Eynard-Mehta theorem, Schur process, and their pfaffian analogs

We give simple linear algebraic proofs of Eynard-Mehta theorem, Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also discuss certain general properties of the spaces of all determinantal and Pfaffian processes on a given finite set.Comment: AMSTeX, 21 pages, a new section adde

Biological researches around the Belarusian Antarctic Expedition's Camp «Vechernyaya Mountain» (East Antarctica)

Местом проведения исследований был район базирования белорусской экспедиции – полевой лагерь «Гора Вечерняя». Лагерь располагается в пределах оазиса Молодежный на побережье моря Космонавтов, окраинное море Восточной Антарктиды, занимающее пространство примерно между 33º и 54º в.д. Выделены три основных группы микроводорослей: Синезелёные – Chyanophyta, Зелёные – Chlorophyta и Эвгленовые – Euglenophyta. Из 79 видов водорослей, обнаруженных нами в исследованных озёрах Антарктики, 75 встречаются в пресноводных озерах Беларуси. Из 19 видов лишайников семь встречаются на территории Беларуси. Все три вида моховидных (Bryophyta) являются обычными для Беларуси. Основными представителями зоопланктона исследованных пресных озер являются коловратки. Среди рыб наиболее массовым является Trematomus newnesi. Проведен учет ластоногих (2 вида) и птиц (10 видов). Определена калорийность рыб. Содержание органического вещества у гидробионтов Антарктики изменяется от 16,8 до 98%, а калорийность от 0,5 до 8,3 кал/мг сухого вещества. Выявлен высокий уровень сходства между фауной и флорой наземных и пресноводных экосистем в районе деятельности БАЭ и умеренной зоны Северного полушария (Европа, Беларусь). Установлена таксономическая близость водорослёво-бактериальных образований донных отложений из пресноводных озёр Антарктики и горячих источников Камчатки

A Time-Space Tradeoff for Triangulations of Points in the Plane

In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm

Sociocultural Component in the Content of Teaching Foreign Languages to Pre-school Children

The paper is aimed at studying efficiency of learning languages by pre-school children. Different types of memory that are at high level of its development at this age promote children's abilities to acquire languages. Also psychologically, pre-school children are fit to develop speech and communication skills by using adequate materials and tasks. A set of criteria are evaluated to introduce socio-cultural content for promoting effective language learning

Formal concept analysis for evaluating intrinsic dimension of a natural language

Some results of a computational experiment for determining the intrinsic dimension of linguistic varieties for the Bengali and Russian languages are presented. At the same time, both sets of words and sets of bigrams in these languages were considered separately. The method used to solve this problem was based on formal concept analysis algorithms. It was found that the intrinsic dimensions of these languages are significantly less than the dimensions used in popular neural network models in natural language processing.Comment: Preprint, 10th International Conference on Pattern Recognition and Machine Intelligence (PReMI 2023

Conformational and Structural Relaxations of Poly(ethylene oxide) and Poly(propylene oxide) Melts: Molecular Dynamics Study of Spatial Heterogeneity, Cooperativity, and Correlated Forward-Backward Motion

Performing molecular dynamics simulations for all-atom models, we characterize the conformational and structural relaxations of poly(ethylene oxide) and poly(propylene oxide) melts. The temperature dependence of these relaxation processes deviates from an Arrhenius law for both polymers. We demonstrate that mode-coupling theory captures some aspects of the glassy slowdown, but it does not enable a complete explanation of the dynamical behavior. When the temperature is decreased, spatially heterogeneous and cooperative translational dynamics are found to become more important for the structural relaxation. Moreover, the transitions between the conformational states cease to obey Poisson statistics. In particular, we show that, at sufficiently low temperatures, correlated forward-backward motion is an important aspect of the conformational relaxation, leading to strongly nonexponential distributions for the waiting times of the dihedrals in the various conformational statesComment: 13 pages, 13 figure

How long does it take to pull an ideal polymer into a small hole?

We present scaling estimates for characteristic times $\tau_{\rm lin}$ and $\tau_{\rm br}$ of pulling ideal linear and randomly branched polymers of $N$ monomers into a small hole by a force $f$. We show that the absorbtion process develops as sequential straightening of folds of the initial polymer configuration. By estimating the typical size of the fold involved into the motion, we arrive at the following predictions: $\tau_{\rm lin}(N) \sim N^{3/2}/f$ and $\tau_{\rm br}(N) \sim N^{5/4}/f$, and we also confirm them by the molecular dynamics experiment.Comment: 4 pages, 3 figure

The development of a heterogeneous MP data model based on the ontological approach

The article discusses the approaches providing symmetric access of all industrial production services to the data of business processes of the enterprise by building a single warehouse of heterogeneous data of a metallurgical production. The warehouse is a part of an automated statistic quality control system for the products of a metallurgical enterprise. The article describes an ontological storage model of data coming from various sources of information in the production process. The concept of “a unit of production of metallurgical production” is introduced that is the connecting component of the entire production life cycle of a metallurgical production. The authors propose an ontological model of the production process, in terms of information flows which are formed in an enterprise at each stage of production. Based on the constructed ontological model, the structure of recording an array of information in the heterogeneous data warehouse is justified and formed. Heterogeneous data warehouse forms a single information space of the enterprise, which serves as the basis for analytical analysis throughout the production and decision—making process. For example, timely response to the deviation reasons from the given physical and chemical properties of the finished product. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.The research was funded by the Russian Foundation for Basic Research No. 19-37-90049\19 of 08/27/2019