On the infimum attained by a reflected L\'evy process

This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected at 0), and focuses on the distribution of $M(t)$, that is, the minimal value attained in an interval of length $t$ (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in terms of Laplace transforms, for spectrally one-sided L\'evy processes (i.e., either only positive jumps or only negative jumps). The second contribution concerns the asymptotics of \prob{M(T_u)> u} (for different classes of functions $T_u$ and $u$ large); here we have to distinguish between heavy-tailed and light-tailed scenarios

Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems

We report the results of certain integrations of quantum-theoretic interest, relying, in this regard, upon recently developed parameterizations of Boya et al of the n x n density matrices, in terms of squared components of the unit (n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized volume elements of the Bures (minimal monotone) metric for n = 2 and 3, obtaining thereby "Bures prior probability distributions" over the two- and three-state systems. Then, as an essential first step in extending these results to n > 3, we determine that the "Hall normalization constant" (C_{n}) for the marginal Bures prior probability distribution over the (n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known to equal 2/pi.) The constant C_{5} is also found. It too is associated with a remarkably simple decompositon, involving the product of the eight consecutive prime numbers from 2 to 23. We also preliminarily investigate several cases, n > 5, with the use of quasi-Monte Carlo integration. We hope that the various analyses reported will prove useful in deriving a general formula (which evidence suggests will involve the Bernoulli numbers) for the Hall normalization constant for arbitrary n. This would have diverse applications, including quantum inference and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in J. Phys. A. We make a few slight changes from the previous version, but also add a subsection (III G) in which several variations of the basic problem are newly studied. Rather strong evidence is adduced that the Hall constants are related to partial sums of denominators of the even-indexed Bernoulli numbers, although a general formula is still lackin

Один из способов управления технологическим процессом дуговой сталеплавильной печи

В статье приводится описание комплексной математической модели, используемой для рационального управления работой дуговых электросталеплавильных печей.In article the description of the complex mathematical model used for rational management by work of arc electrosteel-smelting furnaces is resulted

Author correction : a global database for metacommunity ecology, integrating species, traits, environment and space

Correction to: Scientific Data https://doi.org/10.1038/s41597-019-0344-7, published online 08 January 202

Author correction : a global database for metacommunity ecology, integrating species, traits, environment and space

Correction to: Scientific Data https://doi.org/10.1038/s41597-019-0344-7, published online 08 January 202

Метод неразрушающего контроля толщины и внутренней дефектности стенок металлической трубы

The possibility of an accurate estimation of the pipe wall thickness measured directly from the reconstructed image of the pipe, reconstructed from only a few X-ray projections made in a limited viewing angle, is discussed. Since the effects of radiation scattering and X-ray beam hardening distort up to 50 % of the primary radiation, ignoring these effects leads to blurred images, strong artifacts, and inaccurate sizing. A computerized technique has been developed that takes into account the contribution of scattered radiation and the hardening of the X-ray beam. Iterative Bayesian reconstruction techniques are then used to reconstruct the pipe image using the volumetric and surface-oriented representation of the pipe. Using these methods, the error in estimating the pipe wall thickness can be increased to 300 microns. Обсуждается возможность точной оценки толщины стенки трубы, измеренной непосредственно из реконструированного изображения трубы, восстановленного из всего лишь из нескольких рентгеновских проекций, сделанных в ограниченном угле обзора. Поскольку эффекты рассеяния излучения и ужесточения рентгеновского пучка искажают до 50 % первичного излучения, игнорирование этих эффектов приводит к смазыванию изображения, сильным артефактам, и неточному определению размеров. Была разработана компьютеризированная методика, которая учитывает вклад рассеянного излучения, и ужесточения рентгеновского пучка. Итерационные методы Байесовской реконструкции затем используются для восстановления изображения трубы, с использованием объемного и поверхностно-ориентированного представления трубы. Применяя эти методы, погрешность оценки толщины стенки трубы может быть доведена до 300 мкм

Information scan of quantum states based on entropy-power uncertainty relations

We use Renyi-entropy-power-based uncertainty relations to show how the information probability distribution associated with a quantum state can be reconstructed in a process that is analogous to quantum-state tomography. We illustrate our point with the so-called "cat states", which are of both fundamental interest and practical use in schemes such as quantum metrology, but are not well described by standard variance-based approaches

Queues with Lévy input and hysteretic control

We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion. © The Author(s) 2009