It has been known for some time that the (1, 3) perturbations of the (2k + 1, 2) Virasoro minimal models have conserved currents which are also singular vectors of the Virasoro algebra. This also turns out to hold for the (1, 2) perturbation of the (3k± 1, 3) models. In this paper we investigate the requirement that a perturbation of an extended conformal field theory has conserved currents whi...

This paper presents an O(n2) method based on the twisted factorization for computing the Takagi vectors of an n-by-n complex symmetric tridiagonal matrix with known singular values. Since the singular values can be obtained in O(n2) flops, the total cost of symmetric singular value decomposition or the Takagi factorization is O(n2) flops. An analysis shows the accuracy and orthogonality of Taka...

Abstract This contribution presents a proper generalized decomposition-based nonlinear solver for an efficient solution of geometrically dynamic problems. The is built as sum dyadic products space and time modes, this so-called enrichments truncated when the required accuracy achieved. In proposed algorithm, we apply consistent linearization residual vectors around currently known over whole sp...

A procedure for determining determining a few of the largest singular values and corresponding singular vectors of large sparse matrices is presented. Equivalent eigensystems are solved using a technique originally proposed by Golub and Kent based on the computation of modiied moments. The asynchronicity in the computations of moments and eigenvalues makes this method attractive for parallel im...

The singular vectors of a chemical transport model are the directions of maximum perturbation growth over a finite time interval. They have proved useful for the estimation of error growth, the initialization of ensemble forecasts, and the optimal placement of adaptive observations. The aim of this paper is to address computational aspects of singular vector analysis for atmospheric chemical tr...

HAMID HASSANPOUR School of Information Technology and Computer Engineering, Shahrood University of Technology. ___________________________________________________________________________________ Abstract: In this paper, a new method is presented for noise reduction in signal using partial differential equations. In this approach, the signal is initially represented as a matrix. Then using singu...

We consider a two-tile reconfigurable intelligent surface (RIS) assisted wireless network with two-antenna transmitter and receiver over Rayleigh fading. show that the average received signal-to-noise-ratio (SNR) optimal combining transmission vectors are given by left right singular spaces of RIS-receiver transmit-RIS channel matrices, respectively. Moreover, phases at two tiles RIS determined...

The singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to diverge, and hence, a measure of the predictability of the flow. In this paper, the singular vectors and singular values of stationary and evolving exa...

In this study, we consider a sampling-type algorithm for the fast localization of small electromagnetic inhomogeneities from measured far-field pattern data in limited-aperture inverse scattering problem. For purpose, designed an indicator function based on structure left- and right-singular vectors multistatic response matrix, elements which were data. We then rigorously investigated mathemati...

In this article, we associate a Hermitian matrix to multidigraph G. We call it the complex Laplacian of G and denote by L​C(G). It is shown that generalization graph. But, unlike graph, may not always be singular. obtain necessary sufficient condition for For G, if L​C(G) singular, say L​C-singular. generalize some properties Fiedler vectors undirected graphs eigenvectors corresponding second s...