Related papers: Fibers of Polynomial Mappings Over Rn

This work is divided into three parts. The first part concerns polynomials in one variable with all real roots. We consider linear transformations that preserve real rootedness, as well as matrices that preserve interlacing. The second part…

In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials

We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.

In this paper we introduce a class of constraint logic programs such that their termination can be proved by using affine level mappings. We show that membership to this class is decidable in polynomial time.

In this note we consider roots of multivariate polynomials over a finite grid. When given information on the leading monomial with respect to a fixed monomial ordering, the footprint bound [8, 5] provides us with an upper bound on the…

In this paper we consider polynomial representability of functions defined over $Z_{p^n}$, where $p$ is a prime and $n$ is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to…

Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…

Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…

This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

We prove that a family of varieties is birationally isotrivial if all the fibers are birational to each other.

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…

We prove that polynomial valuations on vector lattices correspond to orthosymmetric multilinear maps. As a consequence we obtain a concise proof of the equivalence of orthosymmetry and orthogonal additivity.

We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…

It is proved that each of compact linear groups of one special type admits a polynomial factorization map onto a real vector space. More exactly, the group is supposed to be non-commutative one-dimensional and to have two connected…

This paper proves that the characteristic polynomial is a complete unitary invariant for pairs of projection matrices. Some special cases involving three or more projections are also considered.

In this paper we study the density of polynomials in some $L^2(M)$ spaces. Two choices of the measure $M$ and polynomials are considered: 1) a $(N\times N)$ matrix non-negative Borel measure on $\mathbb{R}$ and vector-valued polynomials…

In this paper we study the following family of hypergeometric polynomials: $y_n(x) = \frac{ (-1)^\rho }{ n! } x^n {}_2 F_0(-n,\rho;-;-\frac{1}{x})$, depending on a parameter $\rho\in\mathbb{N}$. Differential equations of orders $\rho+1$ and…

In this short note we prove the Iitaka C_nm conjecture for algebraic fiber spaces over surfaces

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…