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Optimal exploitation of the resource in remote state preparation
, Article Physical Review A ; Volume 102, Issue 1 , 15 July , 2020 ; Ramezani, M ; Bahrampour, A ; Sharif University of Technology
American Physical Society
2020
Abstract
Transmission efficiency (TE) of remote state preparation (RSP) with a shared quantum state and one bit of classical communication is considered. Following Dakić et al. [Nat. Phys. 8, 666 (2012)10.1038/nphys2377], the encoding and decoding operators of the protocol are restricted to the physically relevant classes of projective measurements and unitary operators, respectively. It is shown that contrary to the previous arguments, the quadratic fidelity as well as the linear fidelity could be a valid figure of merit to quantify the TE of RSP. Then, the TE of the protocol in terms of both linear and quadratic fidelities is evaluated in a fully optimized scenario which includes the maximization...
Optimal design of two-dimensional porosity distribution in shear deformable functionally graded porous beams for stability analysis
, Article Thin-Walled Structures ; Volume 120 , 2017 , Pages 81-90 ; 02638231 (ISSN) ; Arghavani, J ; Sharif University of Technology
Abstract
In the present study, considering two-dimensional porosity distribution through a functionally graded porous (FGP) beam, its optimal distributions are obtained. A multi-objective optimization problem is defined to maximize critical buckling load and minimize mass of the beam, simultaneously. To this end, Timoshenko beam theory is employed and equilibrium equations for two-dimensional functionally graded porous (2D-FGP) beam are derived. For the solution, we present generalized differential quadrature method (GDQM) and consider two symmetric boundary conditions (Clamped-Clamped and Hinged-Hinged). Solving generalized eigenvalue problem, critical buckling load for 2D-FGP beam is then obtained....
Optimal and robust waveform design for MIMO radars
, Article 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009, Taipei, 19 April 2009 through 24 April 2009 ; 2009 , Pages 2085-2088 ; 15206149 (ISSN); 9781424423545 (ISBN) ; Behnia, F ; Institute of Electrical and Electronics Engineers; Signal Processing Society ; Sharif University of Technology
2009
Abstract
Waveform design for Target identification and classification in MIMO radar systems has been studied in several recent works. While the previous works considered signal independent noise, here we extend the results to the case where signal-dependent noise, clutter, is also present and then we find the optimum waveform for several estimators differing in the assumptions on the given statistics. Computing the optimal waveforms for MMSE estimator leads to the Semi-definite programming (SDP) problem. Finding the optimal transmit signals for CSLS estimator results in a minimax eigenvalue problem. Finally it is shown that equal power waveforms are the best transmit signals for the SLS estimator....
Optical anisotropy of schwarzschild metric within equivalent medium framework
, Article Optics Communications ; Volume 283, Issue 7 , April , 2010 , Pages 1222-1228 ; 00304018 (ISSN) ; Rashidian, B ; Sharif University of Technology
2010
Abstract
It is has been long known that the curved space in the presence of gravitation can be described as a non-homogeneous anisotropic medium in flat geometry with different constitutive equations. In this article, we show that the eigenpolarizations of such medium can be exactly solved, leading to a pseudo-isotropic description of curved vacuum with two refractive index eigenvalues having opposite signs, which correspond to forward and backward travel in time. We conclude that for a rotating universe, time-reversal symmetry is broken. We also demonstrate the applicability of this method to Schwarzschild metric and derive exact forms of refractive index. We derive the subtle optical anisotropy of...
On the static and dynamic stability of thin beam conveying fluid
, Article Meccanica ; Volume 54, Issue 11-12 , 2019 , Pages 1847-1868 ; 00256455 (ISSN) ; Abtahi, H ; Firouz Abadi, R. D ; Sharif University of Technology
Springer Netherlands
2019
Abstract
In this paper, numerical investigation of the statical and dynamical stability of aligned and misaligned viscoelastic cantilevered beam is performed with a terminal nozzle in the presence of gravity in two cases: (1) effect of fluid velocity on the flutter boundary of beam conveying fluid and (2) effect of gravity on the buckling boundary of beam conveying fluid. The beam is assumed to have a large width-to-thickness ratio, so the out-of-plane bending rigidity is far higher than the in-plane bending and torsional rigidities. Gravity vector is considered in the vertical direction. Thus, deflection of the beam because of the gravity effect couples the in-plane bending and torsional equations....
On the prescribed-time attractivity and frozen-time eigenvalues of linear time-varying systems
, Article Automatica ; Volume 140 , 2022 ; 00051098 (ISSN) ; Sharif University of Technology
Elsevier Ltd
2022
Abstract
A system is called prescribed-time attractive if its solution converges at an arbitrary user-defined finite time. In this note, necessary and sufficient conditions are developed for the prescribed-time attractivity of linear time-varying (LTV) systems. It is proved that the frozen-time eigenvalues of a prescribed-time attractive LTV system have negative real parts when the time is sufficiently close to the convergence moment. This result shows that the ubiquitous singularity problem of prescribed-time attractive LTV systems can be avoided without instability effects by switching to the corresponding frozen-time system at an appropriate time. Consequently, it is proved that the time-varying...
On the minimum energy of regular graphs
, Article Linear Algebra and Its Applications ; Volume 581 , 2019 , Pages 51-71 ; 00243795 (ISSN) ; Akbari, S ; Ghasemian, E ; Ghodrati, A. H ; Hosseinzadeh, M. A ; Koorepazan Moftakhar, F ; Sharif University of Technology
Elsevier Inc
2019
Abstract
The energy of a graph G, E(G), is the sum of absolute values of the eigenvalues of its adjacency matrix. Gutman et al. proved that for every cubic graph of order n, E(G)≥n. Here, we improve this result by showing that if G is a connected subcubic graph of order n≥8, then E(G)≥1.01n. Also, we prove that if G is a traceable subcubic graph of order n≥8, then E(G)>1.1n. Let G be a connected cubic graph of order n≥8, it is shown that E(G)>n+2. It was proved that if G is a connected cubic graph of order n, then E(G)≤1.65n. Also, in this paper we would like to present the best lower bound for the energy of a connected cubic graph. We introduce an infinite family of connected cubic graphs whose for...
On the largest eigenvalue of signed unicyclic graphs
, Article Linear Algebra and Its Applications ; Volume 581 , 2019 , Pages 145-162 ; 00243795 (ISSN) ; Belardo, F ; Heydari, F ; Maghasedi, M ; Souri, M ; Sharif University of Technology
Elsevier Inc
2019
Abstract
Signed graphs are graphs whose edges get signs ±1 and, as for unsigned graphs, they can be studied by means of graph matrices. Here we focus our attention to the largest eigenvalue, also known as the index of the adjacency matrix of signed graphs. Firstly we give some general results on the index variation when the corresponding signed graph is perturbed. Also, we determine signed graphs achieving the minimal or the maximal index in the class of unbalanced unicyclic graphs of order n≥3. © 2019
On the existence of periodic solutions for certain differential equations
, Article Journal of Computational and Applied Mathematics ; Volume 174, Issue 2 , 2005 , Pages 239-249 ; 03770427 (ISSN) ; Niksirat, M. A ; Sharif University of Technology
2005
Abstract
Here we are concerned with the problem of the existence of periodic solution for certain second and third-order nonlinear differential equations. Our method here is to consider the problem as an eigenvalue problem and treat it by the topological degree theory. In particular we establish the conditions of the existence of periodic solution first for a simpler system which is homotopic to the original system and then generalize the obtained results for the focal system. The method employed here is applicable also for a system of nonlinear differential equations just with simple modifications. Finally, we present some specific examples numerically to show that the results are valid and...
On the existence of an analytic solution to the 1-D Ising model with nearest and next-nearest neighbor interactions in the presence of a magnetic field
, Article Phase Transitions ; Volume 84, Issue 1 , Dec , 2011 , Pages 77-84 ; 01411594 (ISSN) ; Daryaei, E ; Abroshan, H ; Akbarzadeh, H ; Parsafar, G ; Fortunelli, A ; Sharif University of Technology
2011
Abstract
To solve the controversy, regarding the existence of an analytic solution to the 1-D Ising model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions in the presence of a magnetic field, we apply the transfer matrix method to solve the 1-D Ising model in the presence of a magnetic field, taking both NN and NNN interactions into account. We show that it is possible to write a transfer matrix only if the number of sites is even. Even in such a case, it is impossible to diagonalize the transfer matrix in an analytic form. Therefore, we employ a numerical method to obtain the eigenvalues of the transfer matrix. Moreover, the heat capacity, magnetization, and magnetic...
On the energy of line graphs
, Article Linear Algebra and Its Applications ; Volume 636 , 2022 , Pages 143-153 ; 00243795 (ISSN) ; Alazemi, A ; Anđelić, M ; Hosseinzadeh, M. A ; Sharif University of Technology
Elsevier Inc
2022
Abstract
The energy of a graph G, E(G), is defined as the sum of absolute values of the eigenvalues of its adjacency matrix. In Akbari and Hosseinzadeh (2020) [3] it was conjectured that for every graph G with maximum degree Δ(G) and minimum degree δ(G) whose adjacency matrix is non-singular, E(G)≥Δ(G)+δ(G) and the equality holds if and only if G is a complete graph. Let G be a connected graph with the edge set E(G). In this paper, first we show that E(L(G))≥|E(G)|+Δ(G)−5, where L(G) denotes the line graph of G. Next, using this result, we prove the validity of the conjecture for the line of each connected graph of order at least 7. © 2021 Elsevier Inc
On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes [electronic resource]
, Article Stochastic Processes and their Applications ; Volume 122, Issue 4, April 2012, Pages 1748–1776 ; Javadi, Ramin ; Miclo, Laurent ; Sharif Univercity of Technology
Abstract
Let LL be a reversible Markovian generator on a finite set View the MathML sourceV. Relations between the spectral decomposition of LL and subpartitions of the state space View the MathML sourceV into a given number of components which are optimal with respect to min–max or max–min Dirichlet connectivity criteria are investigated. Links are made with higher-order Cheeger inequalities and with a generic characterization of subpartitions given by the nodal domains of an eigenfunction. These considerations are applied to generators whose positive rates are supported by the edges of a discrete cycle ZNZN, to obtain a full description of their spectra and of the shapes of their eigenfunctions, as...
On nodal domains and higher-order Cheeger inequalities of finite reversible Markov processes
, Article Stochastic Processes and their Applications ; Volume 122, Issue 4 , April , 2012 , Pages 1748-1776 ; 03044149 (ISSN) ; Javadi, R ; Miclo, L ; Sharif University of Technology
2012
Abstract
Let L be a reversible Markovian generator on a finite set V. Relations between the spectral decomposition of L and subpartitions of the state space V into a given number of components which are optimal with respect to min-max or max-min Dirichlet connectivity criteria are investigated. Links are made with higher-order Cheeger inequalities and with a generic characterization of subpartitions given by the nodal domains of an eigenfunction. These considerations are applied to generators whose positive rates are supported by the edges of a discrete cycle Z N, to obtain a full description of their spectra and of the shapes of their eigenfunctions, as well as an interpretation of the spectrum...
On linear transformations preserving at least one eigenvalue
, Article Proceedings of the American Mathematical Society ; Volume 132, Issue 6 , 2004 , Pages 1621-1625 ; 00029939 (ISSN) ; Aryapoor, M ; Sharif University of Technology
2004
Abstract
Let F be an algebraically closed field and T: Mn(F) → Mn(F) be a linear transformation. In this paper we show that if T preserves at least one eigenvalue of each matrix, then T preserves all eigenvalues of each matrix. Moreover, for any infinite field F (not necessarily algebraically closed) we prove that if T: Mn(F) → M n(F) is a linear transformation and for any A ∈ Mn(F) with at least an eigenvalue in F, A and T(A) have at least one common eigenvalue in F, then T preserves the characteristic polynomial
On graphs whose star sets are (co-)cliques
, Article Linear Algebra and Its Applications ; Volume 430, Issue 1 , 2009 , Pages 504-510 ; 00243795 (ISSN) ; Ghorbani, E ; Mahmoodi, A ; Sharif University of Technology
Abstract
In this paper we study graphs all of whose star sets induce cliques or co-cliques. We show that the star sets of every tree for each eigenvalue are independent sets. Among other results it is shown that each star set of a connected graph G with three distinct eigenvalues induces a clique if and only if G = K1, 2 or K2, ..., 2. It is also proved that stars are the only graphs with three distinct eigenvalues having a star partition with independent star sets. © 2008 Elsevier Inc. All rights reserved
On eigensharp and almost eigensharp graphs
, Article Linear Algebra and Its Applications ; Volume 429, Issue 11-12 , 2008 , Pages 2746-2753 ; 00243795 (ISSN) ; Maimani, H. R ; Sharif University of Technology
2008
Abstract
The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b (G). A known lower bound on b (G) states that b (G) ≥max {p (G), q (G)}, where p (G) and q (G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b (G) = max {p (G), q (G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness of graphs with at most one cycle and products of some families of graphs. Among the other results, we show that Pm ∨ Pn, Cm ∨ Pn for m ≡ 2, 3 (mod 4) and Qn when n is odd are eigensharp. We obtain some results on...
On edge star sets in trees
, Article Discrete Mathematics ; Volume 311, Issue 13 , July , 2011 , Pages 1172-1178 ; 0012365X (ISSN) ; Ghorbani, E ; Mahmoodi, A ; Sharif University of Technology
2011
Abstract
Let A be a Hermitian matrix whose graph is G (i.e. there is an edge between the vertices i and j in G if and only if the (i,j) entry of A is non-zero). Let λ be an eigenvalue of A with multiplicity mA(λ). An edge e=ij is said to be Parter (resp., neutral, downer) for λ,A if mA(λ)-mA-e(λ) is negative (resp., 0, positive ), where A-e is the matrix resulting from making the (i,j) and (j,i) entries of A zero. For a tree T with adjacency matrix A a subset S of the edge set of G is called an edge star set for an eigenvalue λ of A, if |S|=mA(λ) and A-S has no eigenvalue λ. In this paper the existence of downer edges and edge star sets for non-zero eigenvalues of the adjacency matrix of a tree is...
On edge-path eigenvalues of graphs
, Article Linear and Multilinear Algebra ; 2020 ; Azizi, S ; Ghorbani, M ; Li, X ; Sharif University of Technology
Taylor and Francis Ltd
2020
Abstract
Let G be a graph with vertex set (Formula presented.) and (Formula presented.) be an (Formula presented.) matrix whose (Formula presented.) -entry is the maximum number of internally edge-disjoint paths between (Formula presented.) and (Formula presented.), if (Formula presented.), and zero otherwise. Also, define (Formula presented.), where D is a diagonal matrix whose i-th diagonal element is the number of edge-disjoint cycles containing (Formula presented.), whose (Formula presented.) is a multiple of J−I. Among other results, we determine the spectrum and the energy of the matrix (Formula presented.) for an arbitrary bicyclic graph G. © 2020 Informa UK Limited, trading as Taylor &...
On edge-path eigenvalues of graphs
, Article Linear and Multilinear Algebra ; Volume 70, Issue 15 , 2022 , Pages 2998-3008 ; 03081087 (ISSN) ; Azizi, S ; Ghorbani, M ; Li, X ; Sharif University of Technology
Taylor and Francis Ltd
2022
Abstract
Let G be a graph with vertex set (Formula presented.) and (Formula presented.) be an (Formula presented.) matrix whose (Formula presented.) -entry is the maximum number of internally edge-disjoint paths between (Formula presented.) and (Formula presented.), if (Formula presented.), and zero otherwise. Also, define (Formula presented.), where D is a diagonal matrix whose i-th diagonal element is the number of edge-disjoint cycles containing (Formula presented.), whose (Formula presented.) is a multiple of J−I. Among other results, we determine the spectrum and the energy of the matrix (Formula presented.) for an arbitrary bicyclic graph G. © 2020 Informa UK Limited, trading as Taylor &...
Numerical modeling of shear band propagation in porous plastic dilatant materials by XFEM
, Article Theoretical and Applied Fracture Mechanics ; Volume 95 , 2018 , Pages 164-176 ; 01678442 (ISSN) ; Liu, P ; Sharif University of Technology
Elsevier B.V
2018
Abstract
This paper studies mixed-mode shear band propagation behaviors in porous plastic dilatant materials by the extended finite element method (XFEM). The Drucker-Prager elastoplastic model is combined with the strong discontinuity method to simulate the dilatant shear band. First, the dissipative nature of the localized area with displacement jump is integrated into the constitutive model by introducing a cohesive law. A new contribution lies that the yielding function is modified in the localized region to calculate the cohesive traction within the framework of the XFEM. The shear band propagation direction is determined by the singularity of the acoustic tensor and the corresponding...