Results 31 to 40 of about 22,180 (168)

First Integrals and Invariants of Systems of Ordinary Differential Equations

Mathematics
We investigate the interplay between monomial first integrals, polynomial invariants of certain group action, and the Poincaré–Dulac normal forms for autonomous systems of ordinary differential equations with a diagonal matrix of the linear part.
Mateja Grašič, Abdul Salam Jarrah, Valery G. Romanovski   +2 more
doaj   +1 more source

Differential operators on monomial curves

Journal of Algebra, 2003
Let \(k\) be a fixed algebraically closed field of characteristic 0, and \(X\) an affine monomial curve defined over \(k\). Then, \(X = \text{Spec}(A)\), where \(A=k[\Gamma]\) is the semigroup algebra over \(k\) defined by a numerical semigroup \(\Gamma\subseteq {\mathbb N}_0\).
openaire   +2 more sources

Insights into New Generalization of q-Legendre-Based Appell Polynomials: Properties and Quasi Monomiality

Mathematics
In this paper, by using the zeroth-order q-Tricomi functions, the theory of three-variable q-Legendre-based Appell polynomials is introduced.
Naeem Ahmad, Waseem Ahmad Khan
doaj   +1 more source

CONNECTION FORMULAS AND REPRESENTATIONS OF LAGUERRE POLYNOMIALS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS

Проблемы анализа, 2019
In this paper, we introduce the notion of Oε-classical orthogonal polynomials, where Oε := I + εD (ε 6= 0). It is shown that the scaled Laguerre polynomial sequence {a −nL (α) n (ax)}n>0, where a = −ε −1 , is actually the only Oε-classical ...
B. Aloui, L. Kheriji
doaj   +1 more source

Dynamical system approach of non-minimal coupling in holographic cosmology

Nuclear Physics B, 2019
We study the dynamical system approach of non-minimally coupled scalar field to induced gravity on the brane in the framework of holographic cosmology. In this context, we derive the modified Friedmann equation and the equation of motion. The dynamics of
Aatifa Bargach, Farida Bargach, Taoufik Ouali   +2 more
doaj   +1 more source

Minimal Involutive Bases

, 1997
In this paper we present an algorithm for construction of minimal involutive polynomial bases which are Groebner bases of the special form. The most general involutive algorithms are based on the concept of involutive monomial division which leads to ...
Blinkov, Yuri A., Gerdt, Vladimir P.
core   +3 more sources

Monomial summability and doubly singular differential equations

Journal of Differential Equations, 2007
In this work, we consider systems of differential equations that are doubly singular, i.e. that are both singularly perturbed and exhibit an irregular singular point. Under a condition that also guanrantees the existence of a unique formal solution, we show that this formal solution is monomially summable, i.e.
Canalis-Durand, Mireille, Mozo-Fernández, Jorge, Schäfke, Reinhard   +2 more
openaire   +3 more sources

Differential operators on monomial rings

Journal of Pure and Applied Algebra, 1999
A similar question as in the paper reviewed above [\textit{A. Eriksson}, Commun. Algebra 26, No. 12, 4007-4013 (1998; Zbl 0943.13020)] is considered under more general assumptions, especially in the case where \(k\) has positive characteristic. Apart from the main result (loc.
openaire   +2 more sources

Bivariate q-Laguerre–Appell polynomials and their applications

Applied Mathematics in Science and Engineering
Recently, the monomiality principle has been extended to q-polynomials, namely, the q-monomiality principle of q-Appell polynomials has been considered.
Mohammed Fadel, Nusrat Raza, Ahmed Al-Gonah, Ugur Duran   +3 more
doaj   +1 more source

QUASI-EXACTLY SOLVABLE SCHRÖDINGER EQUATIONS, SYMMETRIC POLYNOMIALS AND FUNCTIONAL BETHE ANSATZ METHOD

Acta Polytechnica, 2018
For applications to quasi-exactly solvable Schrödinger equations in quantum mechanics, we consider the general conditions that have to be satisfied by the coefficients of a second-order differential equation with at most k + 1 singular points in order ...
Christiane Quesne
doaj   +1 more source