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Item Open Access Estimation of Vaccination Price through Mathematical Epidemic Models to Optimize the Government Cost(faculty of engineering and natural sciences, 2021) Dauzhanov Zh.; Avgustov B.; Shakuova D.These days, humanity is faced with a global Coronavirus pandemic problem, which entails a financial crisis, so the governments want to minimize their financial loss. In this project work by using the epidemic mathematical model we consider on the basic reproduction number, which is important parameter in the epidemiology and also on the optimization problem about how much should be a discount for the vaccination to optimize the government revenue. During this study, we get acquainted with the following topics: mathematical modelling, dynamical systems, epidemic models, stability analysis, optimization methods, simulations on software and etc. Initially, we constructed the epidemic model for COVID-19 and separated infectious individuals by two groups, based on the compartmental SIR model and after that by using two different approaches to analyze the model, namely, Linearization (Hartman-Grobman) and Next Generation matrix method, we obtained the most important formula in epidemiology: the basic reproduction number 1.3. To solve the government cost, we constructed the government cost function which takes into account the cost of vaccination, the cost of treatment, the average wage of citizens. By using the software we solved numerically the system of nonlinear differential equations of our epidemic model, also we optimized the governmental cost function depending on a vaccination discount and obtained the main result of applied part of our project work 1.6, that the government cost is minimized with making the vaccination fully free of charge for citizens. The study will be useful for the Government of Kazakhstan in predicting the number of infectious individuals as well as in planning the income revenue. By changing the initial parameters in our epidemic model, it is easy compute the basic reproduction number and Government cost function for any country.Item Open Access Решение дифференциальных уравнений с помощью исскусственных нейронных сетей(faculty of engineering and natural sciences, 2013) Газизов Т.We should note the special role of differential equations in the solution of many problems in mathematics, physics and engineering, as it is not always possible to establish a functional relationship between the data and the variables, but it is often possible to derive a differential equation that allows you to accurately predict the course of a particular process under certain conditions. Differential equations have great practical importance, being a powerful tool for exploring the many problems of science and technology: they are widely used in mechanics, astronomy, physics, in many problems of chemistry and biology. This is because very often the laws that govern certain processes are recorded in the form of differential equations, and the equations themselves act as a mean of quantitative interpretation of thus laws. To solve thus equations we take the most well suited networks belonging to a class of Hopfield neural networks. These networks have a way of transmitting output signals to the inputs, and the response of such networks is dynamic, i.e. after receive a new input the output is calculated and transmitting by feedback network modifies the input. Then the output is recalculated, and the process is repeated again. For the network, which can be considered as stable, the sequence of iterations lead to smaller changes in outputs, and at the end the output does not become permanent. There is also an unstable network, for which the process of selection of the output may never end. That's the essence of the network settings for gaining the desired result. Of course, there is also a classical numerical methods. But there are situations where these methods may not lead to a solution, or it can be obtained for a very large number of iterations. The neural network is much more flexible in this respect, and generally, an algorithm based on them is more efficient.Item Open Access JORDAN ELEMENTS IN ASSOSYMMETRIC ALGEBRAS(faculty of engineering and natural sciences, 2022) Kudaibergen Y.We consider Jordan brackets in a free assosymmetric algebra. We investigate expansions of left-normed Jordan brackets in free assosymmetric algebra and give a conjecture. In general, we show the proposition and some examples then the proof. For associative algebras P.M. Cohn gave a criterion for Jordanian elements generated by three elements, but we further advanced to assosymetrical algebras not with three elements, but with four, and we showed five elements, but we have the degree and the elements are equal. In general, we have shown a special case, but in the end, there are assumptions that it can work on any dimension n.Item Open Access Cardinality of survivor sets in open dynamical systems(faculty of engineering and natural sciences, 2020) Aitu N.In this thesis, our goal is to learn about open dynamical systems corresponding interval maps. We study the class of dynamical systems with holes: Expanding maps of the interval. In detail, We consider symbolic dynamics with holes. Let H-hole lies in the interval [0, 1) and let T : [0, 1) −→ [0, 1) be a self map. The survivor set Ω(H) := {x ∈ [0, 1) : T nx /∈ H, n ≥ 0}. Depending on location and size of the holes we will characterize and study the survivor set Ω(H) infinite or finite, uncountable or countable and survivor set Ω(H) has positive entropy.Item Open Access The prediction of information security level in the enterprise(faculty of engineering and natural sciences, 2020) Khashimova D.This thesis presents the results of an analysis to identify groups of threats specific to the infrastructure and systems of an enterprise, which is one of the main stages in forecasting. The state of information security at enterprises is considered, the qualifications of security threats and classification methods based on attack methods and the impact of threats are analyzed. Threats for the safe use of the Internet and hacking sites, data theft, phishing attacks and social engineering are assessed; Identification of cloud computing security threats that are encountered in the enterprise's Internet networks. The advantages and disadvantages of Web Application Firewall, which are used to protect attacks, such as DDoS attacks, SQL injections, cross-site scripting, and others, are studied. Works for providing protection using artificial intelligence and machine learning are presented.Item Open Access Приближение интеграла функции с весом на классе Соболева(faculty of engineering and natural sciences, 2013) Нурмагамбетов Б.ТСовременная вычислительная математика ориентирована на использование компьютеров для прикладных расчетов. Любые математические приложения начинаются с построения модели явления, к которому относится изучаемый вопрос. В различных областях науки и техники, экономики математическими моделями служат функции, производные, интегралы, дифференциальные уравнения. Компьютер дает возможность запоминать большие (но конечные) массивы чисел и производить над ними арифметические операции и сравнения с большой (но конечной) скоростью по данной вычислителем программе. Поэтому для использования компьютеров для вычислений эти исходные модели надо приближенно заменить такими, которые описываются конечными наборами чисел с указанием конечных последовательностей действий (конечных алгоритмов) для их обработки. В алгоритмах обработки экспериментальной информации часто возникает необходимость представления в сжатой форме эмпирических зависимостей между параметрами, описывающих поведение сложной системы. Такое сжатие информации в современной математике осуществляется с помощью различных методов приближения функций: интерполирования, аппроксимации, восстановления и др.Item Open Access ЖАЛПЫЛАНҒАН ҮЗІЛІЛІССІЗДІК МОДУЛІМЕН ФУНКЦИЯЛАР КЛАСЫНДА ИНТЕГРАЛДЫ ЖУЫҚТАУ(faculty of engineering and natural sciences, 2013) Намаджанова М.This work is dedicated to the study class of wt(D) of the system Chebyshev on approximation of the integral.The remainder of the quadrature formula is expressed in terms of the Fourier-Chebyshev series.Used definition of the modulus continuity,the Chebyshev polynomials and integration with weight. The errors of quadrature formula power scale estimated.The work is theoretical in nature.Item Open Access НОВИКОВ АЛГЕБРАЛАРЫ ҮШІН ҚАРАСТЫРЫЛҒАН БУХБЕРГЕР АЛГОРИТМІ(faculty of engineering and natural sciences, 2013) Ілияс Д.Т.Given course work describes the Buchberger algorithm to defind Grébner basis for bicommutative algebra.Item Open Access WEIGHTS OF PARTITIONS(faculty of engineering and natural sciences, 2013) Султамуратов Р.С.Studying Sn-module structure of any algebra is the one of the most important problem in algebra. The weight function gives a good classification of Sn-module structure of Novikov algebras. Image ofweight function defines which Specht modules appear in the algebra, moreover, it is a good tool to determine isomorphism between submodules of Novikov algebras and permutation modules. The main part of diploma gives some usefull and interesting properties of weight function. It is defined that if the great common divisor of all parts of a partition is more that one then the partition does not belong to the set of image of the weight. Also, it is found a criteria minimal element with respect to dominance order in the image of weight. That gives huge help to define admissible partitions. However, there remain some important questions in studying this function.Item Open Access THE SOLUTION OF PROBLEMS WITH DISCONTINUOUS COEFFICIENTS OF THERMAL CONDUCTIVITY BY THE INTEGRAL OF THE ERROR FUNCTION(faculty of engineering and natural sciences, 2013) Kospanova G.The present paper attempts to investigate a new effective method of solving problems of thermal conductivity, new methods of solving parabolic equations with moving boundaries. In this paper it was tried to show the use of interdisciplinary connection оп the example of Mathematical Physics course. Using Integral Error Function a new effective method was developed that positively effects on mathematical achievement of students. Approximate and analytical solutions of the boundary-value problems is found using Integral Error Functions and their properties or by IEF method, which enable to solve wide range of heat equations with fixed and moving boundaries. Analytical solution of heat equation with discontinuous coefficients for the thermal conductivity by IEF method is found in this term paper.Item Open Access 12 жылдық мектептегі математикалық білім беруді даралау мен саралау әдістемесі(faculty of engineering and natural sciences, 2013) Кадрушев М.This paper deals with the problem of individualization and differentiation of teaching mathematics in high school. Lack of individualized academic work students hinders the optimal development of their abilities, entails a reduction in the level of knowledge. For effective teaching of mathematics, this problem is of particular importance, in view of the difficulties that typically arise when the students learn it, and due to the increased knowledge of mathematics education in general secondary education. Individualization of learning mathematics and assumes its mandatory differentiation that must be understood as a comprehensive availability and effectiveness of learning for all students and for each of them separately. Individualization of teaching mathematics does not mean abandoning the collective activities of the students in the learning process, it just means the organic unity of individual and collective learning activity of schoolchildren. Methods of individualization and differentiation of teaching mathematics, as a condition for implementing a 12-year education, not well understood in our country.Item Open Access The solution of the heat equation in domains with moving boundaries by the Integral Error Functions method(faculty of engineering and natural sciences, 2013) Temirkul A.ShIn mathematics , development of new analytical methods of solution of the heat transfer problems is very important for various applications because it enables one to analyze an interrelationship of various input parameters on the dynamics of investigating phenomena, while the use of numerical methods is a problem when the number of parameters is great. And from mathematical point of view, most mathematical models based on Verigin, Stefan and inverse Stefan type boundary value problems. Such problems are among the most complicated, formidable and difficult problems in the theory of nonlinear parabolic equations in mathematical physics, since the corresponding integral equations are singular and require new approaches in solving problems analytically and numerically and also which long with the desired solutions of the equations, moving boundaries have to be found. In some cases, heat potentials can be constructed by which the boundaryvalue problems can be reduced to integral equations. However, in the case of domains that are degenerate at the initial time, additional difficulties arise due to the singularity of the integral* equations, which belong to the class of pseudoVolterra equations that are unsolvable inthe general case bythe method of successive approximations. These results are obtained by S.N. Kharin [2]. The method of solving heat transfer problems with moving boundaries and phase transformation is represented'by Integral Error Functions and its properties. The results indicate that Integral Error Functions enable to solve, many practical problems described above in the easier way than classical methods, and could be implemented into the course of teaching mathematical physics, as special methods of solving heat transfer problems with moving boundaries.Item Open Access Conservative extension in various classes of complete theories models(faculty of engineering and natural sciences, 2019) Orynbasarov D.This thesis is devoted to the in-depth study of the Bektur Baizhanov's "conservative extension of models of weakly o-minimal theories" and the solution of the problem whether it is possible to determine through a conservative extension, nonlocally isolated type. I studied the concept of rational section quasi-rational section and irrational section, extension and elementary extension, orthogonality of types, basic properties of types. Notion of quasi-model (or Tarskii-Vaught type) and any types will be isolated or non-isolated and non-isolated type in turn divides by two kind. It's locally isolated (another word strictly definable) and non-locally isolated. Moreover any types will be definable and non-definable and any isolated type is definable. But is an non-isolated type definable? I was looking for the answer to that question and answered in this thesis. Using the concept of a control formula, I proved that a non-locally isolated type can be definable.Item Open Access КРЕДИТТІК ТЕХНОЛОГИЯ НЕГІЗІНДЕ ЖОҒАРЫ МАТЕМАТИКА КУРСЫ БОЙЫНША СТУДЕНТТЕРДІҢ БІЛІМІН БАҒАЛАУДЫҢ ӘДІСТЕМЕЛІК ЕРЕКШЕЛІКТЕРІ(faculty of engineering and natural sciences, 2013) Дильмагамбетов А.Әр мемлекеттің интеллектуалды, экономикалық және мәдени потенциалы сол елдің білім беру жүйесінің заман талабына сәйкес дамытылуына байланысты. | Заман талабына сай білім беру - қоғам мүшелерінің адамгершілік, интелектуалдық, мәдени дамуының жоғары деңгейін және кәсіби біліктілігін қамтамасыз етуге бағытталған тәрбие беру мен оқытудың үздіксіз үдерісі. Нәтижеге бағытталған білім беру жүйесінде білімалушы тек білім қорын жинақтап қана қоймай, сонымен қатар қажетті және жеткілікті дәрежеде жаңа іске бейім, өз бетімен шешім қабылдай алатын, жаңа эстетикалық, мәдени, тарихи құндылықтарды бағалай алатындай, алған білімдерін өз бетімен әрі қарай тереңдетіп, әртүрлі жаңа жағдайларда кеңінен қолдана алатындай жоғары деңгейдегі ойлау қабілеті дамыған тұлға болып қалыптасуы тиіс. Зерттеудің мәселесі: Білім берудің әрбір сатысында - білімді бағалаудың теориялық және әдістемелік негізін жасаудың маңызы артуына байланысты, білім сапасының обьективтік рейтингін анықтайтын ғылыми дәлелденген әдістеме жасау. Зерттеу обьектісі: Жоғары оқу орындарында студенттерге математиканы оқыту үдерісі. Зерттеу пәні: Кредиттік оқыту жүйесінде жоғары математика курсы бойынша студенттердің білімін бақылау мен бағалау әдістемесі. Зерттеудің мақсаты: Жоғары оқу орындарында студенттерді математикаға оқытуды жетілдіруге, оның тиімділігін арттыруға әсер ететін кредиттік оқыту технологиясы негізінде білімді тексеру мен бағалаудың теориялық және практикалық негіздемелерін дайындау және оны эксперименттік тәжірибе арқылы тексеру. Зерттеудің ғылыми болжамы: Егер жоғары оқу орындарында кредиттік оқыту жүйесі жағдайында студенттерді математиканы игертуге технологиялық тұрғыдан келудің ерекшеліктеріне және оқыту үдерісінің технологиялық сипатының критерийлеріне, ал студенттердің білімін тексеру мен бағалау баллдық-рейтигтік жүйенің ерекшеліктеріне сүйене отырып жүзеге асырылса, онда студенттердің танымдық іс-әрекеттерінің белсенділігі мен дербестігі артады, студенттер білімін тексеру мен бағалаудың обьективті деңгейі көтеріледі, студенттердің оқу материалын меңгерудегі оқу-танымдық ісәрекеттерін циклді және бағытты басқаруға мүмкіндік жасалады және студенттер білімдерінің сапасы артады. Зерттеудің мақсаты, пәні және зертеудің ғылыми болжамы зерттеудің келесідей міндеттерін айқындайды: - жоғары білім беру жүйесіне жаңа технологияларды, соның ішінде кредиттік технологияны енгізу арқылы білім сапасын көтеру мәселелеріне және оны енгізуді негіздейтін нормативтік құжаттар мен оның талаптарының практикада жүзеге асырылу жағдайларына талдау жасау; -зерттеу мәселесіне байланысты жоғары оқу орындарында математиканы оқытуды, студенттер білімін тексеру мен бағалауды жетілдіру жолдарына 3 арналған зерттеу жұмыстарына сараптау және талдау жүргізу; - кредиттік оқыту жүйесінде жоғары математика курсынан студенттердің білімін бағалаудың әдістемелік ерекшеліктерін дәстүрлі бағалау әдісімен салыстыра отырып айқындау; - кредиттік оқыту жүйесінде жоғары математика курсынан студенттердің білімін тексеру мен бағалау әдістемесін (баллдық-рейтінгтік жүйесін) құру; - мемлекеттік стандартқа сәйкес математикадан тақырыптар мен негізгі анықтамаларды сипаттай отырып, дидактикалық бірліктерді анықтау негізінде бақылаулық-тестілік материалдар дайындау; - кредиттік оқыту жүйесінде жоғары математика курсынан студенттердің білімін бағалау әдістемесінің тиімділігін эксперимент арқылы анықтау. Зерттеудің жетекші идеясы: Жоғары білім беру сапасын әлемдік білім беру талаптарына сәйкестендіру үшін білім беру жүйесіне жаңа технологияны енгізу жағдайында студенттердің математикадан білімдерін бағалаудың әдістемелік жүйесін жаңарту. .Item Open Access Bistatistics of permutation coding(faculty of engineering and natural sciences, 2013) Balkhozhayeva A. B.This writing showes that bistatistics (lmin(v)» Tmax(v)) ~ (lmax(v)»Tmin(v)) and (Imax(v)» Pmax(v) ) ~ (lmin(v)» Tmin(v)) are equal distributed over Sz, S3, S4 and Ss. Object of the research: as we know in our days in science design and designs are equally distributed. It’s one of the theorems of Eiler-MacMahon’s. it’s very famous theorem over the world. There is unknown another equally distributed theorems like this. Topicality of the research topic: to show that codes are equidistributed over a set of permutations of S2, $3, Sq and Ss (Lmin(o)»Tmaxco)) * (Imaxco)»Tminto)) and (Lmmax(v)» T max(v)) * (Lmin(v) Tmin(v) ) statistics. The aim and problems of the research: prove given general theorems over S2, S3, S4 and Ss. Chronological frame of the research: to show that (lmin(v)» Tmaxtv)) © (lmax(v)» Tmin(v) ) and (Lmax(v) Tmax(v)) = (lmin(v)»T min(v)) are equally distributed biostatistics. Methodological basis of the research work: the novelty of the work to show that (lmin(w), Tmax(v)) ad (lmax(v)s Tmin(v)) and (lmax(v)» Tmax(v) ) ~ (Lmin(v)»Tmin(v)) are equally distributed biostatistics. Structure of dissertation: Introduction, head section, conclusion, reference. Scientific results of the research: Showing that Statistica I,I1,III and IV are equally distributed.Item Open Access Analysis and the development of a mathematical model of the incidence of tuberculosis among adolescents(faculty of engineering and natural sciences, 2019) Zhailaubek A.Tuberculosis is a disease that is highly socialized. Tuberculosis morbidity and mortality of the population are important epidemiological indicators that characterize the tuberculosis infection situation. In addition to demographic and medicoorganizational, a certain contribution is made socio-economic factors to the formation the above indicators. The study's objective is to study the impact of socio-economic factors on tuberculosis incidence and mortality in the Republic of Kazakhstan. The correlation and multiple regression analysis is carried out to define influence of medical service and socio-economic factors on incidence of tuberculosis in the Republic of Kazakhstan.Item Open Access RELATION BETWEEN STATISTICS OF PERMUTATIONS(faculty of engineering and natural sciences, 2013) Fayziyev Sh.Permutations have a remarkably rich combinatorial structure. Part of the reason for this is that a permutation of a finite set can be represented in many equivalent ways, including as a word (sequence), a function, a collection of disjoint cycles, a matrix, etc. Each of these representations suggests a host of natural invariants (or "statistics"), operations, transformations, structures, etc., that can be applied to or placed on permutations. The fundamental statistics, operations, and structures on permutations include descent set (with numerous specializations), excedance set, cycle type, records, subsequences, composition (product), partial orders, simplicial complexes, probability distributions, etc. This paper contains topics that relates to the main part and definitions to understand the main part of this work. In the main part, we consider statistics of permutations, equidistributions of them.Item Open Access Development of a mathematical model of the system for collecting and analyzing data(Faculty of engineering and natural sciences, 2019) Suleizhan T.This thesis is aimed at developing practical skills of building mathematical svstems for data collection and analvsis. The peculiarity of the work is to learn to self-decision-making. to develop research skills. which is especially iniportant in a dynamic world. Data collection is carried out. in almost all areas of science and technology. Over the past few vears. data collection techniques have been applied to applications and new corporations have emerged to commercialize the technology. Many business and financial problems are successfully solved with the use of big data. Problems of management, classification. pattern recognition, forecasting, inherent in almost all application areas. such as medicine. military Affairs. aviation and space, construction, are increasingly solved with the use of this technology. In this regard. vou will see a fundamental understanding of the basic concepts and models of big data, as well as learn how to apply this knowledge - in practice.Item Open Access Analysis and the development of a mathematical model of the children mortality(Faculty of engineering and natural sciences, 2019) Zhumabek D.The mortality rate depends on many different factors: the socio-economic development of the country, the environmental situation. the well-being of the population. the level of stress and much more. After fertility. it takes the second place in its importance in the processes of reproduction of the population. has a serious impact on the population size. its structure. and is closely interconnected with all socio-demographic processes. The causes of mortality in Kazakhstan are classified by the main groups: infectious discases. diseases of the respiratory system. circulatory system, neoplasms. accidents, poisonings and injuries. Mortality of the population is a mirror reflection of the level of socio-economic development of society.Item Open Access Integral power balance method in heat problems with free boundary(Faculty of engineering and natural sciences, 2019) Kassabek DinaOne of the important areas of application of the free boundary problems is the mathematical modelling of phenomena in the low-temperature plasma of an electric arc and in contacts of electrical devices. Analysis of solutions makes it possible to verify the obtained theoretical results, to test the effectiveness of the developed algorithms for specific evolutionary processes in electrical apparatuses, and to interpret the available experimental data. The evolution of contact bridge and arcing processes is so fast (nano- and microsecond range) that their experimental study is very difficult. In some cases, only mathematical modeling can give an idea of their dynamics. Thus, the need for modeling is required not only for optimization of the experiment, but also due to the impossibility of using a some different approach. One of the most effective methods of solving heat problem is the method of heat potentials, which reduces the initial boundary value problems to integral equations. However, in the case of regions degenerating at the initial time, additional difficulties arise releted to the singularity of these integral equations. These difficulties are compounded in the case when an unknown function appears not only in the boundary condition, but also in the coefficients of the equation. This method enables us to obtain an approximate solution with desirable degree of accuracy and to evaluate the approximation error, using the maximum principle. Analytical methods for solution of heat and mass transfer problems have recently received a new stimulus to their futher development due to the growing need to solve multicriteria problems for which numerical methods are unable to estimate the influence of a large number of input parameters on the behaviour of the solution and especially on its dynamics. In particular, an integral thermal balance method, a perturbation method, and a number of other methods are widely used to solve problems of the Stefan type with a free boundary, describing heat transfer with phase transitions. The main problem with the use of this method is the estimation of the approximation error, which, as a rule, is replaced for applied problems by comparison of the analytical solution with the experimental data.