Photonic crystals in biology

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P –12 Poster Session, Tuesday, June 15 Theme A1 - B702 Computing Closed Walks of Nanostar Dendrimers G. H. Fath-Tabar 1 * andA. R. Ashrafi 2 1 Department of Mathematics, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran 2 Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan, Iran Abstract-Suppose G = (V, E) is a simple graph. The sequence of vertices v 0 v 1 …v t v 0 is called a closed walk if v i v i+1 are in E(G). In this paper, the number of closed walks (CW(G, k)), k = 1,2,…, 10 and k = 11, 13, 15, … for three types of nanostar dendrimers are presented. Dendrimers are highly branched macromolecules. They are being investigated for possible uses in nanotechnology, gene therapy, and other fields. The nanostar dendrimer is part of a new group of macromolecules that appear to be photon funnels just like artificial antennas. The topological study of these macromolecules is the aim of this article. In this paper, the word graph refers to a finite, undirected graph without loops and multiple edges. Let G be a graph and {v 1 , ..., v n } be the set of all vertices of G. The adjacency matrix of G is a 01 matrix A(G) = [a ij ], where a ij is the number of edges connecting v i and v j . The spectrum of a graph G is the set of eigenvalues of A(G), together with their multiplicities. Throughout this paper our notation is standard and taken mainly from the standard book of graph theory. A walk is a sequence of graph vertices and graph edges such that the graph vertices and graph edges are adjacent. A closed walk is a walk in which the first and the last vertices are the same. A closed walk has backtracking if, in the closed walk, an edge appears twice in immediate succession. For more information 1-3 about these concept you can see referencesP P. n+2 Cl ( NS1[ n], 2k 1) 0, Cl ( NS [ n], 2) 21.2 - 30, n+2 Cl ( NS1[ n], 4) 48.2 1230. 1 *Corresponding author: ashrafi@kashanu.ac.ir [1] G. H. Fath-Tabar, M. J. Nadjafi-Arani, M. Mogharrab and A. R. Ashrafi, MATCH Commun. Math. Comput. 63 (2010) 145. [2] I. Gutman, Graph Theory Notes of New York 27, 9 (1994). [3] P.V. Khadikar and S. Karmarkar, J. Chem. Inf. Comput. Sci. 41, 934 (2001). Figure 1. The Nanostar Dendrimer NSR2R[2]. We now consider the nanostar dendrimer NS[n], Figures 1. Using a simple calculation, one can show that |V(NS[n])| = n+1 n+1 18.2P and |E(NS[n])| = 21.2P P-15. We prove that: The number of closed walks of the nanostar dendrimer NS[n ] are co mputed as follows: 6th Nanoscience and Nanotechnology Conference, zmir, 2010 355
Poster Session, Tuesday, June 15 Theme A1 - B702 Synthesis and Structural Study of L1 0 - FePt Nanoparticles M. Farahmandjou 1 * 1 Islamic Azad University, Varamin -Pishva Branch, Varamin, Iran Abstract A comparison of the synthesis and structural properties of magnetic FePt nanostructures is presented. The FePt nanop article system is an excellent candidate for ultrahigh-density magnetic recording. Monodisperse FePt nanoparticles were synthesized by superhydride method. The composition of nanocrystals was determined by EDS. Transmission electron microscopy (TEM) images show monosize FePt nanoparticles with a diameter of 3.5 nm. The average distance between the monodispesre particles is nearly 2 nm. In order to determine the stability of nanoparticles colloidal solution, a measure of stability is defined via spectrophotometery analysis. The magnetic measurement shows that as-made FePt is first superparemagnetism at room temperature and after annealing at 600 o C for 4 hours, the nanoparticles can ability to do phase transition to L1 0 - FePt and coersivity of nanocrystals is raised to 6.5 kOe. *Corresponding author: Farahmand_ph@yahoo.com 6th Nanoscience and Nanotechnology Conference, zmir, 2010 356
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Photonic crystals in biology

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