Related papers: On generating relative and absolute invariants of …
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
Loop invariants are properties of a program loop that hold both before and after each iteration of the loop. They are often used to verify programs and ensure that algorithms consistently produce correct results during execution.…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
This note compares the usual (absolute) Gromov-Witten invariants of a symplectic manifold with the invariants that count the curves relative to a (symplectic) divisor D. We give explicit examples where these invariants differ even though it…
An algorithm is given for computing explicit formulas for the generators of relations among the invariant rational functions for vector-valued bilinear forms. These formulas have applications in the geometry of Riemannian submanifolds and…
We present an exposition of a method of discretizing ordinary differential equations while preserving their Lie point symmetries. This method is very general and can be applied to any ODE with a nontrivial symmetry group. The method is…
Always dealing with an arbitrary field we consider the variety $(k^{n\times n})^{p}$ under the action of $GL_{n}$ by simultaneous similarity. We define discrete and continuous invariants which completely determine the orbits. The discrete…
Loop invariants are software properties that hold before and after every iteration of a loop. As such, invariants provide inductive arguments that are key in automating the verification of program loops. The problem of generating loop…
A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra f. Under certain conditions f-invariant systems of differential…
A classification of ordinary differential equations and finite-difference equations in one variable having polynomial solutions (the generalized Bochner problem) is given. The method used is based on the spectral problem for a polynomial…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…
In this work we obtain the general form of polynomial mappings that commute with a linear action of a relative symmetry group. The aim is to give results for relative equivariant polynomials that correspond to the results for relative…
We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and…
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…
A method based on infinite parameter conservation laws is described to factor linear differential operators out of nonlinear partial differential equations (PDEs) or out of differential consequences of nonlinear PDEs. This includes a…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
The invariants of all complex solvable rigid Lie algebras up to dimension eight are computed. Moreover we show, for rank one solvable algebras, some criteria to deduce to non-existence of non-trivial invariants or the existence of…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…