Related papers: Super-Mathematics Functions
This paper develops the basic theory of formal schemes over fields in the supersymmetric setting. We introduce the notion of a formal superscheme and investigate some of its fundamental properties. Particular emphasis is placed on the study…
This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties…
Supersymmetry and super-Lie algebras have been consistently generalized previously. The so-called fractional supersymmetry and $F-$Lie algebras could be constructed starting from any representation $\D$ of any Lie algebra $g$. This involves…
In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation…
Preparing the Fr\'echet-Grassmann (FG-)algebra ${\fR}$ composed with countably infinite Grassmann generators, we introduce the superspace ${\fR}^{m|n}$. After defining Grassmann continuation of smooth functions on ${\euc}^m$ to those on…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
In this work, we examine one two-parameter family of sets consisting of functions holomorphic in the unit disk, previously investigated by several mathematicians. We focus on the set-theoretic properties of this family, identify the general…
A representation-theoretic approach to special functions was developed in the 40-s and 50-s in the works of I.M.Gelfand, M.A.Naimark, N.Ya.Vilenkin, and their collaborators. The essence of this approach is the fact that most classical…
We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct new summation formulas…
A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain…
The rules to construct Lagrangian formulation for $\theta$-superfield theory of fields ($\theta$-STF) are introduced and considered on the whole in the framework of new superfield quantization method for general gauge theories. Algebraic,…
It is shown how to derive fractional supersymmetric quantum mechanics of order k as a superposition of k-1 copies of ordinary supersymmetric quantum mechanics.
We present some results and open problems related to expansions of the field of real numbers by hypergeometric and related functions focussing on definability and model completeness questions. In particular, we prove the strong model…
The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the…
This paper deals with some simple results about spherical functions of type $\delta$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_\sigma$ functions.
The origin of this study is based on not only explicit formulas of finite sums involving higher powers of binomial coefficients, but also explicit evaluations of generating functions for this sums. It should be emphasized that this study…
This PhD thesis aims at combining the framework of noncommutative geometry and supersymmetry. A particular class of non-commutative geometries called almost-commutative geometries can be used to describe particle theories. This thesis…
An explicit formula is given for a fundamental solution for a class of semielliptic operators. The fundamental solution is used to investigate properties of these operators as mappings between weighted function spaces. Necessary and…
In this paper which is the first of a series of papers on smooth structures, the concepts of C-structures and smooth structures are introduced and studied. The notion of smooth structure on semi-integral domains is given. It is shown that…
This report (written in French) is devoted to studying special functions the most used in physics. Special functions are a very broad branch of mathematics, theoretical physics, and mathematical physics. They appeared in the nineteenth…