Related papers: Factorization method for some inhomogeneous Lienar…
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
A new method for finding first integrals of discrete equations is presented. It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) formulation. The method is based on a newly established…
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric…
The scattering matrix for the full-line matrix Schr\"odinger equation is analyzed when the corresponding matrix-valued potential is selfadjoint, integrable, and has a finite first moment. The matrix-valued potential is decomposed into a…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller…
A sharp bound is obtained for the number of ways to express the monomial $X^n$ as a product of linear factors over $\mathbb{Z}/p^{\alpha}\mathbb{Z}$. The proof relies on an induction-on-scale procedure which is used to estimate the number…
This paper is devoted to establishing an enhanced Fritz John type first-order necessary condition for a general constrained nonlinear infinite-dimensional optimization problem. Unlike traditional constraint qualifications in optimization…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
We describe a method of obtaining closed-form complete solutions of certain second-order linear partial differential equations with more than two independent variables. This method generalizes the classical method of Laplace transformations…
Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are computational methods for partial differential equations that are…
In this paper we study the semilinear partial differential equations in the plane the linear part of which is written in a divergence form. The main result is given as a factorization theorem. This theorem states that every weak solution of…
We introduce a version of the Hamiltonian formalism based on the Clairaut equation theory, which allows us a self-consistent description of systems with degenerate (or singular) Lagrangian. A generalization of the Legendre transform to the…
In this paper we use the comparison method for investigation of first order polynomial differential equations. We prove two comparison criteria for these equations. The proved criteria we use to obtain some global solvability criteria for…
The problem of matrix factorization motivated by diffraction or elasticity is studied. A powerful tool for analyzing its solutions is introduced, namely analytical continuation formulae are derived. Necessary condition for commutative…
In this paper, we consider the following nonlinear system involving the fractional Laplacian \begin{equation} \left\{\begin{array}{ll} (-\Delta)^{s} u (x)= f(u,\,v), \\ (-\Delta)^{s} v (x)= g(u,\,v), \end{array} \right. (1) \end{equation}…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
A class of exact solutions is obtained for the Li\'{e}nard type ordinary non-linear differential equation. As a first step in our study the second order Li\'{e}nard type equation is transformed into a second kind Abel type first order…