This paper considers communications and network systems whose properties are characterized by the gaps of the leading eigenvalues of AHA for a matrix A. It is shown that a sufficient and necessary condition for a large eigen-gap is that A is a “hub” matrix in the sense that it has dominant columns. Some applications of this hub theory in multiple-input and multiple-output (MIMO) wireless system...

The paper develops Newton’s method of finding multiple eigenvalues with one Jordan block and corresponding generalized eigenvectors for matrices dependent on parameters. It computes the nearest value of a parameter vector with a matrix having a multiple eigenvalue of given multiplicity. The method also works in the whole matrix space (in the absence of parameters). The approach is based on the ...

OBJECTIVES To investigate the extent of tissue damage in a region of normal appearing corpus callosum (NACC) for different forms of multiple sclerosis (MS) using diffusion tensor and proton magnetic resonance (MR) spectroscopic imaging. METHODS A total of 47 patients with MS and 15 controls were included. Regions of interest from the NACC were manually segmented using high resolution anatomic...

In this a paper perturbations of multiple eigenvalues Schmidt spectral problems is considered. At the usage reductional method suggested in articles [11, 12] investigation perturbation reduced to simple ones. end, as application obtained results problem about boundary for system two Sturm–Liouville with parameter

The complex-valued dual BEM has been employed by Chen and Chen (1998) to solve the acoustic modes of a cavity with or without a thin partition. A novel method using only the real part of the complex-valued dual BEM was found by Chen (1998) to be equivalent to the dual MRM. However, spurious eigenvalues occur. In this paper, we propose the singular value decomposition technique to ®lter out spur...

In this paper, we review analytical methods for a rigorous study of the existence and stability of stationary, multiple spots for reaction-diffusion systems. We will consider two classes of reaction-diffusion systems: activator-inhibitor systems (such as the Gierer-Meinhardt system) and activator-substrate systems (such as the Gray-Scott system or the Schnakenberg model). The main ideas are pre...

that is, the sample covariance matrix of the history of the chain plus a (small) constant ǫ > 0 multiple of the identity matrix I. The lower bound on the eigenvalues of Sn induced by the factor ǫI is theoretically convenient, but practically cumbersome, as a good value for the parameter ǫ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitl...

In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.