We prove polarization theorems for arbitrary classical-quantum (cq) channels. The input alphabet is endowed with an arbitrary Abelian group operation, and an Anion-style transformation is applied using this operation. It is shown that as the number of pola ...
Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...
The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A - lambda B requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations re ...
Information theory is the field in which we study the fundamental limitations of communication. Shannon proved in 1948 that there exists a maximum rate, called capacity, at which we can reliably communicate information through a given channel. However, Sha ...
We introduce a notion of xi-stability on the affine grassmannian (SIC) for the classical groups, this is the local version of the xi-stability on the moduli space of Higgs bundles on a curve introduced by Chaudouard and Laumon. We prove that the quotient ( ...
Fix an algebraically closed field K having characteristic p≥0 and let Y be a simple algebraic group of classical type over K. Also let X be maximal among closed connected subgroups of Y and consider a non-trivial p-restricted irreducible ...
We examine how, in prime characteristic p, the group of endotrivial modules of a finite group G and the group of endotrivial modules of a quotient of G modulo a normal subgroup of order prime to p are related. There is always an inflation map, but examples ...
We address two questions of Simon Thomas. First, we show that for any n >= 3 one can find a four-generated free subgroup of SLn (Z) which is profinitely dense. More generally, we show that an arithmetic group Gamma that admits the congruence subgroup prope ...
Atherosclerosis is the commonest and most important vascular disease. Andrographolide (AND) is the main bioactive component of the medicinal plant Andrographis paniculata and is used in traditional medicine. This study was aimed to evaluate the antiatherog ...
This paper extends the quotient method proposed in [1] and applies it to stabilize a “ball-on-a-wheel” system. The quotient method requires a diffeomorphism to obtain the normal form of the input vector field and uses canonical pro- jection to obtain the q ...
