相关论文: Generalized Number Derivatives

In this paper we detail a number of properties of the affine line of a derivator, including a number of morphisms between $\mathbb{D}$ and $\mathbb{A}^1_{\mathbb{D}}$, a monoidal structure on $\mathbb{A}^1_{\mathbb{D}}$ if $\mathbb{D}$ is…

Let $\mathcal{X}$ be a projective algebraic curve and denote by $\mathcal{X}^{'}$ its strict dual curve. The map $\gamma:\mathcal{X} \longrightarrow \mathcal{X}^{'}$ is called (strict) Gauss map of $\mathcal{X}$. In this manuscript, we…

The purpose of this note is to extend the divergences analyzed in a previous work by application of the Deformed Logarithm in its most general form. In a study on entropic divergences, we have analyzed the different forms of the deformed…

Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…

First, we study the linear equations in general. Second, we focus our attention in periodic sequences over finite fields and de Bruijn directed graph.

The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.

One considers certain degenerations of the generic symmetric matrix over a field $k$ of characteristic zero and the main structures related to the determinant $f$ of the matrix, such as the ideal generated by its partial derivatives, the…

We develop a general deformation theory of objects in homotopy and derived categories of DG categories. The main result is a general pro-representability theorem for the corresponding deformation functor.

In this article we discuss an important students' misconception about derivatives, that the expression of the derivative of the function contains the information as to whether the function is differentiable or not where the expression is…

In this paper, we develop a new deformation and generalization of the Natural integral transform based on the conformable fractional $q$-derivative. We obtain transformation of some deformed functions and apply the transform for solving…

Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, many…

Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the…

The aim of this paper is twofold. Firstly, we investigate a finite sum involving the generalized falling factorial polynomials, in some special cases of which we express it in terms of the degenerate Stirling numbers of the second kind, the…

A type of fractional derivative, referred to as \alpha-derivative, is studied. The \alpha-derivative of fractional type obeys Leibnitz rule. Based on the definition of \alpha-derivative the operations of analysis and differential geometry…

In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional…

In the paper we consider models of generalized counting processes time-changed by a general inverse subordinator, we characterize their distributions and present governing equations for them. The equations are given in terms of the…

Let $\boldsymbol{\Lambda}\,(=\mathbb{F}^{n^{3}})$, where $\mathbb{F}$ is a field with $|\mathbb{F}|>2$, be the space of structure vectors of algebras having the $n$-dimensional $\mathbb{F}$-space $V$ as the underlying vector space. Also let…

The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this…

A group element is called a generalized torsion if a finite product of its conjugates is equal to the identity. We prove that in a nilpotent or FC-group, the generalized torsion elements are all torsion elements. Moreover, we compute the…

Based on the simple and well understood concept of subfields in a finite field, the technique called `field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field…