Related papers: Moment functions on groups
We propose a formalism to derive the maximal bound of generalized Bell type inequalities and shows that the formalism can be applied to various form of Bell functions. The generic Bell function is defined to generate the combinations of all…
We discuss representations of monogenic functions over very regular groups.
The main purpose of this article is to study higher order moments of Kummer sums weighted by $L$-functions using estimates for character sums and analytic methods. The results of this article complement a conjecture of Zhang Wenpeng (2002).…
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
This manuscript introduces the idea of GS-exponential kind of convex functions and some of their algebraic features, and we introduce a new class GS-exponential kind of convex sets. In addition, we describe certain fundamental…
Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on the knowledge of the behavior of the…
The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in…
Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…
We obtain a combinatorial formula for the positive integer moments of the partition function of the $C\beta E_{N}$ field, or equivalently the moments of the moments of the characteristic polynomial of the $C\beta E_{N}$ ensemble. We then…
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…
The paper deals with different properties of polynomials in random elements: bounds for characteristics functionals of polynomials, stochastic generalization of the Vinogradov mean value theorem, characterization problem, bounds for…
Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic…
In this paper local polynomials on Abelian groups are characterized by a "local" Fr\'echet-type functional equation. We apply our result to generalize Montel's Theorem and to obtain Montel-type theorems on commutative groups.
We show that normalizers and permutational isomorphisms of permutation groups given by generating sets can be computed in time simply exponential in the degree of the groups. The result is obtained by exploiting canonical forms for…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
All extremal solutions of the truncated $L$-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality.…
In this paper we define a class of Boolean and generalized Boolean functions defined on $\mathbb{F}_2^n$ with values in $\mathbb{Z}_q$ (mostly, we consider $q=2^k$), which we call landscape functions (whose class containing generalized…
Maximum likelihood learning with exponential families leads to moment-matching of the sufficient statistics, a classic result. This can be generalized to conditional exponential families and/or when there are hidden data. This document…