相关论文: Matrices of infinite dimensions and their applicat…

Motivated by recent works on statistics of matrices over sets of number theoretic interest, we study matrices with entries from arbitrary finite subsets $\mathcal A$ of finite rank multiplicative groups infields of characteristic zero. We…

The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…

We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of…

In the last years a lot of work has been concentrated on the study of the behaviour at infinity of polynomial maps. This behaviour can be very complicated, therefore the main idea was to find special classes of polynomial maps which have,…

We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…

The input and output algebras of an infinite qubit system and their representations are described.

We describe derivations of several important associative and Lie rings of infinite matrices over general rings of coefficients.

We study the metric dimension (strong and weak) of infinite graphs. In particular, our main interest is characterizing infinite graphs with finite dimension. Our main results: (1) graphs with more than one end have infinite strong…

Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are…

In the proposed matrix primes, through which one can readily generate a sequence of primes. The paper also proposes a number of theorems proved by which an infinite number of prime numbers twins

The concept of sequency holds a fundamental significance in signal analysis using Walsh basis functions. In this study, we closely examine the concept of sequency and explore the properties of sequency-complete and sequency-ordered…

This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…

Scientific paper is devoted to research of T-matrix - matrix of composite numbers 6h+1 v 6h-1 in special view, and to her application in number theory.

Infinite dimensional moment problems have a long history in diverse applied areas dealing with the analysis of complex systems but progress is hindered by the lack of a general understanding of the mathematical structure behind them.…

We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.

In this work, we propose a convenient framework for infinite-dimensional analysis (including both real and complex analysis in infinite dimensions), in which differentiation (in some weak sense) and integration operations can be easily…

Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…

We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide range of physics problems are summarized. This paper…

This paper is a brief review of recent developments in random matrix theory. Two aspects are emphasized: the underlying role of integrable systems and the occurrence of the distribution functions of random matrix theory in diverse areas of…

The finitistic dimension of a triangulated category is introduced. For the category of perfect complexes over a ring it is shown that this dimension is finite if and only if the small finitistic dimension of the ring is finite.