Related papers: An improved lower bound for the $L_2$-discrepancy

Determining the induced L2 norm of a linear, parameter-varying (LPV) system is an integral part of many analysis and robust control design procedures. Most prior work has focused on efficiently computing upper bounds for the induced L2…

We show that for $0<\gamma, \gamma' <1$ and for measurable subsets of the unit square with Lebesgue measure $\gamma$ there exist bi-Lipschitz maps with bounded Lipschitz constant (uniformly over all such sets) which are identity on the…

In this paper, we obtain the upper and lower bounds for two inequalities related to the range statistics. The first one is concerning the one-variable case and the second one is about the bivariate case.

The divergence condition is reformulated in the scaled boundary coordinates so as to prevent the spurious solutions in the finite element formulation.

We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds. They almost match the best known bounds for unbounded metric TSP problems. In…

New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…

In this paper we propose an acceptance-rejection sampler using stratified inputs as diver sequence. We estimate the discrepancy of the points generated by this algorithm. First we show an upper bound on the star discrepancy of order…

In this paper we give an improved upper bound, as compared to the one given in [3] for the number of extreme points of the convex set of all G-invariant probability measures on X*Y with given marginals of full support.

Given a large finite point set, $P\subset \mathbb R^2$, we obtain upper bounds on the number of triples of points that determine a given pair of dot products. That is, for any pair of positive real numbers, $(\alpha, \beta)$, we bound the…

We fix an error in the bound obtained in [13] for the crossing number of wrapped butterflies. The new bound finer than the one provided earlier.

We derive lower bounds for the essential spectrum of the Hodge-Laplacian on geometrically finite orbifolds and their suborbifolds.

We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required…

We give a lower bound on the Ulrich complexity of hypersurfaces of dimension $n \ge 6$. The bound improves the result in [BES] for $n \le 78$.

We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.

In this short note we obtain new lower bounds for the constants of the real Hardy--Littlewood inequality for $m$-linear forms on $\ell_{p}^{2}$ spaces when $p=2m$ and for certain values of $m$. The real and complex cases for the general…

In this paper we present three different results dealing with the number of $(\leq k)$-facets of a set of points: 1. We give structural properties of sets in the plane that achieve the optimal lower bound $3\binom{k+2}{2}$ of $(\leq…

An improved lower bound is given for the decay of conical averages of Fourier transforms of measures, for cones of dimension $d \geq 4$. The proof uses a weighted version of the broad restriction inequality, a narrow decoupling inequality…

This paper studies a uniform projection criterion for space-filling designs under the stratified $L_2$-discrepancy. The criterion, denoted by $\Phi_{SD}$, is the average squared stratified $L_2$-discrepancy over all two-dimensional…

Pseudoline arrangements are fundamental objects in discrete and computational geometry, and different works have tackled the problem of improving the known bounds on the number of simple arrangements of $n$ pseudolines over the past…

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…