Related papers: Alternative Orthogonal Rational Functions on a Hal…
We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via…
We study seminormalization of affine complex varieties. We show that polynomials on the seminormalization correspond to the rational functions which are continuous for the Euclidean topology. We further study this type of functions which…
Work in progress concerning alternative formalizations of arithmetic.
A new version of Farkas lemma of alternative linear systems is proposed. One and the same matrix $A$ and vector $b$ have always been used in alternative linear systems. The paper shows a different way of alternative systems involving…
In this paper we study octonion regular functions and the structural differences between regular functions in octonion, quaternion, and Clifford analyses.
Systems of the form $x = (A x^s)^{1/s} + b$ arise in a range of economic, financial and control problems, where $A$ is a linear operator acting on a space of real-valued functions (or vectors) and $s$ is a nonzero real value. In these…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
We argue here that, as it happens in Classical and Quantum Mechanics, where it has been proven that alternative Hamiltonian descriptions can be compatible with a given set of equations of motion, the same holds true in the realm of…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
Notion of an open system of second order is introduced. Characteristic function for such an open system is obtained. Model representations of a quadratic non-self-adjoint operator pencil are found.
The authors review results implicit in their recent paper [2] on the product/quotient representation of rationals by rationals of the type $( an + b )/ ( An+ B )$ and give a detailed account of a particular related non-intuitive…
The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra.…
Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest…
Our paper introduces a novel method for calculating the inverse $\mathcal{Z}$-transform of rational functions. Unlike some existing approaches that rely on partial fraction expansion and involve dividing by $z$, our method allows for the…
The article is devoted to affine and wrap algebras over quaternions and octonions. Residues of functions of quaternion and octonion variables are studied. They are used for construction of such algebras. Their structure is investigated.
A rational function is the ratio of two complex polynomials in one variable without common roots. Its degree is the maximum of the degrees of the numerator and the denominator. Rational functions belong to the same class if one turns into…
Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi method. Integration of a set of equations of motion and the action function is discussed. It is shown that we have two types of integrable systems: a) ${\it…
In this paper we are interested in developments of elliptic functions of Jacobi. In particular a trigonometric expansion of the classical theta functions introduced by the author (Algebraic methods and q-special functions, Editors: C.R.M.…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…