Related papers: Positivity of continuous piecewise polynomials

We consider min-max optimization problems for polynomial functions, where a multivariate polynomial is maximized with respect to a subset of variables, and the resulting maximal value is minimized with respect to the remaining variables.…

Let $f:\mathbb{K}^n\rightarrow\mathbb{K}^m$ be a generically finite polynomial map of degree $d$ between affine spaces. In arXiv:1411.5011 we proved that if $\mathbb{K}$ is the field of complex or real numbers, then the set $S_f$ of points…

A novel method with two variations is proposed with which the number of positive and negative zeros of a polynomial with real coefficients and degree $n$ can be restricted with significantly better determinacy than that provided by the…

Let L be the zero set of a nonconstant monic polynomial with complex coefficients. In the context of constructive mathematics without countable choice, it may not be possible to construct an element of L. In this paper we introduce a notion…

This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…

To directed graphs with unique sink and source we associate a noncommutative associative alsgebra and a polynomial over this algebra. Edges of the graph correspond to pseudo-roots of the polynomial. We give a sufficient condition when…

The main goal of this article is to provide a proof of the Pederson-Roy-Szpirglas theorem about counting common real zeros of real polynomial equations by using basic results from Linear algebra and Commutative algebra. The main tools are…

Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is…

In this paper we consider images of (ordinary) noncommutative polynomials on matrix algebras endowed with a graded structure. We give necessary and sufficient conditions to verify that some multilinear polynomial is a central polynomial, or…

We show that if a compact complex manifold admits a K\"ahler metric whose holomorphic sectional curvature is everywhere non positive and strictly negative in at least one point, then its canonical bundle is positive.

This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…

We introduce the moduli space of generic piecewise circular $n$-gons in the Riemann sphere and relate it to a moduli space of Legendrian polygons. We prove that when $n=2k$, this moduli space contains a connected component homeomorphic to…

In this paper, we consider matrices whose entries are combinatorial sequences which can be expressed in terms of a convolution of elementary and complete homogeneous symmetric functions. We establish the total positivity of these matrices…

The paper studies strictly positive definite kernels on compact Riemannian manifolds. We state new conditions to ensure strict positive definiteness for general kernels and kernels with certain convolutional structure. We also state…

A variant of Li-Tam theory, which associates to each end of a complete Riemannian manifold a positive solution of a given Schr\"odinger equation on the manifold, is developed. It is demonstrated that such positive solutions must be of…

We introduce and study a cone which consists of a class of generalized polynomial functions and which provides a common framework for recent non-negativity certificates of polynomials in sparse settings. Specifically, this…

The paper studies the complex 1-dimensional polynomial vector fields with real coefficients under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a…

The theory of total positivity for reductive groups is here extended to the case of symmetric spaces.

Polynomial completeness results aim at characterizing those functions that are induced by polynomials. Each polynomial function is congruence preserving, but the opposite need not be true. A finite algebraic structure $\mathbf{A}$ is called…

For a polynomial $P$ of degree greater than one, we show the existence of patterns of the form $(x,x+t,x+P(t))$ with a gap estimate on $t$ in positive density subsets of the reals. This is an extension of an earlier result of Bourgain. Our…