相关论文: Discrepancy and approximation of absolutely contin…

For a probability measure $\mu$ on $[0,1]$ without discrete component, the best possible order of approximation by a finite point set in terms of the star-discrepancy is $\frac{1}{2N}$ as has been proven relatively recently. However, if…

For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.

In a recent publication [Ferreira {\it et al.}, Phys. Rev. D89 (2014) 083011] we tested the consistency of current astrophysical tests of the stability of the fine-structure constant $\alpha$ and the proton-to-electron mass ratio…

Standard Quantum Physics states that the outcome of measurements for some distant entangled subsystems are instantaneously statistically correlated, whatever their mutual distance. This correlation presents itself as if there were a…

In this note we study estimates from below of the single radius spherical discrepancy in the setting of compact two-point homogeneous spaces. Namely, given a $d$-dimensional manifold $\mathcal M$ endowed with a distance $\rho$ so that…

Recently, the much-used trace distance of coherence was shown to not be a proper measure of coherence, so a modification of it was proposed. We derive an explicit formula for this modified trace distance of coherence on pure states. Our…

A complete theory of overmeasurement by measuring refinements of observables is presented. It encompasses a wider set of functions of observ- ables (coarsenings) . Thus the theory has a broad potential application.It is applied to a…

This paper is devoted to the study of a discrepancy-type characteristic -- the fixed volume discrepancy -- of the Korobov point sets in the unit cube. It was observed recently that this new characteristic allows us to obtain optimal rate of…

The indeterminacy inherent in quantum measurement is an outstanding character of quantum theory, which manifests itself typically in Heisenberg's error-disturbance uncertainty relation. In the last decade, Heisenberg's relation has been…

This paper shows that finitely additive measures occur naturally in very general Divergence Theorems. The main results are two such theorems. The first proves the existence of pure normal measures for sets of finite perime- ter, which yield…

For a large class of Cantor sets on the real-line, we find sufficient and necessary conditions implying that a set has positive (resp. null) measure for all doubling measures of the real-line. We also discuss same type of questions for…

We present a measurement of the mass difference between top ($t$) and anti-top ($\bar{t}$) quarks using $t\bar{t}$ candidate events reconstructed in the final state with one lepton and multiple jets. We use the full data set of Tevatron…

We construct dynamics for the defocusing real-valued (Miura) mKdV equation on the real line with initial data distributed according to Gibbs measure. We also prove that Gibbs measure is invariant under these dynamics. On the way, we provide…

Problems of absolute G measurements, its temporal and range variations from both experimental and theoretical points of view are discussed, and a new universal space project for measuring G, G(r) and G-dot promising an improvement of our…

In this paper a free analogous of completely random measure is introduced. Furthermore, a representation theorem is proved for free completely random measures that are free infinitely divisible.

It was proven by Ures that $C^1$ diffeomorphism on three dimensional torus that is derived from Anosov admits a unique maximal measure. Here we show that the maximal measure has exponential decay of correlations for H\"older observables,…

The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…

Atomic dark matter is a simple but highly theoretically motivated possibility for an interacting dark sector that could constitute some or all of dark matter. We perform a comprehensive study of precision cosmological observables on minimal…

For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…

Discrepancy measures how uniformly distributed a point set is with respect to a given set of ranges. There are two notions of discrepancy, namely continuous discrepancy and combinatorial discrepancy. Depending on the ranges, several…