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ХАБАРШЫ - bulletin-phmath.kaznpu.kz


Academic year: 2023

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CHARACTERISTICS OF PLANNING AND ORGANIZING PRACTICAL CLASSES ON THE METHODOLOGY TO TEACH THE UPDATED CONTENT OF THE DISCIPLINE. The article discusses examples of the differential equation problem in Python with a graph for high school students. In the second section, exact estimates of the best approximations of certain functions are established.

Вспомогательные утверждения

Оценки наилучших приближений со ступенчатым крестом

The formulation of the inverse problem is formulated, a numerical method for solving the system of equations is described. The oil temperature decreases along the length of the pipeline due to heat transfer from the ground, leading to an increase in oil viscosity and an increase in hydraulic resistance. The dependence of the hydraulic resistance of the pipeline on the parameters of oil pumping is determined by solving the inverse problem.

Кіріспе және негізгі нәтижелер

Көмекші тұжырымдар

A solitary wave theory of the great red spot and other observed features in the Jovian atmosphere // Icarus. WHEN INTERPOLATING THE VALUES OF FUNCTIONS SPECIFIED BY THE TABLE EFFICIENCY OF THE LEAST QUANTUM METHOD. The article provides a general algorithm of the method of least squares (OLS) for compiling a program account, taking into account the characteristics of the Gram matrix.

In fact, the difference and advantage of the OLS over the long-known Langrange and Newton interpolation polynomials is emphasized. The characteristic of the full algorithm of the square version is given using specially selected mathematical formulas. The application of the least squares method has a wide scope, especially for geographical forecasting, hydrometeorological monitoring and metering of geological resources.

In the case of non-self-adjoint ordinary differential operators, the basic property of systems of eigenfunctions and associated functions (E&AF), in addition to the boundary value conditions, can be affected by values ​​of coefficients of the differential operator. Furthermore, it is known that the basic properties of E&AF can be changed by a small change of values ​​of the coefficients.

2 ,sin


Первичную попытку изучения матричного оператора (1) можно найти в [1], где при некоторых предположениях об элементах матрицы  ai,j даны достаточные условия ограничения оператора в пространствах lp . Поэтому целью данной работы является установление нового альтернативного критерия ограниченности матричного оператора (1) от lpv до lqu при 1 pq в предположении условия (2). При этом неравенства вида MK, когда значение положительной константы  не является решающим для наших целей, будут обозначаться M K, а MK будет означать наличие двусторонней оценки M  К М.

Основной результат Пусть

В этой статье кратко рассматривается, как это работает: одна из популярных бесплатных онлайн-платформ под названием «Академия Хана» для изучения математики с точки зрения методики преподавания. Школы по всей Америке используют перевернутые классы вместе с Академией Хана, чтобы эффективно и бесплатно преподавать математику как в классе, так и за его пределами. В статье рассматривается, как с точки зрения методики преподавания работает одна из популярных бесплатных онлайн-платформ для изучения математики «Академия Хана».

Академия Хана — это онлайн-платформа с видеоуроками и пояснениями, а также набором упражнений для изучения таких предметов, как математика, естествознание и многое другое. Спасибо сессиям обратной связи в процессе исследования, которые дали возможность прояснить многие моменты. Главный важный вывод – эффективность и влияние Академии Хана на академический прогресс студентов.

This may be one of the reasons why Kazakhstani schools do not use the free and accessible platform Khan Academy to teach and study Mathematics, Science. Most of the research done by Khan Academy itself on the effectiveness of their tool to learn Maths.

Введение. Исследование решений систем дифференциальных уравнений в частных производных с колебательными свойствами в протяжении как временных, так и пространтвенных переменных

The problem of the existence and the integrated representation of a unique multiperiod solution of a second-order linear inhomogeneous system with constant coefficients and a differentiation operator on the direction of the main diagonal of the space of time variables and the vector fields in the form of Lyapunov systems with respect to space variables was considered. The multiperiodicity of zeros of this operator and the condition for the absence of a non-zero multiperiodic and real-analytic solution of the homogeneous system corresponding to the given system are established. An integrated representation of solutions of an inhomogeneous linear autonomous system that are multiperiodic in time variables and real-analytic in space variables is obtained.

The theorem of the existence of a unique multiperiodic in terms of time variables and real-analytic in terms of spatial variables solution of the original linear system in terms of the Green's function under sufficiently general conditions is substantiated.

Многопериодичесое решение автономной системы

Решение основной задачи о многопериодическом решении

Multiperiod solution of a linear system of equations with the differentiation operator along the main diagonal of the space of independent variables and lagged arguments // Proceedings of the AIP Conference. Multiperiod solution of an autonomous system of equations with the differentiation operator with respect to space and time variables // Scientific magazine Vestnik of Aktobe Regional State University K.Zhubanov. On multi-periodic solutions of quasilinear autonomous systems with differentiation operator in the Lyapunov vector field // KARAGANDA-MATHEMATICS UNIVERSITY BULLETIN.

Research of multiperiod solutions of autonomous linear systems perturbed with differentiation operator in the vector field // News of the National Academy of Sciences of the Republic of Kazakhstan. In this paper, we investigate the norm limit of the convolution operator in anisotropic Triebel-Lizorkin spaces. It is necessary to determine which conditions in the parameters of the spaces from f and g are obtained and to study which space belongs to their convolution.

An analogue of the O'Neil theorem was obtained for the Triebel-Lizorkin space scale Fpταq, where α, τ, p, q are vector parameters. Relations of the form Frμβη Fhνγξ↪Fpταq are obtained, with the corresponding relations of vector parameters αβγ,.


Жұмыста Трибель-Лизоркин кеңістігінің Fpταq шкаласы үшін О'Нил теоремасының аналогы алынды, мұндағы α, τ, p, q векторлық параметрлер. О'Нилдің аналогтық теоремасы Tribel-Lizorkin Fpταq кеңістіктерін масштабтау үшін қағазда алынған, мұндағы α, τ, p, q векторлық параметрлер. Бұл теңсіздіктер гармоникалық талдауда және дербес дифференциалдық теңдеулер теориясында маңызды рөл атқарады [1].

There are generalizations of Young's and O'Neil's inequalities for various functional spaces: weighted Lp spaces, classical and Lorentz weighted spaces, Hardy spaces, Wiener spaces, Orlitz spaces; see and references there. In this paper, we investigate the boundedness of the convolution operator in anisotropic Triebel-Lizorkin spaces.

Anisotropic Triebel–Lizorkin spaces

In the isotropic case, these spaces were investigated in [15], where the interpolation properties were investigated. Estimates of the norm of the convolution operator in anisotropic Besov spaces with the dominated mixed derivative // ​​Bulletin of the Karaganda University-Mathematics, - 2019. The paper considers a boundary value problem for a single perturbed linear differential equation with constant third-order coefficients.

In this problem, a small parameter is indicated before the highest derivatives that are part of the differential equation and the boundary condition at t = 0. The fundamental system of solutions of a homogeneous, singularly perturbed differential equation is constructed from obtained asymptotic representations for the roots of the corresponding characteristic equation. This system was used to construct the Cauchy function, special functions of limit value problems, and also the Green function. Using these functions, an analytic formula is obtained for solving a singularly perturbed boundary value problem and it is found that this solution has an initial jump of zero order at t = 0.

It is proved that the solution of the considered unique perturbed boundary value problem tends towards the corresponding unperturbed problem obtained from the one under  0.

Егер I , II шарттар орындалса, онда (1), (2) сингулярлы ұйытқыған шеттік есептің 1

The article deals with integral equations widely used in various parts of physics (theory of waves on the surface of liquids, quantum mechanics, problems of spectroscopy, crystallography, acoustics, analysis and diagnostics of plasma, etc.), geophysics (problems of gravimetry, kinematic problems of seismics), mechanics (vibrations of structures), etc. When physics introduced aftereffects, there are not enough ordinary differential equations or partial differential equations, otherwise the initial data would determine the future state. To account for the continuous sequence of preceding states, we must use integral and integro-differential equations, where the sign of the integral appears as functions of parameters characterizing the system, which depend on time during some period prior to the moment in question.

In this article, we have considered the solution of Fredholm integral equations of the second kind by the method of successive approximations and the method of repeated nuclei.


STUDY OF THE ELEMENTARY COMPOSITION OF THE FILLER OF THE IRRADIATED POLYMER COMPOSITE USING THE METHOD OF X-ray FLUORESCENCE ANALYSIS. The article examines the elemental composition of fillers (polytetrafluoroethylene and carbon nanopowder) of the polymer composite depending on different concentrations of fillers and electron irradiation and modified polytetrafluoroethylene (PTFE). The elemental composition of the fillers and their distribution along the depth of the polymer composite and modified polytetrafluoroethylene were studied by X-ray fluorescence analysis (XRFA) and confocal micro-X-ray analysis.

The analysis of the X-ray spectra of the modified PTFE samples, shown in Figure 5 a, b, shows that the intensity of the characteristic lines of other chemical elements is significantly reduced due to the decrease in the concentration of atoms of these substances in the sample. The data on the study of the distribution of elements in depth in the modified PTFE samples (Fig. 6 a, b) show peaks. Analysis of X-ray spectra of modified PTFE samples showed that the intensity of the characteristic lines of other chemical elements is significantly reduced due to the decrease in the concentration of atoms of these substances in the sample.

Interdisciplinary communication should be considered as a manifestation of the relationship of different sciences in the educational process. Almost all information about amplitudes can be encoded in the operator algebra of local physical operators.

Figure 1. X-ray spectrum of the composite:
Figure 1. X-ray spectrum of the composite:


Figure 1 – function graphs 𝑥 1 (𝑡), 𝑥 2 (𝑡)  Figure 2 – function graph 𝑥 1 (𝑡) + 𝑥 2 (𝑡)
Table 1. Value of parameters in the problem
Table 2.  Results of iteration calculations
Figure 1. X-ray spectrum of the composite:

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