Related papers: A note on positive partial transpose blocks
In this note we use techniques in the topology of 2-complexes to recast some tools that have arisen in the study of planar tiling questions. With spherical pictures we show that the tile counting group associated to a set $T$ of tiles and a…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
The main result of this paper is that the polytope of the bipartite TSP is significantly different from that of the general TSP. Comb inequalities are known as facet defining ones in the general case. In the bipartite case, however, many of…
This paper investigates the properties of Choi polynomials and their fundamental role in the theory of positive linear maps between matrix algebras. By focusing on Hermitian symmetric biquadratic forms, we establish a connection between the…
In this short note, we prove a formula for the group inverse of a block matrix and consider the pseudo principal pivot transform expressed in terms of group inverses. Extensions of the usual principal pivot transform, where the usual…
Under consideration are the construction and properties of some special class of second other tangent sets on using the technique of nonstandard analysis.
In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
In this paper, we establish some new inequalities for class of SX(h,I) convex functions which are supermultiplicative or superadditive and nonnegative. And we also give some applications for special means.
It is shown that, for the block matrices belonging to $M(nd,\mathbb{C})$ with commuting and normal block entries of dimension $d$, the separability of such a block matrices is equivalent to its semi-positive definity. The separability…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
We discuss a class of linear representations of the product poset of totally ordered sets $P= T_1 \times \cdots \times T_n$ which decompose into interval representations for block intervals. These can be characterised in terms of a…
We propose new conjectures about the relationship between the principal blocks of finite groups for different primes and establish evidence for these conjectures.
This paper is an attempt to compute the decomposition numbers of the blocks of the symmetric group which have "small defect"; that is, blocks of weight smaller than the characteristic. We present various methods for computing such…
This paper is a continuation of our 2005 paper on complex topology and its implication on invertibility (or non-invertibility). In this paper, we will try to classify the complexity of inversion into 3 different classes. We will use…
The Department of Applied Mathematics at the University of Nottingham Malaysia Campus has a responsibility for delivering mathematics modules for engineering students. Due to the significantly large number of students, two methods of…
In this paper, one new classes of convex functions which is called MT-convex functions are given. We also establish some Hadamard-type inequalities.
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
Known or essentially known results about duals of interpolation spaces are presented, taking a point of view sometimes slightly different from the usual one. Particular emphasis is placed on Alberto Calderon's theorem describing the duals…
Accretive partial transpose (APT) matrices have been recently defined, as a natural extension of positive partial transpose (PPT) matrices. In this paper, we discuss further properties of APT matrices in a way that extends some of those…
We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…