相关论文: Real numerical shadow and generalized B-splines

Light from `point sources' such as supernovae is observed with a beam width of order of the sources' size - typically less than 1 AU. Such a beam probes matter and curvature distributions that are very different from coarse-grained…

Using the leading twist approach (LTA) to nuclear shadowing, we calculate the ratios of diffractive and usual parton distributions for a heavy nucleus (Pb) and the proton, $R_{A/p}=(f_{i/A}^{D(3)}/f_{i/A})/(f_{i/p}^{D(3)}/f_{i/p})$, for…

The problem of probabilistic verification of a neural network investigates the probability of satisfying the safe constraints in the output space when the input is given by a probability distribution. It is significant to answer this…

Let $X$ be a compact Hausdorff space, with uniformity $\mathscr{U}$, and let $f \colon X \to X$ be a continuous function. For $D \in \mathscr{U}$, a $D$-pseudo-orbit is a sequence $(x_i)$ for which $(f(x_i),x_{i+1}) \in D$ for all indices…

In the rest frame of the nucleus, shadowing is due to hadronic fluctuations of the incoming virtual photon, which interact with the nucleons. We expand these fluctuations in a basis of eigenstates of interaction and take only the $q\bar q$…

We consider the nuclear shadowing in deep-inelastic scattering corresponding to kinematic regions accessible by future experiments at electron-ion colliders. The gluon distribution at small $x$ is obtained using an improved dipole model…

We consider pure fermionic states with a varying number of quasiparticles and analyze two types of reduced density operators: one is obtained via tracing out modes, the other is obtained via tracing out particles. We demonstrate that…

It is well known that under certain conditions on a Banach space $X$, the set of bounded linear operators attaining their numerical radius is a dense subset. We prove in this paper that if $X$ is assumed to be uniformly convex and uniformly…

The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…

Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of…

Let a continuous random process $X$ defined on $[0,1]$ be $(m+\beta)$-smooth, $0\le m, 0<\beta\le 1$, in quadratic mean for all $t>0$ and have an isolated singularity point at $t=0$. In addition, let $X$ be locally like a $m$-fold…

We obtain new inequalities involving Berezin norm and Berezin number of bounded linear operators defined on a reproducing kernel Hilbert space $\mathscr{H}.$ Among many inequalities obtained here, it is shown that if $A$ is a positive…

We study the thin-shell conjecture for the Schatten classes. In particular, we establish the conjecture for the operator norm; we also improve on the best known bound for the Schatten classes, due to Barthe and Cordero-Erausquin [F. Barthe…

Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of $\mathcal{O}(1/n)$, where $n$ is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279-7292 or Electron.…

Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…

Phase-space distributions are widely applied in quantum optics to access the nonclassical features of radiations fields. In particular, the inability to interpret the Glauber-Sudarshan distribution in terms of a classical probability…

In this paper we revisit the classical method of partitioning classification and study its convergence rate under relaxed conditions, both for observable (non-privatised) and for privatised data. We consider the problem of classification in…

In this paper, subnormal operators, not necessarily bounded, are discussed as generalized observables. In order to describe not only the information about the probability distribution of the output data of their measurement but also a…

Anyone who has ever worked with a variety~$\boldsymbol{\mathscr{A}}$ of algebras with a reduct in the variety of bounded distributive lattices will know a restricted Priestley duality when they meet one---but until now there has been no…

The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…