Sharif Digital Repository

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  

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... 

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... 

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  

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  

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  

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  

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  

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.... 

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,... 

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  

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... 

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  

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... 

Three-dimensional vectorial diffraction analysis of phase and amplitude gratings in conical mounting is presented based on Legendre expansion of electromagnetic fields. In the so-called conical mounting, different fields components are coupled and the solution is not separable in terms of independent TE and TM cases. In contrast to conventional RCWA in which the solution is obtained using state variables representation of the coupled wave amplitudes by expanding space harmonic amplitudes of the fields in terms of the eigenfunctions and eigenvectors of the coefficient matrix defined by rigorous coupled wave equations, here the solution of first order coupled Maxwell's equations is expanded in... 

A new reduced-order modeling approach is presented. This approach is based on fluid eigenmodes and without using the static correction. The vortex lattice method is used to analyze unsteady flows over two-dimensional airfoils and three-dimensional wings. Eigenanalysis and reduced-order modeling are performed using a conventional method with and without the static correction technique. In addition to the conventional method, eigenanalysis and reduced-order modeling are also performed using the new proposed method, that is, without static correction requirement. Numerical examples are presented to demonstrate the accuracy and computational efficiency of the proposed method. Based on the... 

The problem of the characterization of perfect entanglers was investigated. Perfect entanglers have been defined as unitary operators that can generate maximally entangled states from some suitably chosen separable states. Some well defined tools have also been used to measure the entangling properties of quantum operators and two-qubit states. It was found that such tools help to analyze perfect entanglers and also have the unique property of maximally entangling a complete set of orthonormal product vectors. The results show that the qubit gates provided minimum universal gate construction and two of them were necessary and sufficient in implementation of a generic two-qubit gate  

The entanglement between two spins in the ferromagnetic Heisenberg chain at low temperatures was calculated. It was shown that if a magnetic field is applied to a ferromagnetic Heisenberg chain, then pairwise entanglement develops between spins at arbitrary given states. It was also shown that the entanglement profile is a Gaussian with a characteristic length depending on the temperature and the coupling between spins only when the ground state and the one-particle states are populated. The magnetic field was shown to affect only the amplitude of the profile and not its characteristic length  

In this paper the effect of thrust on the bending behaviour of flexible missiles is investigated. For this purpose, the governing equations of motion of a flexible guided missile are derived following the Lagrangian approach. The missile is idealized as a non-uniform beam where the bending elastic deflections are modelled using the method of modal substitution. The vehicle (time varying) bending modeshapes and natural frequencies are determined by modelling variable mass and stiffness distributions with thrust and mass burning effects accounted for. To solve this problem the missile is divided into several segments of uniform stiffness, density and axial force distribution. This approach... 

Implementation of local quantum gate on specific qubits in an array of qubits by carrying a Hamiltonian around a closed loop is discussed. A family of isospectral Hamiltonians with the same spectrum of the projection operator on the main array is constructed by choice of a suitable curve. For every single qubit gate acting on the k-th qubit, a local operator Xk acts nontrivially on the ancilla and the qubit. Imbedding appropriate operators for a suitable set of qubit gates comprises of a universal set of quantum gates. In tensor product of the array one can enact holonomically any set of gates on any subset of qubits