Related papers: On the Structure of Compatible Rational Functions
Algorithms for computing rational generating functions of solutions of one-dimensional difference equations are well-known and easy to implement. We propose an algorithm for computing rational generating functions of solutions of…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…
A permutation rational function $f\in \mathbb{F}_q(x)$ is a rational function that induces a bijection on $\mathbb{F}_q$, that is, for all $y\in\mathbb{F}_q$ there exists exactly one $x\in\mathbb{F}_q$ such that $f(x)=y$. Permutation…
Formal verification using the model checking paradigm has to deal with two aspects: The system models are structured, often as products of components, and the specification logic has to be expressive enough to allow the formalization of…
The extended L\"uroth's Theorem says that if the transcendence degree of $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)/\KK$ is 1 then there exists $f \in \KK(\underline{X})$ such that $\KK(\mathsf{f}_1,\dots,\mathsf{f}_m)$ is equal to $\KK(f)$. In…
A unified algebraic interpretation of both finite families of orthogonal polynomials and biorthogonal rational functions of $q$-Hahn type is provided. The approach relies on the meta $q$-Hahn algebra and its finite-dimensional bidiagonal…
We describe the structure of all codimension-two lattice configurations $A$ which admit a stable rational $A$-hypergeometric function, that is a rational function $F$ all whose partial derivatives are non zero, and which is a solution of…
A rational homogeneous (of degree one) positive real matrix-valued function is presented as the Schur complement of a block of the linear pencil with positive semidefinite matrix coefficients. The partial derivative numerators of a rational…
We describe the qFunctions Mathematica package for $q$-series and partition theory applications. This package includes both experimental and symbolic tools. The experimental set of elements includes guessers for $q$-shift equations and…
We present in this paper a general algorithm for solving first-order formulas in particular theories called "decomposable theories". First of all, using special quantifiers, we give a formal characterization of decomposable theories and…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same…
We characterize pairs of rational functions $A$, $B$ such that $A$ is semiconjugate to $B$, and $B$ is semiconjugate to $A$.
Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $q$-partial differential equations, then, it can be expanded in terms of the product of…
This essay contains three parts. The first part of essay focuses on the hypothesis of the functional semantic constructions (FSC-Hypothesis). This hypothesis explains that a language, a number, a money are the functional semantic…
This paper intends to lay the theoretical foundation for the method of functional maps, first presented in 2012 by Ovsjanikov, Ben-Chen, Solomon, Butscher and Guibas in the field of the theory and numerics of maps between shapes. We show…
We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between…
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…