Related papers: Composition with a two variable function
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
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…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…
Recently, the compositeness, defined as the norm of a two-body wave function for bound and resonance states, has been investigated to discuss the internal structure of hadrons in terms of hadronic molecular components. From the studies of…
We consider a sequence of composite Bernstein operators and the quadrature formulae associated with them. Upper bounds for the approximation error of continuous functions and for the approximation of integrals of continuous functions are…
Derivative-matching approximations are constructed as power series built from functions. The method assumes the knowledge of special values of the Bell polynomials of the second kind, for which we refer to the literature. The presented…
We address a classical open question by H.Brezis and R.Ignat concerning the characterization of constant functions through double integrals that involve difference quotients. Our first result is a counterexample to the question in its full…
We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input…
We apply a symbolic approach of the general quadratic decomposition of polynomial sequences - presented in a previous article referenced herein - to polynomial sequences fulfilling specific orthogonal conditions towards two given…
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…
Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the…
Given two permutable entire functions $f$ and $g,$ we establish vital relationship between escaping sets of entire functions $f, g$ and their composition. We provide some families of transcendental entire functions for which Eremenko's…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…
The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…
This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.