Related papers: Power Series in Several Complex Variables
The purpose of this paper is to study convergence of Monge-Ampere measures associated to sequences of plurisubharmonic functions defined on a hyperconvex subset of ${\mathbb C^n}$.
An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fej\'{e}r's theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to…
It is declared that the aim of simplifying representations of coefficients of power series of classical statistical mechanics is to simplify a process of obtaining estimates of the coefficients using their simplified representations. The…
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…
The article is devoted to the problem of calculating the probability density of a strictly stable law at $x\to\infty$. To solve this problem, it was proposed to use the expansion of the probability density in a power series. A…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
Given a specific collection of curves on an oriented surface with punctures, we associate a power series by counting its intersections with multicurves. This paper presents a reciprocity formula on the power series when multicurves with no…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
In this paper various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notion, a concept of a relevant divided difference and also a…
We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…
In multicentric calculus one takes a polynomial $p$ with distinct roots as a new variable and represents complex valued functions by $\mathbb C^d$-valued functions, where $d$ is the degree of $p$. An application is e.g. the possibility to…
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…
A stochastic dynamics framework for the study of complex systems is presented.
Generalized quantum measurements with N distinct outcomes are used for determining the density matrix, of order d, of an ensemble of quantum systems. The resulting probabilities are represented by a point in an N-dimensional space. It is…
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…