Related papers: Graphical criteria for positive solutions to linea…
We describe a method for solving linear systems over the localization of a commutative ring $R$ at a multiplicatively closed subset $S$ that works under the following hypotheses: the ring $R$ is coherent, i.e., we can compute finite…
Semipositive matrices (matrices that map at least one nonnegative vector to a positive vector) and minimally semipositive matrices (semipositive matrices whose no column-deleted submatrix is semipositive) are well studied in matrix theory.…
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…
We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (i) if the underlying generalized chemical reaction network has an effective…
We derive a closed expression for the number of nonnegative solutions of a certain system of linear Diophantine equations. The motivation comes from high energy physics where the nonnegative solutions play a crucial role in the perturbative…
We discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities. We prove the existence of…
Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a…
In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of…
An appropriate visualization of multiobjective non-dominated solutions is a valuable asset for decision making. Although there are methods for visualizing the solutions in the design space, they do not provide any information about their…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
In this paper, we present and analyze methods for solving a system of linear equations over idempotent semifields. The first method is based on the pseudo-inverse of the system matrix. We then present a specific version of Cramer's rule…
We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our…
Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…
A system of linear equations $L$ is said to be norming if a natural functional $t_L(\cdot)$ giving a weighted count for the set of solutions to the system can be used to define a norm on the space of real-valued functions on…
A system of linear equations is normally understood as a linear mapping between two vector spaces. However, most direct solutions (e.g., QR, LU, ...) rely on the inelegant approach of back-substitution: a significant departure from such a…
We investigate the existence, non-existence, and multiplicity of positive solutions to a class of quasilinear Schrodinger equations with a prescribed mass condition in higher dimensions. Using the dual approach, the equation is transformed…
We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a…