Related papers: Systems of functional equations, the generalized s…
We describe a procedure for determining the generalised scaling functions $f_n(g)$ at all the values of the coupling constant. These functions describe the high spin contribution to the anomalous dimension of large twist operators (in the…
This paper develops one of the methods for study of nonlinear Partial Differential equations. We generalize Sato equation and represent the algorithm for construction of some classes of nonlinear Partial Differential Equations (PDE)…
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…
By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…
In this paper we generalize a shift theorem, which plays a key role in studying representations of FI$^m$, the product category of the category of finite sets and injections, and classify finitely generated injective FI$^m$-modules over a…
We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these…
Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put…
In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some…
We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…
Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or…
A generalized exponential matrix based on the construction of kernel operators for generalized summability is defined and analyzing its main properties, generalizing the classical exponential matrix and fractional exponential matrix. This…
The article $-$ part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules $-$ presents a straightforward…
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard…
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
We use generalized Taylor formulae in order to give some simple constructions in the real closure of an \ovfz. We deduce a new, simple quantifier elimination algorithm for \rcvfs and some theorems about constructible subsets of real…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures. Alesker showed that these operations agree with the…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent…