Law of large numbers for certain cylinder flows

We construct new examples of cylinder flows, given by skew product extensions of irrational rotations on the circle, that are ergodic and rationally ergodic along a subsequence of iterates. In particular, they exhibit law of large numbers. This is accomplished by explicitly calculating, for a subsequence of iterates, the number of visits to zero, and it is shown that such number has a gaussian distribution.Comment: 25 pages, referee suggestions incorporated, to appear in Ergodic Theory and Dynamical System

A compact form of a cubic equation from the 7-point algorithm

One of the popular approaches to estimate the fundamental matrix of a stereo pair is a 7-point algorithm. One of the key elements of the algorithm is a solution of a cubic equation. This paper provides a compact representation of the equation, helping researchers to implement less error-prone computer vision software faster

Plausible rectification from the fundamental matrix

Rectification of a stereo pair from the fundamental matrix (also known as uncalibrated rectification [1]) is a procedure that results in a new pair of images that have strictly horizontal epipolar lines. Moreover, the corresponding epipolar lines of the two images acquire the same vertical position. This means that the vertical disparity between corresponding pixels becomes small enough (e.g. zero, if we speak about integer pixel coordinates), and efficient stereo matching algorithms can be applied further. This article presents a plausible algorithm to achieve this. The plausibility consists in the fact that the algorithm works not for all cases, and these cases are studied in detail in this paper. However, authors claim that the presented algorithm deserves attention because of implementation and explanation simplicity

Activities at Kyzylkala Settlement in 2021 and Preliminary Analysis of Ceramic Material

The paper highlights the results of studies conducted at Kyzylkala settlement in the Mangystau region of the Republic of Kazakhstan in 2021. The results of the primary analysis of ceramics obtained during the excavation of the monument are presented. The complex was subdivided into three technological groups, and the categories and types of vessels are briefly described. An analysis of these materials demonstrated their proximity to the pottery complex of Samosdelskoye settlement located in Astrakhan Oblast. Ceramics of group 2 find analogies in the collection from the excavations of Derbent. The main types of glazed ceramics are connected by their origin with the territory of Transcaucasia. Their dating makes it possible to clarify the dating of the monument, which has been determined as the 11th– 13th centuries

Проблемы оптимизации энергопотребления домохозяйств в задачах повышения энергоэффективности жилищного сектора

The aim of the work is to study the problem of optimizing energy consumption and practical application of methods for  improving energy efficiency in the housing sector. Optimization of  energy efficiency management allows to reduce the expenditure of  energy resources in the performance of various works, heating of buildings, etc. The creation of optimization methods will make it  possible to reduce payments for utilities in a short time, and in  general for the industry, will help reduce the consumption of various  resources and improve the ecological state of the region. Unlike  other approaches, the emphasis in this paper is on the convenience  and simplicity necessary for using this technique by the population in households. The proposed integrated approach uses methods of  probability theory, linear programming, heat exchange models. The  conducted research confirms the effectiveness of the solution  obtained and can serve as a basis for the creation of training and  research stands. The article consists of two parts: the first part  analyzes the leading works in this field and identifies the reasons  that make it difficult to apply the solutions proposed in these papers. Further, the statement of the problem was proposed and justified,  and a number of basic requirements to the mathematical model of  energy consumption, necessary for the constructed technique to be  used to optimize energy consumption in households, were  formulated. In the second part, a mathematical model of their  functioning is proposed using examples of specific household  electrical appliances. When researching existing methods for  optimizing energy consumption in households, problems were  identified that were difficult to apply these methods in practice and  recommendations were obtained that allowed to formulate the basic  principles of constructing an optimization technique that was  convenient for practical application. It was shown that when  constructing such a technique, the primary question is the data that  the user can provide. The minimum composition of input data was  determined, according to which the necessary algorithms for  optimizing energy consumption were designed. A number of  algorithms for determining some input indicators that are easy to use in households have also been proposed. Thus, the general plan of research in this paper is as follows:• carry out grouping of devices by the way of setting functionalrequirements;• determine the acceptable composition and type of input data forthe user;• define the minimum set of input data for formalizing the limitationof the total power consumption;• design optimization algorithms that work with the input dataspecified above. The most important results of the work performed are the following:• the methodology for forecasting the graph of the maximum totalpower consumption has been developed.• methods for optimizing energy consumption for each of the selected subsets of household appliances have been developed.• the optimization algorithms obtained have been simulated, which showed their operability, efficiency and the possibility of their practical application without any adaptation.Thus, the article proposes the solution of the problem of optimization of energy consumption in the housing sector, oriented to practical application.Целью работы является исследование проблемы оптимизации энергопотребления и  практического применения методов повышения энергоэффективности в жилищном секторе.  Оптимизация управления энергоэффективностью позволяет уменьшать расходование  энергоресурсов при выполнении различных работ, отопление зданий и т.д. Создание  методов оптимизации позволит в короткие сроки снизить платежи за коммунальные услуги,  а в целом для отрасли, будет способствовать уменьшению потребления различных ресурсов  и улучшению экологического состояния региона. В отличии от других подходов, акцент в  данной работе ставится на удобство и простоту, необходимую для использования этой  методики населением в домашних хозяйствах. В предложенном комплексном подходе  используются методы теории вероятностей, линейного программирования, модели теплообмена. Проведенное исследование подтверждает эффективность полученного  решения и может служить основой для создания учебно-исследовательских стендов. Статья  состоит из двух частей: в первой части выполнен анализ ведущих работ в этой тематике и  определены причины, затрудняющие массовое применение предлагаемых в этих работах  решений. Далее предложена и обоснована постановка задачи и сформулирован ряд  основных требований к математической модели энергопотребления, необходимых для того, чтобы сконструированную методику можно было применять для оптимизации  энергопотребления в домашних хозяйствах. Во второй части на примерах конкретных  бытовых электроприборов предлагается математическая модель их функционирования. При  исследовании существующих методов оптимизации энергопотребления в домохозяйствах  были выявлены проблемы, заключающиеся в сложности применения этих методов на практике и получены рекомендации, позволяющие сформулировать основные принципы  построения методики оптимизации, удобной для практического применения. Было показано, что при построении такой методики первичным является вопрос о данных, которые может  предоставить пользователь. Был определен минимальный состав входных данных, по которым сконструированы необходимые алгоритмы оптимизации энергопотребления. Так же был предложен ряд алгоритмов определения некоторых входных показателей, которые  легко использовать в домашних хозяйствах. Таким образом, общий план исследований в  данной работе заключается в следующем:• провести группировку приборов по способу задания функциональных требований;• выяснить приемлемый для пользователя состав и вид входных данных;• определить минимальный набор входных данных для формализации ограничения суммарной потребляемой мощности;• сконструировать алгоритмы оптимизации, работающие с указанными выше входными данными.Важнейшими результатами выполненной работы являются следующие:• разработана методика прогнозирования графика максимальной суммарной мощности потребления.• разработаны методики оптимизации энергопотребления для каждого из выделенных подмножеств бытовых приборов.• выполнено моделирование полученных алгоритмов оптимизации, которое показало их  работоспособность, эффективность и возможность их практического применения без какой- либо адаптации.Таким образом, в статье предложено решение задачи оптимизации энергопотребления в  жилищном секторе, ориентированное на практическое применение

The formation of human populations in South and Central Asia

By sequencing 523 ancient humans, we show that the primary source of ancestry in modern South Asians is a prehistoric genetic gradient between people related to early hunter-gatherers of Iran and Southeast Asia. After the Indus Valley Civilization’s decline, its people mixed with individuals in the southeast to form one of the two main ancestral populations of South Asia, whose direct descendants live in southern India. Simultaneously, they mixed with descendants of Steppe pastoralists who, starting around 4000 years ago, spread via Central Asia to form the other main ancestral population. The Steppe ancestry in South Asia has the same profile as that in Bronze Age Eastern Europe, tracking a movement of people that affected both regions and that likely spread the distinctive features shared between Indo-Iranian and Balto-Slavic languages

EPR of Yb 3+ ions in a monoclinic KY(WO 4) 2 single crystal

The electron paramagnetic resonance (EPR) of Yb 3+ ions in a KY(WO 4) 2 single crystal was investigated at T=4.2 K and fixed frequency of 9.38 GHz. The resonance absorption observed on the lowest Kramers doublet represents the complex superposition of three spectra, corresponding to the ytterbium isotopes with different nuclear moments. The EPR spectrum is characterized by a strong anisotropy of the g-factors. The temperature dependence of the g-factors is shown to be caused by the strong spin-orbital and orbital-lattice coupling. The resonance lines broaden with increasing temperature due to the short spin-lattice relaxation times. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200775.30.Gw Magnetic anisotropy, 76.30.-v Electron paramagnetic resonance and relaxation,

Application of the particle-in-cell method to calculate the parameters of molecular beams from gasdynamic sources

The particle-in-cell method is used to calculate the flow fields of gases formed by supersonic nozzles of different shapes under flow conditions typical of gasdynamic sources of molecular beams. The proposed calculation scheme is tested by comparing the calculated flow fields from an acoustic nozzle with the semiempirical calculations made by Ashkenas and Sherman. For a nozzle with a conical supersonic section the calculations are compared with the results of time-of-flight measurements made using the molecular beam generator at the St. Petersburg Institute of Nuclear Physics of the Russian Academy of Sciences. Prospects for the further use of these calculation methods to develop and optimize gasdynamic sources of molecular beams are discussed. © 1998 American Institute of Physics