Related papers: Achievable Cantorvals almost without reversed Kake…
We prove a conjecture of Lecouvey, which proposes a closed, positive combinatorial formula for symplectic Kostka-Foulkes polynomials, in the case of rows of arbitrary weight. To show this, we construct a new algorithm for computing…
The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskii, Tseitin, Kreisel, and Lacombe assert the existence of NON-empty co-r.e. closed sets devoid of computable points: sets which are…
This paper presents a new derivation method of converse bounds on the non-asymptotic achievable rate of discrete weakly symmetric memoryless channels. It is based on the finite blocklength statistics of the channel, where with the use of an…
The paper is devoted to the study of extremal points of $\mathcal{C}$, the family of all two-variate coherent distributions on $[0,1]^2$. It is well-known that the set $\mathcal{C}$ is convex and weak$^*$ compact, and all extreme points of…
New estimates of the potentials of solutions to the compressible Navier-Stokes equations are derived. The result obtained are applied to boundary value problems for the compressible Navier-Stokes equations with the critical adiabatic…
Renormalized vacuum expectation values of electromagnetic stress-energy tensor are calculated in the background spherically-symmetrical metric of the wormhole's topology. Covariant geodesic point separation method of regularization is used.…
It was pointed out to us that the proof of a crucial lemma (Lemma 5.3) in the paper is incorrect. Thus the approximation theorem (Theorem 0.1) for L^2 torsion of an amenable covering of a finite simplicial complex remains unproved. However,…
Weak values are quantities accessed through quantum experiments involving weak measurements and post-selection. It has been shown that 'anomalous' weak values (those lying beyond the eigenvalue range of the corresponding operator) defy…
This paper is concerned with qualitative properties of solutions to nonlocal reaction-diffusion equations of the form$$ \int\_{\mathbb{R}^N\setminus K} J(x-y)\,\big( u(y)-u(x) \big)\,\D y+f(u(x))=0, \quad x\in\R^N\setminus K,$$set in a…
The relaxation limit in critical Besov spaces for the multidimensional compressible Euler equations is considered. As the first step of this justification, the uniform (global) classical solutions to the Cauchy problem with initial data…
Using mountain pass arguments and the Karsuh-Kuhn-Tucker Theorem, we prove the existence of at least two positive solution of the anisotropic discrete Dirichlet boundary value problem. Our results generalize and improve those of [15].
For a sequence of nonnegative random variables, we provide simple necessary and sufficient conditions to ensure that each sequence of its forward convex combinations converges in probability to the same limit. These conditions correspond to…
Let $(\Omega, \mathcal{A}, \mu)$ be a probability space. The classical Borel-Cantelli Lemma states that for any sequence of $\mu$-measurable sets $E_i$ ($i=1,2,3,\dots$), if the sum of their measures converges then the corresponding…
For any $0 < \alpha <1$, we construct Cantor sets on the parabola of Hausdorff dimension $\alpha$ such that they are Salem sets and each associated measure $\nu$ satisfies the estimate $\|{\widehat{f d\nu}}\|_{L^p(\mathbb{R}^2)} \leq C_p…
In work with P. Chru\'sciel, L. Nguyen and T.-T. Paetz [8], a positive mass theorem was obtained for asymptotically locally hyperbolic manifolds with boundary, having a toroidal end. The proof made use of properties of marginally outer…
The tensor complementarity problem is a specially structured nonlinear complementarity problem, then it has its particular and nice properties other than ones of the classical nonlinear complementarity problem. In this paper, it is proved…
The cosmic curvature density parameter has been constrained in the present work independent of any background cosmological model. The reconstruction is performed adopting the non-parametric Gaussian Processes (GP). The constraints on…
The Holevo bound is a keystone in many applications of quantum information theory. We propose "weak maximal Holevo quantity" with weak measurements as the generalization of the standard Holevo quantity which is defined as the optimal…
In acousto-electric tomography the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is penetrated by a time-dependent acoustic…
We consider Choquet integrals with respect to dyadic Hausdorff content of non-negative functions which are not necessarily Lebesgue measurable. We study the theory of Lebesgue points. The studies yield convergence results and also a density…