Related papers: Topics on Meixner families
Geometrical pictures for the family structure of fundamental particles are developed. They indicate that there might be a relation between the family repetition structure and the number of space dimensions.
We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…
We first investigate two kinds of Fricke families consisting of Fricke functions and Siegel functions, respectively. And, in terms of their special values we generate ray class fields of imaginary quadratic fields, which is related to the…
The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric…
A model-independent formulation of anyons as spinning particles is presented. The general properties of the classical theory of (2+1)-dimensional relativistic fractional spin particles and some properties of their quantum theory are…
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…
We sketch some connecting relations involving fractional and quantum calculi, fractal structure, thermodynamics, and quantum mechanics.
In this short review, I'll discuss the background, applicability and prospects of collinear factorization in quantum chromodynamics.
The characterization of information within a multiparty system is both significant and complex. This paper presents the concept of generalized conditional mutual information, along with a family of multiparty quantum mutual information…
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…
We give a rigorous description of a model of the quantized electromagnetic field interacting with quantized current fields. In the special case of classical currents our results agree with common knowledge about the problem. A toy model of…
We introduce notions of being "triangle-free" and "strongly triangle-free" for operator systems in M_n(C) considered as quantum graphs. Several examples and non-examples are discussed. We provide a complete characterization of strongly…
We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. The dynamics for arities of…
The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges and the Chern character…
We study the analogue of Kummer distribution in free probability. We prove characterization of free-Kummer and free Poisson distributions by freeness properties together with some assumptions about conditional moments. Our main tools are…
We prove or conjecture several relations between the multizeta values for positive genus function fields of class number one, focusing on the zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or…
We construct a family of right-angled Coxeter groups which provide counter-examples to questions about the stable boundary of a group, one-endedness of quasi-geodesically stable subgroups, and the commensurability types of right-angled…
We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum invariants. We also review categorification, which adds an additional layer of…
We review the linearization of Poisson brackets and related problems, in the formal, analytic and smooth categories.