Related papers: Equivalence for Differential Equations
We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…
We examine an elementary problem on prime divisibility of binomial coefficients. Our problem is motivated by several related questions on alternating groups.
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.
The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the…
A quandle will be called quasi-affine, if it embeds into an affine quandle. Our main result is a characterization of quasi-affine quandles, by group-theoretic properties of their displacement group, by a universal algebraic condition coming…
In this paper we prove transference inequalities for regular and uniform Diophantine exponents in the weighted setting. Our results generalize the corresponding inequalities that exist in the `non-weighted' case.
We show that the umbral correspondence between differential equations can be achieved by means of a suitable transformation preserving the algebraic structure of the problems. We present the general properties of these transformations,…
The law of transformation of affine connection for n-dimensional manifolds as the system of nonlinear equations on local coordinates of manifold is considered. The extension of the Darboux-Lame system of equations to the spaces of constant…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
Group classification of classes of mKdV-like equations with time-dependent coefficients is carried out. The usage of equivalence transformations appears a crucial point for the exhaustive solution of the problem. We prove that all the…
In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems would contribute substantially to the…
This paper studies systems of linear difference equations on the lattice $\Z^n$ that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of…
In this paper, we study non-linear differential equations associated with Legendre polynomials and their applications. From our study of non- linear differential equations, we derive some new and explicit identities for Legendre…
This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the H\"older regularity of the data. By…
The main aim of this paper is the investigation of the stability problem for ordinary delay differential equations. More precisely, we would like to study the following problem. Assume that for a continuous function a given delay…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…