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Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…
We find a formula for the number of solutions of linear congruence systems, by using elementary methods.
In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases.
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
This note considers fairly general quasi-homogeneous systems of first-order nonlinear ODEs and homogeneous systems of second-order nonlinear ODEs that contain arbitrary functions of several arguments. It presents several exact solutions to…
In this paper, we first show the existence of solutions to the following system of nonlinear equations \begin{eqnarray*}\left\{\begin{array}{l} a_{11}x_1+a_{12}x_2+a_{13}x_3+\cdots+a_{1n}x_{n} =…
This paper presents a finite step method for computing the binary solution to an overdetermined system of linear algebraic equations Ax = b, where A is an m x n real matrix of rank n < m, and b is a real m-vector. The method uses the…
In this work, we study the existence and nonexistence of solution for strongly coupled elliptic systems to m-parameters.
We give a method to determine an explicit solution to a system of two inhomogeneous linear recursive sequences of higher order. Our approach can be used efficiently in solving certain combinatorial problems. We finish the paper by…
This note further addresses the global optimization problem for max-plus linear systems considered in [Automatica 119 (2020) 109104]. Firstly, the operations between infinity elemens and real numbers involved in the formulas of solving…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
In order to nd a non-negative solution to a system of inequalities, the corresponding dual problem is composed, which has a suitable unity basic matrix. In such a formulation, the objective function is replaced by set of constraints based…
We introduce and study minimal (with respect to inclusion) solutions of systems of tropical linear differential equations. We describe the set of all minimal solutions for a single equation. It is shown that any tropical linear differential…
In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in…
Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…
We investigate the doubling inequality and nodal sets for the solutions of bi-Laplace equations. A polynomial upper bound for the nodal sets of solutions and their gradient is obtained based on the recent development of nodal sets for…
Equivalencies of many basic elementary inequalities are given
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…