Related papers: A comparison principle for convolution measures wi…
We generalize the Yao-Yao partition theorem by showing that for any smooth measure in $R^d$ there exist equipartitions using $(t+1)2^{d-1}$ convex regions such that every hyperplane misses the interior of at least $t$ regions. In addition,…
We study the corrections to $\epsilon^\prime /\epsilon$ in the minimal supersymmetric model at the leading order in QCD and QED. Supersymmetry can increase the standard model prediction for $\epsilon^\prime /\epsilon$ by at most 40\% for…
We present a direct confirmation of the validity of the equivalence principle for unstructured test bodies in scalar tensor gravity. Our analysis is complementary to previous approaches and valid for a large class of scalar-tensor theories…
In this review we aim to describe the most stringent tests of the strong equivalence principle, the fundamental principle of General Relativity, using pulsar timing. For this purpose, we first construct the parametrized post-Newtonian and…
Building on the first two authors' previous results, we prove a general criterion for convergence of (possibly singular) Bergman measures towards equilibrium measures on complex manifolds. The criterion may be formulated in terms of growth…
We prove convolution estimates for affine arclength measure on certain flat curves in dimensions 2, 3, and 4.
We postulate the applicability of the general form-invariance principle in special relativity. It is shown that this principle holds in classical mechanics. Some examples of transformations between the reference frames which satisfy this…
Given $n$ independent random marked $d$-vectors $X_i$ with a common density, define the measure $\nu_n = \sum_i \xi_i $, where $\xi_i$ is a measure (not necessarily a point measure) determined by the (suitably rescaled) set of points near…
In this paper, we investigate the convergence properties of Fourier partial sums associated with general orthonormal systems, focusing on functions that belong to specific differentiable function classes. While classical Fourier analysis…
We give examples of measures on certain k-surfaces in R^d. These measures satisfy convolution estimates which are nearly optimal.
For a convex domain $D$ that is enclosed by the hypersurface $\partial D$ of bounded normal curvature, we prove an angle comparison theorem for angles between $\partial D$ and geodesic rays starting from some fixed point in $D$, and the…
We prove mean comparison from a different perspective, where we introduce the concept of partial convolution.
We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…
Derived from the results in [Giang et al.: \emph{Convolutions for the Fourier transforms with geometric variables and applications}, Math. Nachr. 283(12) (2010), 1758--1770], in this paper, we devoted to studying the boundedness properties…
This paper investigates the relationship between various measure-theoretic properties of U-statistics with fixed sample size $N$ and the same properties of their kernels. Specifically, the random variables are replaced with elements in some…
We introduce cosurfaces with values in the group \(\PC_n(H)\) of \(H\)-valued reciprocal pairwise comparison matrices. The composition law is covariant on upper triangular coefficients and contravariant on lower triangular coefficients,…
The next generation of large scale surveys will not only measure cosmological parameters within the framework of General Relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations,…
In this work we analyze a convex-programming method for estimating superpositions of point sources or spikes from nonuniform samples of their convolution with a known kernel. We consider a one-dimensional model where the kernel is either a…
We examine Fourier frames and, more generally, frame measures for different probability measures. We prove that if a measure has an associated frame measure, then it must have a certain uniformity in the sense that the weight is distributed…
Let $d\ge3$ and $\mathbb{F}_q^{\,d}$ be the $d$-dimensional vector space over a finite field of order $q$, where $q$ is an odd prime power. Let $X_\pi$ be the set of lines through the origin intersecting the slice $\pi\cap S^{d-1}$, where…