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#### A methodology for analyzing the transient availability and survivability of a system with repairable components

, Article Applied Mathematics and Computation ; Volume 184, Issue 2 , 2007 , Pages 300-307 ; 00963003 (ISSN) ; Ghassemi Tari, F ; Sharif University of Technology
2007

Abstract

In this paper we present a method for transient analysis of availability and survivability of a system with the identical components and identical repairmen. The considered system is supposed to consist of series of k-out-of-n or parallel components. We employed the Markov models, eigen vectors and eigenvalues for analyzing the transient availability and survivability of the system. The method is implemented through an algorithm which is tested in MATLAB programming environment. The new method enjoys a stronger mathematical foundation and more flexibility for analyzing the transient availability and survivability of the system. © 2006 Elsevier Inc. All rights reserved

#### Intrinsic expressions for arbitrary stress tensors conjugate to general strain tensors

, Article Scientia Iranica ; Volume 14, Issue 5 , 2007 , Pages 486-493 ; 10263098 (ISSN) ; Naghdabadi, R ; Asghari, M ; Sharif University of Technology
Sharif University of Technology
2007

Abstract

In this paper, a unified explicit tensorial relation is sought between two stress tensors conjugate to arbitrary and general Hill strains. The approach used for deriving the tensorial relation is based on the eigenprojection method. The result is, indeed, a generalization of the relations that were derived by Farahani and Naghadabadi [1] in 2003 from a component to intrinsic form. The result is unified in the sense that it is valid for all cases of distinct and coalescent principal stretches. Also, in the case of three dimensional Euclidean inner product space, using the derived unified relation, some expressions for the conjugate stress tensors are presented. © Sharif University of...

#### Unified basis-free relation between two stress tensors conjugate to arbitrary Hill's strain measures

, Article ASME PVP2006/ICPVT-11 Conference, Vancouver, BC, 23 July 2006 through 27 July 2006 ; Volume 2006 , 2006 ; 0277027X (ISSN); 0791837823 (ISBN); 9780791837825 (ISBN) ; Naghdabadi, R ; Sharif University of Technology
American Society of Mechanical Engineers(ASME)
2006

Abstract

The concept of energy conjugacy for stress and strain measures states that a stress tensor T is conjugate to a strain measure E if T: Ė provides the rate of change of the internal energy per unit reference volume of the body in an adiabatic process. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear analysis of solids. In this paper using eigenprojection method, unified explicit basis-free relation between two arbitrary stress tensors T(f) and T (g), respectively conjugate to two measures of Hill's strains is determined. The result is valid for arbitrary dimension of the Euclidean inner product space and for all cases of...

#### The multiplicity of Laplacian eigenvalue two in unicyclic graphs

, Article Linear Algebra and Its Applications ; Vol. 445 , 2014 , pp. 18-28 ; Kiani, D ; Mirzakhah, M ; Sharif University of Technology
Abstract

Let G be a graph and L(G) be the Laplacian matrix of G. In this paper, we explicitly determine the multiplicity of Laplacian eigenvalue 2 for any unicyclic graph containing a perfect matching

#### A relation between the Laplacian and signless Laplacian eigenvalues of a graph

, Article Journal of Algebraic Combinatorics ; Volume 32, Issue 3 , 2010 , Pages 459-464 ; 09259899 (ISSN) ; Ghorbani, E ; Koolen, J. H ; Oboudi, M. R ; Sharif University of Technology
2010

Abstract

Let G be a graph of order n such that ∑n i=0(-1) iailambdan-i and ∑n i=0(-1) iailambdan-i are the characteristic polynomials of the signless Laplacian and the Laplacian matrices of G, respectively. We show that a i ≥b i for i=0,1,⋯,n. As a consequence, we prove that for any α, 0<α≤1, if q 1,⋯,q n and μ 1,⋯,μ n are the signless Laplacian and the Laplacian eigenvalues of G, respectively, then q 1 alpha+⋯+qα n≥μ α 1+⋯+μα n

#### The algebraic connectivity of a graph and its complement

, Article Linear Algebra and Its Applications ; Volume 555 , 2018 , Pages 157-162 ; 00243795 (ISSN) ; Akbari, S ; Moghaddamzadeh, M. J ; Mohar, B ; Sharif University of Technology
Elsevier Inc
2018

Abstract

For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that λ2(G)+λ2(G‾)≥1, where G‾ is the complement of G. In this paper, it is shown that max{λ2(G),λ2(G‾)}≥[Formula presented]. © 2018 Elsevier Inc

#### 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

#### Some results on the Laplacian spread conjecture

, Article Linear Algebra and Its Applications ; Volume 574 , 2019 , Pages 22-29 ; 00243795 (ISSN) ; Akbari, S ; Sharif University of Technology
Elsevier Inc
2019

Abstract

For a graph G of order n, let λ 2 (G) denote its second smallest Laplacian eigenvalue. It was conjectured that λ 2 (G)+λ 2 (G‾)≥1, where G‾ is the complement of G. For any x∈R n , let ∇ x ∈R (n2) be the vector whose {i,j}-th entry is |x i −x j |. In this paper, we show the aforementioned conjecture is equivalent to prove that every two orthonormal vectors f,g∈R n with zero mean satisfy ‖∇ f −∇ g ‖ 2 ≥2. In this article, it is shown that for the validity of the conjecture it suffices to prove that the conjecture holds for all permutation graphs. © 2019 Elsevier Inc

#### Color PCA eigenimages and their application to compression and watermarking

, Article Image and Vision Computing ; Volume 26, Issue 7 , 2008 , Pages 878-890 ; 02628856 (ISSN) ; Kasaei, S ; Sharif University of Technology
Elsevier Ltd
2008

Abstract

From the birth of multi-spectral imaging techniques, there has been a tendency to consider and process this new type of data as a set of parallel gray-scale images, instead of an ensemble of an n-D realization. However, it has been proved that using vector-based tools leads to a more appropriate understanding of color images and thus more efficient algorithms for processing them. Such tools are able to take into consideration the high correlation of the color components and thus to successfully carry out energy compaction. In this paper, a novel method is proposed to utilize the principal component analysis in the neighborhoods of an image in order to extract the corresponding eigenimages....

#### Free vibration analysis of cross-ply layered composite beams with finite length on elastic foundation

, Article International Journal of Computational Methods ; Volume 5, Issue 1 , 2008 , Pages 21-36 ; 02198762 (ISSN) ; Kargarnovin, M. H ; Ahmadian, M. T ; Sharif University of Technology
2008

Abstract

In this paper, free vibration analysis of cross-ply layered composite beams (LCB) with finite length and rectangular cross-section rested on an elastic foundation is investigated by finite element method. Based on the Timoshenko beam theory which includes the shear deformation and rotary inertia, the stiffness and mass matrices of a LCB are obtained using the energy method. Then, the natural frequencies are calculated by employing eigenvalue technique. The obtained results are verified against existing data in the literatures for a LCB with no foundation and uniform cross-section. Good agreements are observed between these cases. In the same way, the natural frequencies of a specific case,...

#### A methodology for analyzing the transient reliability of systems with identical components and identical repairmen

, Article Scientia Iranica ; Volume 14, Issue 1 , 2007 , Pages 72-77 ; 10263098 (ISSN) ; Ghassemi Tari, F ; Sharif University of Technology
Sharif University of Technology
2007

Abstract

In this paper, the Markov models, eigenvectors and eigenvalue concepts are used to propose a methodology for analyzing the transient reliability of a system with identical components and identical repairmen. The components of the systems under consideration can have two distinct configurations, namely; they can be arranged in series or in parallel. A third case is also considered, in which the system is up (good) if k-out-of-n components are good. For all three cases, a procedure is proposed for calculating the transient probability of the system availability and the duration of the system to reach the steady state. © Sharif University of Technology, February 2007

#### An efficient reduced-order modelling approach based on fluid eigenmodes and boundary element method

, Article Journal of Fluids and Structures ; Volume 23, Issue 1 , 2007 , Pages 143-153 ; 08899746 (ISSN) ; Nobari, A. S ; Behbahani Nejad, M ; Haddadpour, H ; Sharif University of Technology
2007

Abstract

This paper presents an efficient reduced-order modelling approach based on the boundary element method. In this approach, the eigenvalue problem of the unsteady flows is defined based on the unknown wake singularities. By constructing this reduced-order model, the body quasi-static eigenmodes are removed from the eigensystem and it is possible to obtain satisfactory results without using the static correction technique when enough eigenmodes are used. In addition to the conventional method, eigenanalysis and reduced-order modelling of unsteady flows over a NACA 0012 airfoil, a wing with NACA 0012 section and a wing-body combination are performed using the proposed reduced order modelling...

#### Graph homomorphisms and nodal domains

, Article Linear Algebra and Its Applications ; Volume 418, Issue 1 , 2006 , Pages 44-52 ; 00243795 (ISSN) ; Hajiabolhassan, H ; Sharif University of Technology
2006

Abstract

In this paper, we derive some necessary spectral conditions for the existence of graph homomorphisms in which we also consider some parameters related to the corresponding eigenspaces such as nodal domains. In this approach, we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix. Also, we present some applications in graph decompositions where we prove a general version of Fisher's inequality for G-designs. © 2006 Elsevier Inc. All rights reserved

#### Photonic crystal devices analysis based on perturbation theory

, Article Photonic Crystal Materials and Devices IV, San Jose, CA, 23 January 2006 through 26 January 2006 ; Volume 6128 , 2006 ; 0277786X (ISSN); 0819461709 (ISBN); 9780819461704 (ISBN) ; Khorasani, S ; Atabaki, A ; SPIE ; Sharif University of Technology
2006

Abstract

A novel approach for photonic crystals devices analysis, based on perturbation theory is reported. In this method the photonic crystal device is considered as the superposition of a parent lattice and a perturbing one. Then the solution is investigated in terms of the eigensolutions of the parent lattice. This way, one can easily obtain analytic expressions within the first order perturbation, describing the effects of different parameters on the eigensolutions of the structure. The perturbation theory employed in this work is typical of what is conventionally used in quantum mechanics literature. The proposed method is explicit, works fast, and does not involve complicated numerical...

#### Connectedness of users-items networks and recommender systems

, Article Applied Mathematics and Computation ; Vol. 243 , 2014 , Pages 578-584 ; ISSN: 00963003 ; Jalili, M ; Sharif University of Technology
Abstract

Recommender systems have become an important issue in network science. Collaborative filtering and its variants are the most widely used approaches for building recommender systems, which have received great attention in both academia and industry. In this paper, we studied the relationship between recommender systems and connectivity of users-items bipartite network. This results in a novel recommendation algorithm. In our method recommended items are selected based on the eigenvector corresponding to the algebraic connectivity of the graph - the second smallest eigenvalue of the Laplacian matrix. Since recommending an item to a user equals to adding a new link to the users-items bipartite...

#### The electro-elastic scattered fields of an SH-wave by an eccentric two-phase circular piezoelectric sensor in an unbounded piezoelectric medium

, Article Mechanics of Materials ; Vol. 75 , 2014 , pp. 1-12 ; ISSN: 01676636 ; Jarfi, H ; Rashidinejad, E ; Sharif University of Technology
Abstract

The dynamic equivalent inclusion method (DEIM) which was first proposed by Fu and Mura (1983), in its original context has some shortcomings, which were pointed out and remedied by Shodja and Delfani (2009) who introduced the new consistency conditions along with the related micromechanically substantiated notion of eigenstress and eigenbody-force fields. However, these theories are bound to elastic media with isotropic phases. The present work extends the idea of the above-mentioned new DEIM to the dynamic electro-mechanical equivalent inclusion method (DEMEIM) for the treatment of the scattering of SH-waves by a two-phase circular piezoelectric obstacle bonded to a third phase...

#### MIMO radar beamforming using orthogonal decomposition of correlation matrix

, Article Circuits, Systems, and Signal Processing ; Volume 32, Issue 4 , 2013 , Pages 1791-1809 ; 0278081X (ISSN) ; Behnia, F ; Sharif University of Technology
2013

Abstract

MIMO radar is the next generation radar which transmits arbitrary waveforms at each one of its apertures. It has been shown that the design of waveforms for MIMO radars in order to synthesize a desired spatial beampattern is mapped into a waveform correlation matrix R design in the narrowband case. As of now, given a desired beampattern or estimated locations information of targets, calculating R has been modeled as an optimization problem like semi-definite programming. Also, in some special cases like rectangular beampattern, closed-form solutions for R has been proposed. In this paper, we introduce a fast algorithm which is capable of designing R in order to achieve more arbitrary...

#### Limiting spectral distribution of the sample covariance matrix of the windowed array data

, Article Eurasip Journal on Advances in Signal Processing ; Volume 2013, Issue 1 , 2013 ; 16876172 (ISSN) ; Gazor, S ; Bastani, M. H ; Sharif University of Technology
2013

Abstract

In this article, we investigate the limiting spectral distribution of the sample covariance matrix (SCM) of weighted/windowed complex data. We use recent advances in random matrix theory and describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We obtain an approximation for the spectral distribution of the SCM obtained from windowed data. We also determine a condition on the coefficients of the window, under which the fragmentation of the support of noise eigenvalues can be avoided, in the noise-only data case. For the commonly used exponential window, we derive an explicit expression for the l.s.d of the noise-only data. In addition, we present a method to...

#### Spectral distribution of the exponentially windowed sample covariance matrix

, Article ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 25 March 2012 through 30 March 2012, Kyoto ; 2012 , Pages 3529-3532 ; 15206149 (ISSN) ; 9781467300469 (ISBN) ; Bastani, M. H ; Gazor, S ; Sharif University of Technology
IEEE
2012

Abstract

In this paper, we investigate the effect of applying an exponential window on the limiting spectral distribution (l.s.d.) of the exponentially windowed sample covariance matrix (SCM) of complex array data. We use recent advances in random matrix theory which describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We derive an explicit expression for the l.s.d. of the noise-only data. Simulations are performed to support our theoretical claims

#### A lower bound for algebraic connectivity based on the connection-graph- stability method

, Article Linear Algebra and Its Applications ; Volume 435, Issue 1 , Sep , 2011 , Pages 186-192 ; 00243795 (ISSN) ; Jalili, M ; Hasler, M ; Sharif University of Technology
2011

Abstract

This paper introduces the connection-graph-stability method and uses it to establish a new lower bound on the algebraic connectivity of graphs (the second smallest eigenvalue of the Laplacian matrix of the graph) that is sharper than the previously published bounds. The connection-graph-stability score for each edge is defined as the sum of the lengths of the shortest paths making use of that edge. We prove that the algebraic connectivity of the graph is bounded below by the size of the graph divided by the maximum connection-graph-stability score assigned to the edges