Related papers: Topics on Meixner families
In this work, we present several aspects of the interplay between classical and quantum theories. After reviewing the equivalence between positivity and complete positivity in the commutative setting, we introduce and analyze intermediate…
This article focuses on the connection between the possibility of quantum computers, the predictability of complex quantum systems in nature, and the issue of free will.
The paper discusses the following topics: spinor coverings for the full Lorentz group, intrinsic parity of fermions, Majorana fermions, spinor structure of space models, two types of spacial spinors, parametrization of spinor spaces by…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
A characterization of freeness for plane curves in terms of the Hilbert function of the associated Milnor algebra is given as well as many new examples of rational cuspidal curves which are free. Some stronger properties are stated as…
Strong correlation effects in classical and quantum plasmas are discussed. In particular, Coulomb (Wigner) crystallization phenomena are reviewed focusing on one-component non-neutral plasmas in traps and on macroscopic two-component…
Description of system containing classical and quantum subsystems by means of tomographic probability distributions is considered. Evolution equation of the system states is studied.
We examine $q-$series related to higher forms. These forms are cubics, quartics, etc. In some points, in the article we add parts from previous works, in such a way, the article be more complete and readable.
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 types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmetric orbits in $sl(n)^*$ is constructed. A twisted version of…
We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…
We study glued tensor and free products of compact matrix quantum groups with cyclic groups -- so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In…
This is a brief review of various families of coherent and squeezed states (and their generalizations) for a charged particle in a magnetic field, that have been constructed for the past 50 years. Although the main attention is paid to the…
Recently the new q-Euler numbers are defined. In this paper we derive the the Kummer type congruence related to q-Euler numbers and we introduce some interesting formulae related to these q-Euler numbers.
The characterization of normal subgroups M, N of free group F for which the quotient group F/[M,N] is finitely presented is given.
We obtain a number of results regarding freeness, quasiconvexity and separability for subgroups of Coxeter groups, Artin groups and one-relator groups with torsion.
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
Two recent studies have presented new information relevant to the transition from quantum behavior to classical behavior, and related this to parameters characterizing the universe as a whole. The present study based on a separate approach…
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…