Related papers: A Refined Denominator Bounding Algorithm for Multi…
In this paper we propose a conseptual framework for the observed properties of discriminants of polylinear forms. The connection with classical problems of linear algebra is shown. A new class of algebraic varieties (hypergrassmanians) is…
The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures,…
There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…
This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…
In this paper, we investigate how the initial models and the final models for the polynomial functors can be uniformly specified in matching logic.
We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.
We present a new algorithm for solving a polynomial program P based on the recent "joint + marginal" approach of the first author for, parametric optimization. The idea is to first consider the variable x1 as a parameter and solve the…
We are concerned with the problem of decomposing the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains.…
A class of self-inversive polynomials includes all the self-reciprocal polynomials. Let A denote the set of all self-reciprocal polynomials with n+1 coefficients. Let B denote the set of certain self-inversive and non self-reciprocal…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…
For any polynomial $P \in \mathbb{C}[X_1,X_2,...,X_n]$, we describe a $\mathbb{C}$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$…
The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor…
A new deterministic algorithm for finding square divisors, and finding $r$-power divisors in general, is presented. This algorithm is based on Lehman's method for integer factorization and is straightforward to implement. While the…
In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…