This work considers the solution of the Dirichlet problem for the Laplace equation in the case when the domain is bounded by a circle. The Laplace equation and its basic properties are introduced, and the transition to polar coordinates is carried out. The formulation of the Dirichlet problem on a circle with given boundary conditions is presented. The method of solving this problem using trigonometric series and the Fourier series to satisfy the boundary conditions is described. Specific examples of solving the Dirichlet problem on a circle with illustrations and numerical results are provided. In conclusion, the importance and practical significance of the obtained solutions for various applied problems are emphasized.

This work considers the solution of the Neumann problem on a ring-shaped domain. First, the definition of the domain and the formulation of the Neumann boundary conditions on the inner and outer edges of the ring are provided. To solve the problem, the method of separation of variables in polar coordinates is used. The general solution of the Laplace equation in the ring is obtained, and then, by applying the Neumann boundary conditions, the coefficients in this general solution are determined. As an example, a specific Neumann boundary value problem on a ring is considered, the coefficients in the general solution are calculated, and the final solution is constructed. This work can be useful in the study and solution of partial differential equations in ring-shaped domains.

The article is about specificity of the modern education — problem teaching. Using different methods of teaching is effective. The information technologies are the methods of problem teaching. Methods of problem teaching are defined. Different explanation on problem teaching are offered..

Ischemic stroke is a growing medical, social and economic problem, the scope of which is becoming epidemic (Graeme J.H., 2016). Despite relatively stable incidence rates and a decrease in mortality over the past two decades, there has been an increase in the number of years of life adjusted for disability and stroke-related deaths (Feigin V.L. et al., 2014). Despite the undoubted achievements in this area, the problem of the negative impact of neurological deficit on the effectiveness of rehabilitation measures, short-term and long- term prognosis, functional status and quality of life of patients does not become less significant. (Kliper E. et al., 2016).

Kasr tartibli tenglamalarning fizik, texnik va biologik jarayonlarga tadbiqi katta boʻlgani uchun butun dunyo olimlari tomonidan kasr tartibli hosila qatnashgan yuqori tartibli tenglamalarni oʻrganishga boʻlgan qiziqish ortib bormoqda. Bugungi kunda kasr tartibli hosila qatnashgan yuqori tartibli aralash tipdagi tenglamalar uchun boshlang’ich chegaraviy masalalarni oʻrganish va yechish dolzarb masalaga aylandi. Ushbu ishida Miller-Ross ma’nosidagi kasr tartibli hosila qatnashgan ayrim xususiy hosilali differensial tenglama uchun silindrik sohadagi boshlang’ich – chegaraviy masala va Sobolev sinfida yuqori tartibli kasr hosilali differensial tenglama uchun boshlang’ich – chegaraviy masalalar oʻrganilgan. Sferik funksiyalar bizga matematik fizika masalalarining yechimlarini soddaroq, oson va tezroq topishga imkon yaratadigan usuldir. Bu funksiyalar orqali bir muncha murakkab boʻlgan masalalarni ham osongina yechimini topish mumkin.

This article presents the problem of short-term planning of open-pit mining processes and work shifts in mines and the design process of technological mine parameters in open mines is shown. The problem is mine and waste as well several problematic situations in truck parks and drop-off points are highlighted. Truck distribution is dynamic to permit each truck must be assigned multiple routes. The problem is deciding which one facades should be mined and specify the number of trucks, their routes and directions, and the amount of material transported by them to each drop-off point is satisfactory we can see the calculation ratio and their indicators as needed. The goals are to minimize the deviations starting with production targets, chemical grade and particle size range of each parameter control in each plant and reduce the number of trucks we can give examples of processes. To solve the problem, we developed a mixed integer linear objective programming model and tested it using real data from an iron ore mine. The results showed the proposed approach supports decision makers in sizing and allocation and in meeting the required targets of truck fleets and production and control parameters by ore processing plants in a day-to-day scenario such as low availability the flexibility of shovels and trucks, ore quality, and the need to increase production have been widely discussed.

Аннотация В статье в практической деятельности учителя непрерывного образования, в процессе эффективной организации уроков и решения проблемы непрерывного образования старших классов важным этапом мыслительной деятельности учащихся является обдумывание пути решения. это или выдвинуть гипотезу и обосновать гипотезу. Учебная проблема разрабатывается последовательно с проблемными вопросами, и каждый вопрос служит этапом ее решения. Компоненты проблемы, характер взаимоотношений известного и неизвестного, создают потребность в знаниях и побуждают к поиску активных знаний.

Важным аспектом организации и проведения проблемного обучения в системе непрерывного образования является то, что преподаватель должен хорошо понимать как его образовательную, так и воспитательную функции. Учитель никогда не должен давать ученикам готовую истину или решение, а должен мотивировать их к получению знаний, помогать им обрабатывать в сознании информацию, события, время и явления, необходимые в обучении и жизнедеятельности.

The boundary value problem with nonlocal conditions for a system of partial differential equations of the second order is investigated. The parameterization method is used to establish coefficient sufficient conditions for the correct solvability of the problem under consideration in terms of the initial data. The algorithm for finding a solution is proposed.

This work considers the formulation and solution of the Dirichlet problem on a sphere. The domain of the problem is a sphere, and the boundary conditions are given on its surface. The solution is presented in spherical coordinates using the method of separation of variables. A general solution is obtained in the form of a series of spherical functions, and the coefficients of the series are determined from the boundary conditions.

The boundary value problem with nonlocal conditions for a system of partial differential equations of the second order is investigated. The parameterization method is used to establish coefficient sufficient conditions for the correct solvability of the problem under consideration in terms of the initial data. The algorithm for finding a solution is proposed.

В статье исследуется место гендерной проблематики в государственной политике и государственном устройстве. На основе анализа международной и отечественной литературы раскрывается место проблемы гендерного равенства в политико-идеологическом регулировании. Рассматривается, что обеспечение гендерного равенства является приоритетным направлением политики не только Узбекистана, но и стран всего мира.

The article is devoted to one of the pressing problems – the problem of reading among students and young people. The reasons for the decrease in their interest in reading are studied; the role of understanding and interpreting the text in improving the culture of reading is emphasized.

The problem of comprehensive evaluation of the efficiency of capital investments (investments) has been in the constant focus of various levels of economists-scientists and practitioners-managers and has not lost its relevance even now. In the last decade, many scientific manuals devoted to this problem have been published, and various methodological instructions and guidelines have been developed in the field of economic justification of capital investments for investment objects intended for use at the national, sectoral and regional levels.

The following text provides an overview of the problem of falsification of medicinal products and the scale of this issue worldwide. Kazakhstan is part of the global community and has not escaped this problem. According to official data, in Kazakhstan, more than 1% of medicinal products are falsified, and in reality, this figure is undoubtedly higher. In recent years, the state has devoted a lot of attention to this issue and has taken a series of effective measures to enhance national security in providing the population with medicines.

Rickets occupies an important place in the structure of the morbidity of young children and is an urgent problem of pediatrics. This problem requires special attention to the problem of rickets, which has a negative impact on the reactivity of the body, the course and outcome of somatic diseases, especially in children of the first year of life.

Promoting of critical thinking of students involves asking students questions and understanding of the problem that needs to be solved. Critical thinking is social in nature, since every thought is tested and honed when it is shared with others. This technique increases the involvement of students in the implementation of group decisions. Critical thinking is individual and independent, each generates its own ideas, formulates its own assessments and beliefs independently of the others, finds its own solution to the problem and supports it with convincing reason.

Ushbu maqola fizika fanidan masalalar yechish metodikasini takomillashtirishga bag'ishlangan. Tadqiqot fizika o'qituvchilarining masalalar yechish metodikasini tahlil qilish va yangi yondashuvlarni joriy etish orqali o'quvchilarning fizika fanidan bilim va ko'nikmalarini oshirishni maqsad qilgan. Tadqiqot natijalariga ko'ra, fizika fanidan masalalar yechishda interfaol metodlar, vizual vositalar va muammoli o'qitish texnologiyalarini qo'llash samarali ekanligi aniqlandi. Maqola fizika o'qituvchilari va metodistlari uchun foydali bo'lishi mumkin.

In the cognitive structure, the formal formulation of the problem and model synthesis, the choice of method and the concept of solving the problem are based, a brief description of the systematic-cognitive analysis (SC-analysis) method, its theoretical premises are revealed, the mathematical model, digital computing techniques, special software tools of SC-analysis are described. .analysis ("Eidos" system), cognitive structure of the subject area, formal statement of the problem and formation of a study sample.

On the Internet, where the number of choices is overwhelming, there is need to filter, prioritize and efficiently deliver relevant information in order to alleviate the problem of information overload, which has created a potential problem to many Internet users. Recommender systems solve this problem by searching through large volume of dynamically generated information to provide users with personalized content and services. This paper explores the different function of recommendation systems in order to serve as a compass for research and practice in the field of recommendation systems.

В статье рассматривается история возникновения и этапы развития ТРИЗ (Теории решения изобретательских задач), основанной Генрихом Сауловичем Альтшуллером в середине XX века. Анализируются ключевые принципы и методы ТРИЗ, её эволюция от практической методики до полноценной научной дисциплины. Особое внимание уделяется роли ТРИЗ в современной системе инновационного мышления, а также её применению в различных отраслях науки, техники и образования.

It takes critical thought to create a feeling of crisis while writing for students about any problem. This ability is necessary to build a framework based on self-reflection, exploration, and problem-solving in their daily lives, at work, and in school. The purpose of this essay is to improve critical writing for research conducted by undergraduate students. The descriptive method with a qualitative approach is the research methodology adopted. Many research articles in international journals that emphasize the importance of critical writing for conducting research proposals provided the data utilized for analysis. The research discussion and findings indicate that students must have the ability to write critically. It deals with reflecting and examining the concerns of study topics, as well as brainstorming solutions. Also, depending on the rules of the research proposal, students should be able to write the research background, research problem, review of related literature, and research technique. The writing ability related to the capability of the organization, elaborating material, paying attention to mechanics, language use, and vocabulary become the leading and supporting capital to be effective in carrying out the study project.

The problem of diagnosing traumatic brain injury (TBI) of mild and moderate severity is becoming increasingly relevant in modern neurotraumatology. According to world statistics, mild and moderate TBI accounts for up to 80-85% of all cases of traumatic brain injury, which determines the high socio-economic significance of this problem. Of particular importance is the fact that the main group of victims are people of working age, which significantly affects the demographic and economic indicators of society.

This article examines the issues of ensuring employment and reducing the unemployment rate in Uzbekistan’s economy by creating new jobs. This problem is of not only economic but also social significance, playing an important role in improving the well-being of the population and ensuring the sustainable development of the state. The article highlights the impact of technological development on employment and issues related to the informal labor market. It analyzes measures to address the unemployment problem, employment and unemployment indicators in the Republic of Uzbekistan, as well as the distribution of employed individuals across formal and informal sectors

The article is devoted to the problem of teaching students, learners, or children with disabilities in English lessons. The relevance of this problem lies in the fact that ensures the general cultural, personal and cognitive development of children.

The article discusses the main environmental problems such as air pollution in cities, at the moment the existence of cities cannot be imagined without human anthropogenic impact. Humanity actively influences the state of the environment. The authors analyze the problem of urban pollution. The city is one of the types of social and spatial organization of the population, emerging and developing on the basis of the concentration of industrial, scientific, cultural, administrative and other functions.