相关论文: Power series coefficients for probabilities in fin…
In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…
We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant…
A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…
We study multivariate generalizations of the $q$-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely…
Let $U_q$ be the quantum group corresponding to a complex simple Lie algebra $\mathfrak g$ with root system $R$. Assume the quantum parameter $q\in \C$ is a root of unity. In this paper we study the extensions between simple modules in the…
The paper studies logarithmic convexity and concavity of power series with coefficients involving q-gamma functions or q-shifted factorials with respect to a parameter contained in their arguments. The principal motivating examples of such…
We prove an irreducibility criterion for polynomials with power series coefficients generalizing previous known results concerning quasi-ordinary polynomials.
We deal with the algebraicity of an iterated Puiseux series in several variables in terms of the properties of its coefficients. Our aim is to generalize to several variables the results from [HM15]. We show that the algebraicity of such a…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
The strong isomorphism classes of extensions of finite groups are parametrized by orbits of a prescribed action on the second cohomology group. We study these orbits in the case of extensions of a finite abelian $p$-group by a cyclic factor…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
In this paper we study the modulus of continuity of weak solutions to a singular elliptic equation in the plane under very weak assumption on the integrability of the elliptic coefficients. Our investigation reveals that the modulus of…
We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest…
By making use of the familiar Mathieu series and its generalizations, the authors derive a number of new integral representations and present a systematic study of probability density functions and probability distributions associated with…
This article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers. Algorithms are described that compute the maximum integer modulo which two monic coprime integral polynomials…
We prove a recursive formula for the exterior and symmetric powers of modules for a cyclic 2-group. This makes computation straightforward. Previously, a complete description was only known for cyclic groups of prime order.
We reveal a duality in classical and quantum mechanics. Dual systems are related by duality transforms. All mechanical systems that are dual to each other form a duality family. In a duality family, once a system is solved, all other…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An…