Related papers: The generalized Gassert-Shor formula as combinator…
The characterization of commutators in associative algebras is a classical problem in ring theory. In this paper, we address this problem for the natural class of generalized block-triangular algebras. To this end, we introduce a new…
We prove a generalized Fej\'er's theorem for locally compact groups.
The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme $G$ over a regular local ring $R$ is trivial. We settle it in the case when $G$ is quasi-split and $R$ is unramified. Some of…
We consider a version of generalised $q$-oscillators and some of their applications. The generalisation includes also "quons" of infinite statistics and deformed oscillators of parastatistics. The statistical distributions for different…
We introduce some general and special formulations of general position theorem for parametrized families of fractals and explain the techniques of its application to prove the existence of self-similar sets with prescribed special…
Using the Kuznetsov trace formula, we prove a spectral decomposition for the sums of generalized Dirichlet $L$-functions. Among applications are an explicit formula relating norms of prime geodesics to moments of symmetric square…
In this paper, we consider some generalized commutator equations in a finite group and show that the number of solutions of such equations are characters of that group. We also obtain explicit formula for this character, considering the…
We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…
A parameter-free method, namely the generalization of the Gauss-Seidel (GGS) method, is developed to solve generalized absolute value equations. Convergence of the proposed method is analyzed. Numerical results are given to demonstrate the…
The generalized number-theoretic transformation (NPT) is formulated on the basis of the exponential function theorem, which allows us to replace operations modulo the expression as a whole by modulo operations on the exponent of this…
In this paper, we consider the set $\textit{NR}(G)$ of natural numbers which are not in the numerical semigroup generated by a compound sequence $G$. We generalize a result of Tuenter which completely characterizes $\textit{NR}(G)$. We use…
We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions - the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead to…
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.
I connect an old result of mine on a Lie algebra generalization of the Amitsur-Levitski theorem with equations for sheets in a reductive Lie algebra and with recent results of Kostant-Wallach on the variety of singular elements in a…
The method of exhaustion is generalized to a simple formula that can be used to integrate functions under very general conditions, provided that the integral exists. Both a geometric proof (following the usual procedure for the method of…
This is the second paper in a sequence devoted to giving manifestly non-negative formulas for generalized exponents of small representations in all types. It contains a first formula for generalized exponents of small weights which extends…
In the present note a generalization of Borel-Cantelli Lemma is proposed.
Fractional supersymmetry denotes a generalisation of supersymmetry which may be constructed using a single real generalised Grassmann variable, $\theta = \bar{\theta}, \, \theta^n = 0$, for arbitrary integer $n = 2, 3, ...$. An explicit…