les équations go
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290 Touihri et al.Tol N It (Newt) t
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292 Touihri et al.5. Bibliographie[
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Décomposition de domaine pour un m
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DDM pour les fractures 297et−→
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DDM pour les fractures 299dont l’
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Arlequin method: Practical impacts
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Arlequin method 303of the Arlequin
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Arlequin method 3052.2. Penalized A
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Arlequin method 307refinements of t
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Reduction methods and uncertaintypr
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Reduction methods and uncertainty p
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Reduction methods and uncertainty p
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0.00e+00 1.00e−11 2.00e−11 3.00
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Homogénéisation d’un problème
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Problème de conduction-rayonnement
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Problème de conduction-rayonnement
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Equation d’Hamilton-Jacobi 3231.
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Equation d’Hamilton-Jacobi 325qui
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0Equation d’Hamilton-Jacobi 3272
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Détermination du nombre de région
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Simulation des courants de Foucault
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Une méthode d’accélération de
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Schéma SRNHS 3491. IntroductionUn
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Schéma SRNHS 3513. Application du
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Schéma SRNHS 3535. ConclusionLes r
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Smoothing and compressing surfaces
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Problème de convection en milieu p
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0
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Condensation de masse pour la méth
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Condensation de masse 367montre que
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Condensation de masse 369Le terme h
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Condensation de masse 371Aet Qile f
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VIIIModèles CinétiquesKinetic Mod
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376 Ben Abdallah et al.1. Introduct
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378 Ben Abdallah et al.where B ∓
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380 Ben Abdallah et al.ture that th
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382 Degond et al.1. IntroductionOn
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384 Degond et al.q φ s (x, t)/(|q|
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386 Degond et al.Enfin l’opérate
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Les métaheuristiques : application
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Les métaheuristiques 391simulé fu
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Les métaheuristiques 393Fig. 1 Dia
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Les métaheuristiques 395Fig.4 : R
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Prices after capacity addition in m
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Multi-user elastic demand communica
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Shape optimization 4051. Introducti
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Shape optimization 4072.1. Variatio
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Shape optimization 409(a)(b)(c)(d)F
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Problèmes d’optimisation en éco
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Assimilation de données pour l’e
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Écart à la Réciprocité et ident
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Identification de fissures planes 4
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Algorithme de Kohn et Vogelius 4331
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Algorithme de Kohn et Vogelius 435l
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Algorithme de Kohn et Vogelius 4375
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Résolution d’un problème de Cau
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Problème inverse géométrique 445
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Identification de fissures 4511. In
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−0.5 −0.4 −0.3 −0.2 −0.1
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Application de l’algorithme deNeu
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Complétion de données en élastic
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Complétion de données en élastic
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Analytic extensions on an annulus:a
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Analytic extensions on an annulus 4
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Analytic extensions on an annulus 4
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−1 −0.8 −0.6 −0.4 −0.2 0
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Cauchy problem for Laplace’s equa
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Modélisation asymptotique des onde
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Ondes de relief 479 uuuv 1 1 pu v
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Ondes de relief 481( )ˆeiZw( C e D
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Ondes de relief 4836. Bibliographie
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Régularisation pour l’aéroacous
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Miroir à retournement temporel 491
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Vibro-acoustique instationnaire 497
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Vibro-acoustique instationnaire 499
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Ondes dans les milieux poroélastiq
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The implicitly restarted Arnoldi me
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¨§¨ §IRAM method 509To overcome
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IRAM method 511The application of t
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XIIScience du VivantLife Science513
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516 Achchab1. IntroductionDans la m
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518 AchchabNous montrons dans le pa
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520 Achchab5. Bibliographie[1 ] AIE
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522 Derbel et al.1. IntroductionLa
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524 Derbel et al.On se propose de d
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A Stochastic partial differential e
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528 El Saadidiffusion process to a
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530 El Saadiwhere δ Xi(t) is the D
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532 El Saadi5. References[1] A. L.
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534 Ben Miled et al.1. Introduction
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536 Ben Miled et al.nature de l’e
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538 Ben Miled et al.Ensuite on étu
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Optimal spatial distribution of a b
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542 Mchich et al.at time t. The com
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544 Mchich et al.3∑where r = r i
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XIIIStructureStructure547
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550 Ayadi1. IntroductionConsider a
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552 AyadiFor all 0 ≤ p ≤ i, P p
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554 AyadiFigure 3. The curves above
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Analyse mathématique et numérique
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558 Chamekh et al.2. Modèle de tig
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560 Chamekh et al.Γ sr(s)r(σ)Figu
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Modélisation de l’effet dynamiqu
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564 RahmaniI 2 étant l’identité
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566 Rahmani• ( u 1δ1∫+ ,0u 1δ
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Résolution d’un systéme d’ela
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570 Saidoù u vérifie :n∑n∑j=1
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572 SaidEn effet :∣ u(y, s) 1+α
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Régularisation d’un problème d
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576 Achchab et al.On définit : F +
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578 Achchab et al.3. Estimation a p
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Modélisation d’un pieuR. Aboulai
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582 Aboulaich et al.Figure 1. Struc
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584 Aboulaich et al.5. Résultats n
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XIVThéorie des GraphesGraph Theory
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590 Hlaoui1. IntroductionMore and m
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592 Hlaoui3. The New Graph Represen
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594 Hlaoui1 1 2 3 4 1 1 3 411 421 4
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596 M. Nekri et al.1. IntroductionL
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598 M. Nekri et al.proposés. Ces m
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600 M. Nekri et al.cycle de longueu
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TAMTAM -Tunis- 2005 602
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El Guarmah, M., 218El Kacimi, A., 2
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