Related papers: Noncommutative Algebraic Equations and Noncommutat…

In this research paper, structured bi-matrix variate, matrix quadratic equations are considered. Some lemmas related to determining the eigenvalues of unknown matrices are proved. Also, a method of determining the diagonalizabe unknown…

Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…

The perturbative expansion of static force and potential is reanalyzed concerning its practical applicability. A well behaved perturbative prediction is given by the integration of the renormalization group equation for the coupling…

The invariants of solvable triangular Lie algebras with one nilindependent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are constructed using an original algebraic algorithm based on Cartan's…

We study the homogeneous coordinate rings of real multiplication noncommutative tori as defined by A. Polishchuk. Our aim is to understand how these rings give rise to an arithmetic structure on the noncommutative torus. We start by giving…

We study the combinatorial and algebraic properties of Nonnegative Matrices. Our results are divided into three different categories. 1. We show a quantitative generalization of the 100 year-old Perron-Frobenius theorem, a fundamental…

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation…

We examine a method for solving an infinite-dimensional tensor eigenvalue problem $H x = \lambda x$, where the infinite-dimensional symmetric matrix $H$ exhibits a translational invariant structure. We provide a formulation of this type of…

The perturbative framework of the space-time non-commutative real scalar field theory is formulated, based on the unitary S-matrix. Unitarity of the S-matrix is explicitly checked order by order using the Heisenberg picture of Lagrangian…

We consider the following problem: given $d \times d$ rational matrices $A_1, \ldots, A_k$ and a polyhedral cone $\mathcal{C} \subset \mathbb{R}^d$, decide whether there exists a non-zero vector whose orbit under multiplication by $A_1,…

Let $\R $ be a ring with unit 1 and $a\in \R, \bar{a}=a+\delta a\in \R $ such that $a^#$ exists. In this paper, we mainly investigate the perturbation of the group inverse $a^#$ on $\R$. Under the stable perturbation, we obtain the explicit…

We have discovered that the gauge invariant observables of matrix models invariant under U($N$) form a Lie algebra, in the planar large-N limit. These models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We study here…

We consider the symmetric group $S_n$-module of the polynomial ring with $m$ sets of $n$ commuting variables and $m'$ sets of $n$ anti-commuting variables and show that the multiplicity of an irreducible indexed by the partition $\lambda$…

We axiomatize and study the matrices of type $H\in M_N(A)$, having unitary entries, $H_{ij}\in U(A)$, and whose rows and columns are subject to orthogonality type conditions. Here $A$ can be any $C^*$-algebra, for instance $A=\mathbb C$,…

The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…

Let A and E be Hermitian self-adjoint matrices, where A is fixed and E a small perturbation. We study how the eigenvalues and eigenvectors of A+E depend on E, with the aim of obtaining first order formulas (and when possible also second…

The eigenvalue problem for an irreducible non negative matrix $A=[a_{ij}]$ in the max-algebra is the form $A \otimes x = \lambda x$ where $(A \otimes x)_i = \max (a_{ij}x_j), x=(x_1,x_2, \dots, x_n)^t $ and $\lambda $ refers to maximum…

I dedicated the volume $1$ of monograph 'Introduction into Noncommutative Algebra' to studying of algebra over commutative ring. The main topics that I covered in this volume: definition of module and algebra over commutative ring; linear…

We study a class of matrices with noncommutative entries, which were first considered by Yu. I. Manin in 1988 in relation with quantum group theory. They are defined as "noncommutative endomorphisms" of a polynomial algebra. More explicitly…

We consider a superlinear perturbation of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential. Using variational tools and critical groups, we show that when $\lambda$ is close to a nonprincipal…