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This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
Many authors studied numeric algorithms for solving the linear systems of the pentadiagonal type. The well-known Fast Pentadiagonal System Solver algorithm is an example of such algorithms. The current article are described new numeric and…
The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known…
We give several algorithms addressing computations of intersections of conjugate subgroups.
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
A method is presented for using the consistent part of inconsistent axiomatic systems.
In the paper we consider the linear underdetermined system of a special type. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a…
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
The congruence orbit of a matrix has a natural connection with the linear complementarity problem on simplicial cones formulated for the matrix. In terms of the two approaches -- the congruence orbit and the family of all simplicial cones…
Motivated by the theory of self-duality which provides a variational formulation and resolution for non self-adjoint partial differential equations \cite{G1, G2}, we propose new templates for solving large non-symmetric linear systems. The…
Based the homogeneous balance method, a general method is suggested to obtain several kinds of exact solutions for some kinds of nonlinear equations. The validity and reliability of the method are tested by applying it to the Bousseneq…
In this paper we study the existence of solutions to an isotropic differential inclusion.
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.