Related papers: A Schwartz-Zippel Type Estimate for Homogenous Fin…

In this article we study the limiting empirical measure of zeros of higher derivatives for sequences of random polynomials. We show that these measures agree with the limiting empirical measure of zeros of corresponding random polynomials.…

We study global distribution of zeros for a wide range of ensembles of random polynomials. Two main directions are related to almost sure limits of the zero counting measures, and to quantitative results on the expected number of zeros in…

It is shown how the gauge of the ``regular finite initial value problem at spacelike infinity'' can be used to construct a certain type of estimates for the Maxwell field propagating on a Schwarzschild background. These estimates are…

We utilize the same technique as in [arXiv:2205.04254 (2022)] to provide some representations of polynomials non-negative on a basic semi-algebraic set, defined by polynomial inequalities, under more general conditions. Based on each…

We compute the maximum number of rational points at which a homogeneous polynomial can vanish on a weighted projective space over a finite field, provided that the first weight is equal to one. This solves a conjecture by Aubry, Castryck,…

There are several numerical methods for computing approximate zeros of a given univariate polynomial. In this paper, we develop a simple and novel method for determining sharp upper bounds on errors in approximate zeros of a given…

The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising…

We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…

In this paper, we study the arithmetics of skew polynomial rings over finite fields, mostly from an algorithmic point of view. We give various algorithms for fast multiplication, division and extended Euclidean division. We give a precise…

We describe two methods for computing the low-dimensional integral homology of the Mathieu simple groups and use them to make computations such as $H_5(M_{23},\ZZ)=\ZZ_7$ and $H_3(M_{24},\ZZ)=\ZZ_{12}$. One method works via Sylow subgroups.…

We utilize Cauchy's argument principle in combination with the Jacobian of a holomorphic function in several complex variables and the first moment of a ratio of two correlated complex normal random variables to prove explicit formulas for…

We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…

The polynomial method has been used recently to obtain many striking results in combinatorial geometry. In this paper, we use affine Hilbert functions to obtain an estimation theorem in finite field geometry. The most natural way to state…

In this short note, we describe the so-called homogeneous involution on finite-dimensional graded-division algebra over an algebraically closed field. We also compute their graded polynomial identities with involution. As pointed out by L.…

We study the supremum of some random Dirichlet polynomials and obtain sharp upper and lower bounds for supremum expectation that extend the optimal estimate of Hal\'asz-Queff\'elec and enable to cunstruct random polynomials with unusually…

We construct an effective algorithmic method to compute the homological monodromy of a complex polynomial which is tame. As an application we show the existence of conjugated polynomials in a number field which are not topologically…

This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed…

In this paper, by employ the cutoff function and the maximum principle, some Hamilton-Souplet-Zhang type gradient estimates for porous medium type equation are deduced. As a special case, an Hamilton-Souplet-Zhang type gradient estimates of…

We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials,…

We study the graded polynomial identities with a homogeneous involution on the algebra of upper triangular matrices endowed with a fine group grading. We compute their polynomial identities and a basis of the relatively free algebra,…