On Compound Poisson Processes Arising in Change-Point Type Statistical Models as Limiting Likelihood Ratios

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these likelihood ratios, which is an exponential functional of a two-sided Poisson process driven by some parameter, can be approximated (for sufficiently small values of the parameter) by another one, which is an exponential functional of a two-sided Brownian motion. In this paper we consider yet another likelihood ratio, which is the exponent of a two-sided compound Poisson process driven by some parameter. We establish, that similarly to the Poisson type one, the compound Poisson type likelihood ratio can be approximated by the Brownian type one for sufficiently small values of the parameter. We equally discuss the asymptotics for large values of the parameter and illustrate the results by numerical simulations

Modern state of use of solar desalination

Water is the most necessary resource for mankind, animals and plants. Although 71% of the Earth’s surface is covered by water, 97% of it is salt water, that is, water that is not suitable for consumption. Also, continuous pollution of surface and underground water is increasing the shortage of drinking water. In solving the above problems, desalination of salt water is an important way of increasing drinking water resources. However, the high energy consumption, increased greenhouse gas emissions, large amounts of wastewater and the high cost of fresh water in desalination limit the widespread adoption of desalination technology in the industry. To solve these limitations, solar energy, which is one of the renewable energy sources, is environmentally friendly, ubiquitous, convenient to use, safe and sustainable. Currently, several constructions of SD are proposed, the main part of which is a pool construction. This research paper presents the results of comparison of the constructional structures of one- and two-basin SD, their heat-technical parameters, device productivity and economic indicators

Comparison and verification of research results of geodesic works carried out in meliorative systems with the help of geoinformation software

The article covers the issues of creation, optimization and rational use of a system that provides the current status, dynamics and changes of location indicators by conducting geodetic and topographic research using modern technologies of mapping based on geoinformation systems, as well as the problems of geodetic and topographic research

AR and MA representation of partial autocorrelation functions, with applications

We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.Comment: Published in Probability Theory and Related Field

Minimax estimation of the Wigner function in quantum homodyne tomography with ideal detectors

We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared pulses. The state is represented through the Wigner function, a ``quasi-probability density'' on $\mathbb{R}^{2}$ which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics. The data consists of $n$ i.i.d. observations from a probability density equal to the Radon transform of the Wigner function. We construct an estimator for the Wigner function, and prove that it is minimax efficient for the pointwise risk over a class of infinitely differentiable functions. A similar result was previously derived by Cavalier in the context of positron emission tomography. Our work extends this result to the space of smooth Wigner functions, which is the relevant parameter space for quantum homodyne tomography.Comment: 15 page

Формирование единого и внешне интегрированного транспортного пространства в Центральной Азии

Competently built strategy for development of international transport corridors passing through the countries of Central Asia ensures economic development of not only the states located in this region, but also of other countries participating in transportation processes. At the same time, the practices of development of international transport corridors reveal several problems which comprise inconsistency of regulatory acts of the parties involved, differences in technical standards, lack of uniformity of railway gauge, duration of customs clearance. The objective of the work was to study transport corridors of Central, Western and South Asia and the existing infrastructural, organizational, and technological limitations for their development. The methods of economic, statistical, and engineering analysis were used. The research has considered problems in development of international transport corridors and possible solutions there-of through organization of intermodal transportation by a single transport operator of Uzbekistan, as well as the current state of transport corridors linking Central, Western, South Asia and China with the EU countries, including development of China–EU railway corridors. In that context, the article suggests the analysis of several legal, organizational, technological factors , as well as of infrastructural restrictions using the example of the Kashgar (China)–Osh (Kyrgyzstan) railway section, prior to construction of which it is proposed to use intermodal transportation. The proposals refer to creating the Shanghai Cooperation Organisation (SCO) transport and logistics association and to developing the design of universal wagons with variable gauge wheel sets adapted for operation on railways of various gauges.Грамотно выстроенная стратегия формирования и развития международных транспортных коридоров, проходящих через страны Центральной Азии, обеспечивает экономическое развитие не только расположенных в этом регионе государств, но и других стран-участниц перевозок. Вместе с тем, в практике формирования международных транспортных коридоров существует ряд проблем: несоответствие нормативно-правовых актов участвующих сторон, различия технических стандартов, неунифицированность железнодорожной колеи, длительность таможенного оформления. Цель работы заключалась в исследовании транспортных коридоров Центральной, Западной и Южной Азии и существующих для их развития инфраструктурных, организационных итехнологических ограничений. Использовались методы экономического, статистического, инженерного анализа. Рассмотрены проблемы в формировании международных транспортных коридоров и их решение с помощью организации перевозок единым оператором Узбекистана. Изучено современное состояние транспортных коридоров, связывающих Центральную, Западную, Южную Азию и Китай со странами Евросоюза, в том числе, вопросы формирования железнодорожных коридоров Китай–Евросоюз. В этом контексте анализируется ряд правовых, организационных, технологических факторов, а также инфраструктурных ограничений на примере железнодорожной линии на участке Кашгар (Китай)–Ош (Кыргызстан), до строительства которой предлагается использовать на этом участке перевозки другими видами транспорта. Также выдвинуты идеи создания транспортнологистической ассоциации ШОС и разработки конструкции универсальных вагонов с раздвижными колёсными парами, адаптированных к эксплуатации на железных дорогах различной колеи

Математическое моделирование комбинированной системы теплоснабжения солнечного дома)

Today, increasing energy efficiency in residential heating systems, saving fuel and energy resources, and improving the efficiency of using devices based on renewable energy sources is an urgent issue. The purpose of the article is to develop a mathematical model of the heat balance and conduct a theoretical study of one-story rural houses based on the use of solar energy in a non-stationary mode. To achieve this goal, an experimental one-story solar house with autonomous heat supply was built. The heat supply of the experimental solar house mainly uses solar energy, and when the heat supply load exceeds this load, the traditional boiler device is used. The power supply of the experimental solar house is provided by a solar panel (photovoltaic converter). A heat balance scheme for a solar house with autonomous heat supply and an electrothermal scheme of a physical model are proposed. Based on the proposed schemes, a mathematical model of heat balance and a calculation algorithm based on the heat balance equation of the dynamic state of the heat supply system of a one-story experimental solar house in a non-stationary mode have been developed. On the basis of mathematical modeling, the influence of the heat capacity of the wall structure on the temperature regime of the building was studied. On the basis of the MATLAB-Simulink program, the main temperature characteristics were built, on which the change in the temperature of the internal air of the building was analyzed depending on the ambient temperature. On the basis of the program, a modular scheme of the dynamic model was built. Based on the modular scheme, the results of the experiment on changing the air inside the solar house and the outdoor temperature are presented in the form of a graph. The mathematical model of the thermal balance of the building in dynamic mode and the obtained calculation results are recommended for use in the development of energy-efficient solar houses.Вопросы экономии топливно-энергетических ресурсов, повышения эффективности систем теплоснабжения жилых помещений, а также использования устройств на основе возобновляемых источников энергии на сегодняшний день имеют особую актуальность. Цель статьи – разработать математическую модель теплового баланса и провести теоретическое исследование одноэтажных сельских домов, использующих солнечную энергию в нестационарном режиме. Для ее реализации построен экспериментальный одноэтажный солнечный дом с автономным теплоснабжением на основе преимущественно солнечной энергии. В случаях, если нагрузка на теплоснабжение превышает солнечную нагрузку, применяется традиционное котельное устройство. Электроснабжение экспериментального дома обеспечивается солнечной панелью (фотоэлектрическим преобразователем). Предложены схема теплового баланса солнечного дома с автономным теплоснабжением и электротепловая схема физической модели. На их основе разработаны математическая модель и алгоритм расчета, базирующийся на уравнении теплового баланса динамического состояния системы теплоснабжения экспериментального дома в нестационарном режиме. Исследовано влияние теплоемкости стеновой конструкции на температурный режим здания. В среде моделирования MATLAB-Simulink построены основные температурные характеристики, на которых проанализировано изменение температуры внутреннего воздуха здания в зависимости от температуры окружающей среды. Построена модульная схема динамической модели, результаты эксперимента по изменению воздуха внутри солнечного дома и температуры наружного воздуха представлены в виде графика. Математическая модель теплового баланса здания в динамическом режиме и результаты расчетов могут использоваться при разработке энергоэффективных солнечных домов

CFD model of acceleration of thermal-hydrodynamic processes in solar air collectors

Recent studies on increasing the thermal-hydrodynamic efficiency of solar air collectors have been carried out on the installation of barriers of various shapes on the surface of the absorber, and this method ensures a significant increase in the energy efficiency of the collector. The transfer of the air flow washing the surface of the absorber from a laminar flow state to an accelerated lumped air flow is carried out by installing obstacles. Installation of barriers is the main factor in increasing the heat transfer in solar air collectors and prolongs the time of air flow in the collector. The barrier solar air collector has a high local heat transfer coefficient, and the Nusselt number value is up to 3.5 times higher than that of the flat plate solar air collector. Also, this article presents the results of CFD modeling of the air flow in the solar air collector, the results of which can be used in the theoretical research of the solar air collector

Mathematical Modeling of the Combined Heat Supply System of a Solar House

Today, increasing energy efficiency in residential heating systems, saving fuel and energy resources, and improving the efficiency of using devices based on renewable energy sources is an urgent issue. The purpose of the article is to develop a mathematical model of the heat balance and conduct a theoretical study of one-story rural houses based on the use of solar energy in a non-stationary mode. To achieve this goal, an experimental one-story solar house with autonomous heat supply was built. The heat supply of the experimental solar house mainly uses solar energy, and when the heat supply load exceeds this load, the traditional boiler device is used. The power supply of the experimental solar house is provided by a solar panel (photovoltaic converter). A heat balance scheme for a solar house with autonomous heat supply and an electrothermal scheme of a physical model are proposed. Based on the proposed schemes, a mathematical model of heat balance and a calculation algorithm based on the heat balance equation of the dynamic state of the heat supply system of a one-story experimental solar house in a non-stationary mode have been developed. On the basis of mathematical modeling, the influence of the heat capacity of the wall structure on the temperature regime of the building was studied. On the basis of the MATLAB-Simulink program, the main temperature characteristics were built, on which the change in the temperature of the internal air of the building was analyzed depending on the ambient temperature. On the basis of the program, a modular scheme of the dynamic model was built. Based on the modular scheme, the results of the experiment on changing the air inside the solar house and the outdoor temperature are presented in the form of a graph. The mathematical model of the thermal balance of the building in dynamic mode and the obtained calculation results are recommended for use in the development of energy-efficient solar houses