Related papers: Composition with a two variable function
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
In the present article, composition operators induced by Rational Inner Functions on the bidisc $\mathbb{D}^2$ are studied, acting on the weighted Bergman space $A^2_{\beta}(\mathbb{D}^2).$ We prove that under mild conditions that Rational…
In this work, we construct commutative rings of two variable matrix differential operators that are isomorphic to a ring of meromorphic functions on a rational manifold obtained from the $CP^1\times CP^1$ by identification of two lines with…
We present two theorems concerned with algorithmic randomness and differentiability of functions of several variables. Firstly, we prove an effective form of the Rademacher's Theorem: we show that computable randomness implies…
If two random variables X and A are functionally related via f(X)=A for some strictly monotone continuously differentiable function f:R->R, the distribution of X may easily be computed from the distribution of A.
We define two natural classes of functions, called 2-open and 2-closed, that are closest to open and closed functions. We show that they have the following property: there are $X_i \subset X$ $ (i=1,2,...$) such that $f|X_i$ are open or…
The examples of rhythmical signals with variable period are considered. The definition of periodic function with the variable period is given as a model of such signals. The examples of such functions are given and their variable periods…
A simple and very accurate method to approximate a function with a finite number of discontinuities is presented. This method relies on hyperbolic tangent functions of rational arguments as connecting functions at the discontinuities, each…
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…
The aim of this work is to develop a theory parallel to that of motivic complexes based on cycles and correspondences with coefficients in quadratic forms. This framework is closer to the point of view of $\mathbb{A}^1$-homotopy than the…
The circular orbits and elliptical orbits of moving objects in a gravitational field are essential information in astronomy. There have been many methods developed in the literature and textbooks to describe these orbits. In this report, I…
Various formulas for reciprocals of densely defined weighted composition operators in $L^2$-spaces as well as for their adjoints are provided. The relation between the reciprocal of a weighted composition operator and the product of the…
It is obtained necessary and sufficient conditions of dependence on $\aleph$ coordinates for functions of several variables, each of which is a product of metrizable factors. The set of discontinuity points of such functions is…
In this work we show a technique that allows for the musical interpretation of the brightness variations of stars. This method allows composers a lot of freedom to incorporate their own ideas into the score, based on the melodic line…
In this paper we present a mathematical way of defining musical modes, we derive a formula for the total number of modes and define the musicality of a mode as the total number of harmonic chords whithin the mode. We also give an algorithm…
We achieve compositions rules for the geometric parameters of the composed rotations, which is in a certain sense analogous to the well known Rodrigues formula. We also obtain a necessary and sufficient condition for a composition of two…
Modifiable combining functions are a synthesis of two common approaches to combining evidence. They offer many of the advantages of these approaches and avoid some disadvantages. Because they facilitate the acquisition, representation,…
Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal…
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.