相关论文: Inverse Approach In The Study Of Ordinary Differen…
We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the $\mathfrak{su}(1,1)$ current algebra. We introduce raising, lowering, and neutral…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
Since its original publication in 1916 under the title "The Algebraic Theory of Modular Systems", the book by F. S. Macaulay has attracted a lot of scientists with a view towards pure mathematics (D. Eisenbud,...) or applications to control…
Current techniques for formally verifying circuits implemented in Galois field (GF) arithmetic are limited to those with a known irreducible polynomial P(x). This paper presents a computer algebra based technique that extracts the…
We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces,…
We consider the problem of reconstruction of an $n\times n$ matrix with coefficients depending rationally on $x\in \mathbb P^1$ from the data of: (a) its characteristic polynomial and (b) a line bundle of degree $g+n-1$, with $g$ the…
Under investigation in this work is the robust inverse scattering transform of the discrete Hirota equation with nonzero boundary conditions, which is applied to solve simultaneously arbitrary-order poles on the branch points and spectral…
We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
The classical Center-Focus Problem posed by H. Poincar\'e in 1880's is concerned on the characterization of planar polynomial vector fields $X=(-y+P(x,y))\dfrac{\partial}{\partial x}+(x+Q(x,y))\dfrac{\partial}{\partial y},$ with…
We focus on a chaotic differential system in 3-dimension, including an absolute term and a line of equilibrium points. Which describes in the following This system has an implementation in electronic components. The first purpose of this…
In this paper we will discuss the Dirichlet problem of nonlinear second order partial differential equations resolved with any derivatives. First, we transform it into generalized integral equations. Next, we discuss the existence of the…
In this work, we propose a new approach called ``stationary reduction method based on nonisospectral deformation of orthogonal polynomials" for deriving discrete Painlev\'{e}-type (d-P-type) equations. We apply this approach to…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…
The paper represents the method for construction of the families of particular solutions to some new classes of $(n+1)$ dimensional nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic…
In the last two decades, many algebras of generalized functions have been constructed, particularly the so-called generalized Sobolev algebras. Our goal is to study the latter and some of their main properties. In this framework, we pose…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
We prove that to each real singularity $f: (\mathbb{R}^{n}, 0) \to (\mathbb{R}^k, 0)$ with $k\geq 2$ one can associate systems of differential equations $\mathfrak{g}^{k}_f$ which are pushforwards in the category of $\mathcal{D}$-modules…
Here we give a complete group classification of the general case of linear systems of three second-order ordinary differential equations excluding the case of systems which are studied in the literature. This is given as the initial step in…