The classic and the Lévy-Gnedenko central limit theorems play a key role in theory of probabilities, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the random variables that are being summed. A generalization of the BG theory, usually referred to as nonextensive statistical mechanics and characterized by the index...

We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted forms of distributivity. At the same time, we explore ways in which “local” decision or heuristic procedures for fragments of the theory of the reals can be amal...

The number A(q) shows the asymptotic behaviour of the quotient of the number of rational points over the genus of non-singular absolutely irreducible curves over IFq . Research on bounds for A(q) is closely connected with the so-called asymptotic main problem in Coding Theory. In this paper, we study some generalizations of this number for nonirreducible curves, their connection with A(q) and i...

We analyse here the monadic theory of the rational order, the monadic theory of the real line with quantification over "small" subsets and models of these theories. We prove that the results are in some sense the best possible. ?0. Introduction. A chain is a linearly ordered set. A chain is short iff it embeds neither Wi nor O1. Shortness is expressible in the monadic language of order. For con...

A recent theory of a compressible Fermi-liquid like state at Landau level filling factors ν = 1/q or 1 − 1/q, q even, is reviewed, with emphasis on the basic physical concepts.

This paper establishes a version of Nevanlinna theory based on Jackson difference operator $D_{q}f(z)=\frac{f(qz)-f(z)}{qz-z}$ for meromorphic functions zero order in the complex plane $\mathbb{C}$. We give logarithmic lemma, second fundamental theorem, defect relation, Picard theorem and five-value sense $q$-difference operator. By using this theory, we investigate growth entire solutions line...

Later various generalizations of these operators were discovered. It has been proved as a powerful tool for numerical analysis, computer aided geometric design and solutions of differential equations. In last two decades, the applications of q-calculus has played an important role in the area of approximation theory, number theory and theoretical physics. In , Lupaş [] and in , Phillip...

In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic (QS) integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures, on a space-time σ-field FX, of the QS integration. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative D is proved. Finally...

Cotangent bundle reduction theory is a basic and well developed subject in which one performs symplectic reduction on cotangent bundles. One starts with a (free and proper) action of a Lie group G on a configuration manifold Q, considers its natural cotangent lift to T ∗Q and then one seeks realizations of the corresponding symplectic or Poisson reduced space. We further develop this theory by ...