Related papers: Note on lower estimates of multiplicities
In this note, we provide a wide range of upper bounds for the moduli of the zeros of a complex polynomial. The obtained bounds complete a series of previous papers on the location of zeros of polynomials.
Define a(k,q) to be the smallest positive multiple of k such that the sum of its digits in base q is equal to k. The asymptotic behavior, lower and upper bound estimates of a(k,q) are investigated. A characterization of the minimality…
We consider the optimal discrimination of bipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition for a measurement to…
In this paper we show some multiplicity estimates theorems for a connected algebraic group (not necessarily commutative) $G$ over an algebraically closed subfield of $\mathbb{C}$. More specifically, under particular assumptions on the…
We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
We give a lower bound for the degree of an irreducible factor of a given polynomial. This improves and generalizes the results obtained in [4, On the irreducible factors of a polynomial, Proc. Amer. Math. Soc., 148 (2020] 1429 -- 1437].
We use an old elementary arithmetic argument to find new upper and lower bounds for Sylvester's denumerant function. These bounds are tight enough to get the asymptotic behavior of the denumerant.
We obtain a non--trivial upper bound for the multiplicative energy of any sufficiently large subset of a subvariety of a finite algebraic group. We also find some applications of our results to growth of conjugates classes, estimates of…
In this paper I prove a conjecture which gives a lower bound for the largest absolute value of the coefficients of the n-th cyclotomic polynomial for some n. Moreover this estimate is essentially sharp.
In this paper, based on a known formula, we use a simple idea to get a new representation for the density of Malliavin differentiable random variables. This new representation is particularly useful for finding lower bounds for the density.
We prove upper bounds for the Hilbert-Samuel multiplicity of standard graded Gorenstein algebras. The main tool that we use is Boij-S\"oderberg theory to obtain a decomposition of the Betti table of a Gorenstein algebra as the sum of…
We give upper bounds for the bottom of the essential spectrum of properly immersed minimal submanifolds of $\mathbb{R}^{n}$ in terms of their volume growth. Our result improves the extrinsic version of Brook's essential spectrum estimate…
The exact lower bound on the probability of the occurrence of exactly one of $n$ random events each of probability $p$ is obtained.
Depth of the Tukey median is investigated for empirical distributions. A sharper upper bound is provided for this value for data sets in general position. This bound is lower than the existing one in the literature, and more importantly…
We consider the approximate minimization of a given polynomial on the standard simplex, obtained by taking the minimum value over all rational grid points with given denominator ${r} \in \mathbb{N}$. It was shown in [De Klerk, E., Laurent,…
We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy lower bounds when the initial problem formulation exhibits a high degree of symmetry. Our main technical theorem allows us to reduce the study of the positive…
We give an exponential lower bound for Berge-Ramsey problems.
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…
We provide an elementary proof of the lower bound for the variance of continuous unimodal distributions and obtain analogous bounds for the higher order central moments. A lower bound for the rth central moment of discrete distribution is…