相关论文: On the operations of sequences in rings and binomi…
Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to…
We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted…
Our basic concept is the set $\mathcal{E}(H)$ of effects on a finite dimensional complex Hilbert space $H$. If $a,b\in\mathcal{E}(H)$, we define the sequential product $a[\mathcal{I}]b$ of $a$ then $b$. The sequential product depends on the…
Motivated by Hirano-Tominaga's work \cite{HT} on rings for which every element is a sum of two idempotents and by de Seguins Pazzis's results \cite{de} on decomposing every matrix over a field of positive characteristic as a sum of…
New sequences of hyperoperations \cite{BE15,HI26,ACK28,GO47,TAR69} are presented together with their local algebraic properties. The commutative hyperoperations reported by Bennet \cite{BE15} are presented as a sequence of monoids. After…
Here we consider the degenerate Bernstein polynomials as a degenerate version of Bernstein polynomials, which are motivated by Simsek's recent work 'Generating functions for unification of the multidimensional Bernstein polynomials and…
In this paper we give a convolution identity for the complete and elementary symmetric functions. This result can be used to proving and discovering some combinatorial identities involving $r$-Stirling numbers, $r$-Whitney numbers and…
The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
Let $R$ be a commutative ring with identity and $T(R)$ its total quotient ring. We extend the notion of well-centered overring of an integral domain to an arbitrary commutative ring and we investigate the transfer of this property to…
The classical work of Feferman Vaught gives a powerful, constructive analysis of definability in (generalized) product structures, and certain associated enriched Boolean structures. %structures in terms of definability in the component…
We define a ring R of geometric objects G generated by finite abstract simplicial complexes. To every G belongs Hodge Laplacian H as the square of the Dirac operator determining its cohomology and a unimodular connection matrix L). The sum…
We construct and study sequences of linear operators of Bernstein-type acting on bivariate functions defined on the unit disk. To this end, we study Bernstein-type operators under a domain transformation, we analyse the bivariate…
Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we first introduce and study the notions of $s$-pure exact sequences and $s$-absolutely pure modules which extend the classical notions of…
We present a unified algebraic framework utilizing the formal Bell transform to bridge the Dirichlet convolution of arithmetic functions with the combinatorial structure of infinite Euler-type products. By analyzing the logarithmic…
Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…
We establish an operator--theoretic correspondence between periodic Bernoulli kernels and Hermite polynomials, framed through the umbral calculus and a quantum analogy. Starting from the analytic master function $F^\ast$, the periodic…
Functions satisfying the functional equation \begin{align*} \sum_{r=0}^{n-1} (-1)^r f(x+ry, ny) = f(x,y), \quad \text{for any positive odd integer $n$}, \end{align*} are named the alternating invariant functions. Examples of such functions…
In the present note we discuss two different ring structures on the set of holomorphic discrete series of a causal symmetric space of Cayley type $G/H$ and we suggest a new interpretation of Rankin-Cohen brackets in terms of intertwining…
A sequence is a fractal sequence if it contains itself as a proper subsequence. (The self-containment property resembles that of visual fractals) A doubly fractal sequence of integers is defined by operations called upper trimming and lower…