scholarly journals Moment Functions on Groups

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Żywilla Fechner ◽  
Eszter Gselmann ◽  
László Székelyhidi
Keyword(s):  
Commutative Group ◽  
Bell Polynomials ◽  
Exponential Polynomials ◽  
Bell Polynomial ◽  
Rank One ◽  
Moment Functions ◽  
Binomial Type ◽  
Higher Rank ◽  
Generalized Moment

AbstractIn this paper generalized moment functions are considered. They are closely related to the well-known functions of binomial type which have been investigated on various abstract structures. The main purpose of this work is to prove characterization theorems for generalized moment functions on commutative groups. At the beginning a multivariate characterization of moment functions defined on a commutative group is given. Next the notion of generalized moment functions of higher rank is introduced and some basic properties on groups are listed. The characterization of exponential polynomials by means of complete (exponential) Bell polynomials is given. The main result is the description of generalized moment functions of higher rank defined on a commutative group as the product of an exponential and composition of multivariate Bell polynomial and an additive function. Furthermore, corollaries for generalized moment function of rank one are also stated. At the end of the paper some possible directions of further research are discussed.

On a generalization of the Rényi–Srivastava characterization of the Poisson law

2021 ◽  
Vol 58 (1) ◽  
pp. 68-82
Author(s):  
Jean-Renaud Pycke
Keyword(s):  
Life Insurance ◽  
Collective Model ◽  
New Method ◽  
Bell Polynomials ◽  
Explicit Formulas ◽  
Compound Distributions ◽  
Poisson Law ◽  
Pierre Loti

AbstractWe give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generalization of a characterization of Poisson law due to Rényi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions occurring in the extended collective model in non-life insurance.

A Geometric Characterization of Nonnegative Bands

2004 ◽  
Vol 47 (2) ◽  
pp. 257-263
Author(s):  
Alka Marwaha
Keyword(s):  
Invariant Subspace ◽  
Geometric Structure ◽  
Finite Rank ◽  
Special Kind ◽  
Maximal Rank ◽  
Geometric Characterization ◽  
Idempotent Operators ◽  
Rank One ◽  
Standard Subspace

AbstractA band is a semigroup of idempotent operators. A nonnegative band S in having at least one element of finite rank and with rank (S) > 1 for all S in S is known to have a special kind of common invariant subspace which is termed a standard subspace (defined below).Such bands are called decomposable. Decomposability has helped to understand the structure of nonnegative bands with constant finite rank. In this paper, a geometric characterization of maximal, rank-one, indecomposable nonnegative bands is obtained which facilitates the understanding of their geometric structure.

scholarly journals On Degenerate Truncated Special Polynomials

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 144 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Bernstein Polynomials ◽  
Stirling Numbers ◽  
Bell Polynomials ◽  
Euler Polynomials ◽  
Exponential Polynomials ◽  
Special Polynomials ◽  
Summation Formulas ◽  
Special Cases ◽  
Proof Techniques

The main aim of this paper is to introduce the degenerate truncated forms of multifarious special polynomials and numbers and is to investigate their various properties and relationships by using the series manipulation method and diverse special proof techniques. The degenerate truncated exponential polynomials are first considered and their several properties are given. Then the degenerate truncated Stirling polynomials of the second kind are defined and their elementary properties and relations are proved. Also, the degenerate truncated forms of the bivariate Fubini and Bell polynomials and numbers are introduced and various relations and formulas for these polynomials and numbers, which cover several summation formulas, addition identities, recurrence relationships, derivative property and correlations with the degenerate truncated Stirling polynomials of the second kind, are acquired. Thereafter, the truncated degenerate Bernoulli and Euler polynomials are considered and multifarious correlations and formulas including summation formulas, derivation rules and correlations with the degenerate truncated Stirling numbers of the second are derived. In addition, regarding applications, by introducing the degenerate truncated forms of the classical Bernstein polynomials, we obtain diverse correlations and formulas. Some interesting surface plots of these polynomials in the special cases are provided.

scholarly journals Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 112 ◽  
Author(s):  
Irem Kucukoglu ◽  
Burcin Simsek ◽  
Yilmaz Simsek
Keyword(s):  
Probability Distribution ◽  
Generating Functions ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Distribution Functions ◽  
Binomial Coefficients ◽  
Bell Polynomials ◽  
Exponential Polynomials ◽  
Charlier Polynomials ◽  
Combinatorial Sums

The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new families, but also derive many new identities, relations, derivative formulas, and combinatorial sums with the inclusion of binomials coefficients, falling factorial, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), the Poisson–Charlier polynomials, combinatorial numbers and polynomials, the Bersntein basis functions, and the probability distribution functions. Furthermore, by applying the p-adic integrals and Riemann integral, we obtain some combinatorial sums including the binomial coefficients, falling factorial, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), and the Cauchy numbers (or the Bernoulli numbers of the second kind). Finally, we give some remarks and observations on our results related to some probability distributions such as the binomial distribution and the Poisson distribution.

scholarly journals Purely infinite simple Kumjian–Pask algebras

2018 ◽  
Vol 30 (1) ◽  
pp. 253-268 ◽  
Author(s):  
Hossein Larki
Keyword(s):  
Commutative Ring ◽  
Path Algebras ◽  
Higher Rank ◽  
Leavitt Path Algebras ◽  
Unital Simple

Abstract Given any finitely aligned higher-rank graph Λ and any unital commutative ring R, the Kumjian–Pask algebra {\mathrm{KP}_{R}(\Lambda)} is known as the higher-rank generalization of Leavitt path algebras. After the characterization of simple Kumjian–Pask algebras by Clark and Pangalela among others, in this article we focus on the purely infinite simple ones. Briefly, we show that if {\mathrm{KP}_{R}(\Lambda)} is simple and every vertex of Λ is reached from a generalized cycle with an entrance, then {\mathrm{KP}_{R}(\Lambda)} is purely infinite. We also prove a dichotomy for simple Kumjian–Pask algebras: If each vertex of Λ is reached only from finitely many vertices and {\mathrm{KP}_{R}(\Lambda)} is simple, then {\mathrm{KP}_{R}(\Lambda)} is either purely infinite or locally matritial. This result covers all unital simple Kumjian–Pask algebras.

Characterization of Dini–Lipschitz functions for the Helgason Fourier transform on rank one symmetric spaces

2016 ◽  
Vol 7 (4) ◽  
Author(s):  
Salah El Ouadih ◽  
Radouan Daher
Keyword(s):  
Fourier Transform ◽  
Symmetric Spaces ◽  
Translation Operator ◽  
Lipschitz Functions ◽  
Generalized Translation Operator ◽  
Generalized Translation ◽  
Rank One

AbstractIn this paper, using a generalized translation operator, we obtain an analog of Younis’ theorem, [

Rings with A Finitely Generated Total Quotient Ring

1974 ◽  
Vol 17 (1) ◽  
pp. 1-4 ◽  
Author(s):  
John Conway Adams
Keyword(s):  
Prime Ideal ◽  
Commutative Ring ◽  
Quotient Ring ◽  
Finitely Generated ◽  
Zero Divisors ◽  
Rank One ◽  
Definition Of

Let R be a commutative ring with non-zero identity and let K be the total quotient ring of R. We call R a G-ring if K is finitely generated as a ring over R. This generalizes Kaplansky′s definition of G-domain [5].Let Z(R) be the set of zero divisors in R. Following [7] elements of R—Z(R) and ideals of R containing at least one such element are called regular. Artin-Tate's characterization of Noetherian G-domains [1, Theorem 4] carries over with a slight adjustment to characterize a Noetherian G-ring as being semi-local in which every regular prime ideal has rank one.

scholarly journals OBSTRUCTIONS TO A GENERAL CHARACTERIZATION OF GRAPH CORRESPONDENCES

2013 ◽  
Vol 95 (2) ◽  
pp. 169-188
Author(s):  
S. KALISZEWSKI ◽  
NURA PATANI ◽  
JOHN QUIGG
Keyword(s):  
Directed Graph ◽  
Discrete Space ◽  
Topological Graphs ◽  
Locally Compact ◽  
General Characterization ◽  
Product Systems ◽  
Vertex Set ◽  
Higher Rank

AbstractFor a countable discrete space $V$, every nondegenerate separable ${C}^{\ast } $-correspondence over ${c}_{0} (V)$ is isomorphic to one coming from a directed graph with vertex set $V$. In this paper we demonstrate why the analogous characterizations fail to hold for higher-rank graphs (where one considers product systems of ${C}^{\ast } $-correspondences) and for topological graphs (where $V$ is locally compact Hausdorff), and we discuss the obstructions that arise.

The spectrum and heat dynamics of locally symmetric spaces of higher rank

2014 ◽  
Vol 35 (5) ◽  
pp. 1524-1545 ◽  
Author(s):  
LIZHEN JI ◽  
ANDREAS WEBER
Keyword(s):  
Symmetric Spaces ◽  
Chaotic Behavior ◽  
Heat Semigroup ◽  
Locally Symmetric Spaces ◽  
Rank One ◽  
Higher Rank

The aim of this paper is to study the spectrum of the$L^{p}$Laplacian and the dynamics of the$L^{p}$heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in the rank-one case, it turns out that the$L^{p}$heat semigroup on$M$has a certain chaotic behavior if$p\in (1,2)$, whereas for$p\geq 2$such chaotic behavior never occurs.

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