A. The paper can be considered as a complement to previous papers of the authors. An insight into applied asymptotic analysis of boundary value problems in singularly perturbed domains is presented. As a result, the asymptotic expansions of eigenvalues are obtained and discussed in terms of integral attributes of the geometrical perturbations including the virtual mass tensor, polarizati...

Let λ be a simple eigenvalue of an n-by-n matrix A. Let y and x be left and right eigenvectors of A corresponding to λ, respectively. Then, for the spectral norm, the condition number cond(λ,A) := ‖x‖2 ‖y‖2/|yx| measures the sensitivity of λ to small perturbations in A and plays an important role in the accuracy assessment of computed eigenvalues. R. A. Smith [Numer. Math., 10(1967), pp.232-240...

The present paper investigates state space analysis of memristor based series and parallel RLCM circuits. The stability analysis is carried out with the help of eigenvalues formulation method, pole-zero plot and transient response of system. The state space analysis is successfully applied and eigenvalues of the two circuits are calculated. It is found that the, system follows negative real par...

the main aim of this paper is to extend the recently developed methods for calculating the buckling loads of planar symmetric frames to include the effect of semi-rigidity of the joints. this is achieved by decomposing a symmetric model into two submodels and then healing them in such a manner that the ::::union:::: of the eigenvalues of the healed submodels result in the eigenvalues of the ent...

‎Let $G$ be a graph without an isolated vertex‎, ‎the normalized Laplacian matrix $tilde{mathcal{L}}(G)$‎ ‎is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$‎, where ‎$mathcal{D}$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎G‎$‎‎. ‎The eigenvalues of‎ $tilde{mathcal{L}}(G)$ are ‎called as ‎the ‎normalized Laplacian eigenva...

The statistical analysis of the eigenvalues of quantum systems has become an important tool in understanding the connections between classical and quantum physics. The statistical properties of the eigenvalues of a quantum system whose classical counterpart is integrable match those of random numbers. The eigenvalues of a chaotic classical system have statistical properties like those of the ei...

In the previous note, we obtained the solutions to a homogeneous linear system with constant coefficients. x = A x under the assumption that the roots of its characteristic equation |A − λI| = 0, — i.e., the eigenvalues of A — were real and distinct. In this section we consider what to do if there are complex eigenval­ ues. Since the characteristic equation has real coefficients, its complex ro...

this paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. it is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.

In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95, 230201 (2005)], an exact solution was reported for the probability pn,k to find exactly k real eigenvalues in the spectrum of an n × n real asymmetric matrix drawn at random from Ginibre’s Orthogonal Ensemble (GinOE). In the present paper, we offer a detailed derivation of the above result by concentrating on the proof...

We describe a general framework for avoiding spurious eigenvalues — unphysical unstable eigenvalues that often occur in hydrodynamic stability problems. In two example problems, we show that when system stability is analyzed numerically using descriptor notation, spurious eigenvalues are eliminated. Descriptor notation is a generalized eigenvalue formulation for differntial-algebraic equations ...