This paper considers the controllability and Riesz basis generation property of linear infinite dimensional systems with group generators and one-dimensional admissible input operators. The corresponding results of [Advances in Mathematical Systems Theory, 2000, pp. 221-242] under the assumption of algebraic simplicity for eigenvalues of the generator are generalized to the case in which the ei...

If A =D+E where D is the matrix of diagonal elements of A , then when A has some multiple or very close eigenvalues E has certain characteristic properties. These properties are considered both for hermitian and nonhermitian A . The properties are important in connexion with several algorithms for diagonalizing matrices by similarity transformations. *Mathematics Division, National Physical Lab...

Multiple-input-multiple-output (MIMO) technique is often employed to increase capacity in comparing to systems with single antenna. However, the computational complexity in evaluating channel capacity or transmission rate (data rate) grows proportionally to the number of employed antennas at both ends of the wireless link. Recently, the QR decomposition (QRD) based detection schemes have emerge...

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...

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.

The sum capacity on a symbol-synchronous CDMA system having processing gain N and supporting K power constrained users is achieved by employing at most 2N 1 sequences. Analogously, the minimum received power (energy-per-chip) on the symbol-synchronous CDMA system supporting K users that demand specified data rates is attained by employing at most 2N 1 sequences. If there are L oversized users i...

The Lanczos method is often used to solve a large scale symmetric matrix eigen-value problem. It is well-known that the single-vector Lanczos method can only find one copy of any multiple eigenvalue and encounters slow convergence towards clustered eigenvalues. On the other hand, the block Lanczos method can compute all or some of the copies of a multiple eigenvalue and, with a suitable block s...

An extra-stabilized Morley finite element method (FEM) directly computes guaranteed lower eigenvalue bounds with optimal a priori convergence rates for the bi-Laplacian Dirichlet eigenvalues. The smallness assumption in 2D (resp., 3D) on maximal mesh-size makes computed th discrete bound . This holds multiple and clusters of eigenvalues serves localization eigenvalues, particular coarse meshes....