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Some topological properties of star graphs: The surface area and volume
, Article Discrete Mathematics ; Volume 309, Issue 3 , 2009 , Pages 560-569 ; 0012365X (ISSN) ; Sarbazi Azad, H ; Akl, S. G ; Sharif University of Technology
2009
Abstract
The star graph, as an interesting network topology, has been extensively studied in the past. In this paper, we address some of the combinatorial properties of the star graph. In particular, we consider the problem of calculating the surface area and volume of the star graph, and thus answering an open problem previously posed in the literature. The surface area of a sphere with radius i in a graph is the number of nodes in the graph whose distance from a given node is exactly i. The volume of a sphere with radius i in a graph is the number of nodes within distance i from the given node. In this paper, we derive explicit expressions to calculate the surface area and volume in the star graph....
A new proof of the molecular Hamiltonian in Radau coordinates for triatomic molecules based on tensor form
, Article Molecular Physics ; Volume 106, Issue 5 , 2008 , Pages 643-648 ; 00268976 (ISSN) ; Tafazzoli, M ; Sharif University of Technology
2008
Abstract
A generalized coordinates molecular Hamiltonian for polyatomic molecules has been obtained. Using this Hamiltonian in Radau coordinates as the orthogonal coordinates, the molecular Hamiltonian is derived for tri-atomic molecules. An exact derivation is presented of the molecular Hamiltonian in different axis embedding such as bond embedding, bisector embedding, and the linear combination of Radau vector coordinates. In addition, the symmetrized Radau coordinates are considered as an example for this general formulation. This new approach is greatly simplified. Also presented are simple and explicit expressions without cross-terms in Radau coordinates as vibrational variables
Derivation of the rovibrational Hamiltonian based on the tensor form: A new approach to generalized internal coordinates depending on the external parameters
, Article Molecular Physics ; Volume 106, Issue 19 , 2008 , Pages 2263-2269 ; 00268976 (ISSN) ; Tafazzoli, M ; Sharif University of Technology
2008
Abstract
The transformation of the complete (non-relativistic) molecular Hamiltonian from Cartesian to generalized coordinates based on the tensor form has been obtained. By taking generalized internal coordinates depending on two parameters we present an exact derivation of the molecular Hamiltonian that has simple and explicit expressions for general triatomic molecules, and all rovibrational couplings are determined. Our approach is applicable to various kinds of internal coordinates in a straightforward way. In this derivation, no approximations and no restrictions are imposed on the nature of the vibrational variables. We also introduce a straightforward method with minimum equations to obtain...
Natural frequencies and buckling of pressurized nanotubes using shear deformable nonlocal shell model
, Article Journal of Mechanical Science and Technology ; Volume 26, Issue 2 , 2012 , Pages 563-573 ; 1738494X (ISSN) ; Fotouhi, M. M ; Permoon, M. R ; Haddadpour, H ; Sharif University of Technology
Abstract
The small-scale effect on the natural frequencies and buckling of pressurized nanotubes is investigated in this study. Based on the firstorder shear deformable shell theory, the nonlocal theory of elasticity is used to account for the small-scale effect and the governing equations of motion are obtained. Applying modal analysis technique and based on Galerkin's method a procedure is proposed to obtain natural frequencies of vibrations. For the case of nanotubes with simply supported boundary conditions, explicit expressions are obtained which establish the dependency of the natural frequencies and buckling loads of the nanotube on the small-scale parameter and natural frequencies obtained by...
Multimedia multicast based on multiterminal source coding
, Article IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences ; Volume E93-A, Issue 9 , 2010 , Pages 1639-1649 ; 09168508 (ISSN) ; Nooshyar, M ; Rabiee, H. R ; Mikaili, E ; Sharif University of Technology
2010
Abstract
Multimedia multicast with two servers based on the mul- titerminal source coding is studied in some previous researches. Due to the possibility of providing an approach for practical code design for more than two correlated sources in IMTSC/CEO setup, in this paper, the framework of Slepian-Wolf coded quantization is extended and a practical code design is presented for IMTSC/CEO with the number of encoders greater than two. Then the multicast system based on the IMTSC/CEO is applied to the cases with three, four and five servers. Since the underlying code design approach for the IMTSC/CEO problem has the capability of applying to an arbitrary number of active encoders, the proposed MMBMSC...
Assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories
, Article Journal of Sound and Vibration ; Volume 329, Issue 11 , May , 2010 , Pages 2241-2264 ; 0022460X (ISSN) ; Mehri, B ; Sharif University of Technology
2010
Abstract
Dynamic analysis of nanotube structures under excitation of a moving nanoparticle is carried out using nonlocal continuum theory of Eringen. To this end, the nanotube structure is modeled by an equivalent continuum structure (ECS) according to the nonlocal Euler-Bernoulli, Timoshenko and higher order beam theories. The nondimensional equations of motion of the nonlocal beams acted upon by a moving nanoparticle are then established. Analytical solutions of the problem are presented for simply supported boundary conditions. The explicit expressions of the critical velocities of the nonlocal beams are derived. Furthermore, the capabilities of various nonlocal beam models in predicting the...