Unique solvability of boundary value problem for functional differential equations with involution

In this paper we consider a boundary value problem for systems of Fredholm type integral-differential equations with involutive transformation, containing derivative of the required function on the right-hand side under the integral sign. Applying properties of an involutive transformation, original boundary value problem is reduced to a boundary value problem for systems of integral-differential equations, containing derivative of the required function on the right side under the integral sign. Assuming existence of resolvent of the integral equation with respect to the kernel K˜2(t, s) (this is the kernel of the integral equation that contains the derivative of the desired function) and using properties of the resolvent, integral-differential equation with a derivative on the right-hand side is reduced to a Fredholm type integral-differential equation, in which there is no derivative of the desired function on the right side of the equation. Further, the obtained boundary value problem is solved by the parametrization method created by Professor D. Dzhumabaev. Based on this method, the problem is reduced to solving a special Cauchy problem with respect to the introduced new functions and to solving systems of linear algebraic equations with respect to the introduced parameters. An algorithm to find a solution is proposed. As is known, in contrast to the Cauchy problem for ordinary differential equations, the special Cauchy problem for systems of integral-differential equations is not always solvable. Necessary conditions for unique solvability of the special Cauchy problem were established. By using results obtained by Professor D. Dzhumabaev, necessary and sufficient conditions for the unique solvability of the original problem were established.

Gauss-Simpson Quadrature Algorithm for Calcaulting Additional Stress in Foundation Soils

The additional pressure at the bottom of a building’s foundation produces an additional stress in the foundation soils under the building’s foundation. In order to overcome the limitations of traditional elastic theory methods and the finite element method when calculating the additional stress in foundation soils, we use the Gauss-Simpson formula to derive the Gauss-Simpson Quadrature Algorithm based on the elasticity theory. The Gauss-Simpson Quadrature Algorithm is a method designed to calculate the additional stress in foundation soils under an irregularly shaped foundation and an irregular load distribution. This new method is based on the fact that the Gaussian quadrature formula and the Simpson formula are independent of the specific type of integrand. The finite element method with n interpolation points can only achieve an algebraic accuracy of n. The interpolation points of the Gaussian quadrature formula are n zeros of orthogonal polynomials, which can achieve an algebraic accuracy of 2n + 1. Moreover, the weights of the nodes in the quadrature formula are all positive, and thus, it has a high numerical stability. In the proposed method, the Simpson formula is necessary. The Simpson formula is used to transform the implicit additional stress formula with the integral sign into an explicit cumulative integral, which can be considered similar to the rectangular domain case to obtain an explicit analytical algebraic formula for solving the additional stress approximation. In engineering applications, we only need to provide the field engineers with the locations of the interpolation points of the Gauss-Legendre formula, the interpolated weight coefficients, and the specific type of Simpson's formula, and then, the results of the additional stress can be calculated manually, which is nearly impossible using the traditional methods and finite element methods. From the point of view of academic rigor and theoretical completeness, it is possible to use the compound Gauss-Simpson Quadrature Algorithm in conjunction with the looping function in computer programs. Under standard conditions, the proposed Gauss-Simpson Quadrature Algorithm is in good agreement with the results of the traditional elasticity theory.

Difference methods for solving nonlocal boundary value problems for fractional-order differential convection-diffusion equations with memory effect

In the present paper, in a rectangular domain, we study nonlocal boundary value problems for one-dimensional in space differential equations of convection-diffusion of fractional order with a memory effect, in which the unknown function appears in the differential expression and at the same time appears under the integral sign. The emergence of the integral term in the equation is associated with the need to take into account the dependence of the instantaneous values of the characteristics of the described object on their respective previous values, i.e. the effect of its prehistory on the current state of the system. For the numerical solution of nonlocal boundary value problems, two-layer monotone difference schemes are constructed that approximate these problems on a uniform grid. Estimates of solutions of problems in differential and difference interpretations are derived by the method of energy inequalities. The obtained a priori estimates imply the uniqueness, as well as the continuous and uniform dependence of the solution on the input data of the problems under consideration and, due to the linearity of the problem under consideration, the convergence of the solution of the difference problem to the solution of the corresponding differential problem with the rate $O(h^2+\tau^2)$.

AN ANALYSIS OF TITLE FUNCTIONS (ON THE MATERIAL OF DARYA DONTSOVA’S IRONIC DETECTIVE NOVELS)

Целью нашей статьи является исследование семиотической природы заголовков детективных романов Д. Донцовой исходя из трех измерений семиозиса: семантики, синтактики и прагматики. Главным методом исследования служит семиотический анализ. Вспомогательными являются методики контекстуально-интерпретационного, структурного, лингвостилистического и прагматического анализа, метафорического моделирования и жанрового анкетирования. Гипотеза исследования − предположение о том, что основная функция заголовка художественного текста, в отличие от масс-медийного или научного и др., маркирующая, индексирующая текст как целостный знак, информативная же функция может быть реализована лишь в результате понимания целого произведения, установления его жанровой принадлежности, с учетом всеобъемлющей диалогичности текста с творчеством автора в целом, интертекстом литературного процесса. В рекламных целях в заглавиях некоторых произведений может вообще отсутствовать какая-либо ориентация на прогнозирование смысла последующего текста. Особенностями заголовков романов Д. Донцовой являются парадоксальность, проявляющаяся в семантической несовместимости составляющих библионима, насыщенность прецедентными знаками, интертекстуальность и интерсемиотичность, карнавализация, языковая игра, пародирование, персуазивность и суггестивность. Семантический параметр семиозиса библионимов предполагает установление их содержательной связи не только с последующим текстом, но и с фондом интертекстовых и интерсемиотических знаний читателя. Семантика заглавий иронических детективов Д. Донцовой соотносится со структурными компонентами жанра иронического детектива, нередко второстепенными, характеризуется метафорическим заимствованием лексем из различных донорских доменов. Синтактика библионимов реализуется в связях с различными компонентами озаглавленного текста, с мегатекстом, интертекстом, невербальными семиосферами культуры, в том числе и с прецедентными феноменами. Прагматика библионимов Д. Донцовой ориентирована на возбуждение интереса, любопытства, желания разрешить парадоксы заглавия путем прочтения и понимания содержания книги. Свойственная заголовкам иронических детективов парадоксальность служит мощным суггестогеном, воздействующим не только на сознание читателей, но и на бессознательные ресурсы психики. Перспективы изучения данной проблематики заключаются в выявлении стратегических программ коммуникативного воздействия заглавий произведений массовой литературы, проведении экспериментальных исследований по выявлению индекса информативности библионимов и их прогностичности по отношению к последующему тексту. The aim of the article is to examine the semiotic nature of the titles of detective novels by Darya Dontsova based on the three dimensions of semiosis: semantics, syntactics and pragmat-ics. Semiotic analysis serves as the main research method. Contextual interpretation, structural, stylistic and pragmatic analysis, metaphorical modeling and genre questionnaire are auxiliary methods. The research hypothesis lies in a supposition that the basic function of the title of a lit-erary text, unlike that of a mass media, scientific, etc. text, is to label, index a text as an integral sign. An informative function of the title can be realized after understanding the whole text, de-termining its genre, and taking into consideration the overall dialogism of the text with the au-thor’s oeuvre and with the intertext of the literary process. For advertising purposes, some titles are not intended to predict the sense of subsequent texts. The features of Dontsova’s titles are paradoxicality (elements of titles are semantically incompatible), abundance of precedent signs, intertextuality, intersemioticity, carnivalization, language game, parody, persuasion, and sug-gestiveness. The semantic parameter of title semiosis presupposes clarifying the content-related link of the titles not only with subsequent texts but also with the reader’s intertextual and in-tersemiotic knowledge. The semantics of the titles of Dontsova’s ironic detective novels is corre-lated with the frequently secondary structural components of this genre and is characterized by the metaphorical borrowing of lexemes from different source domains. The syntactics of the ti-tles is realized through relations with different components of the texts, with megatext and in-tertext, with nonverbal cultural semiospheres, including precedent phenomena. The pragmatics of the titles is to spark interest, curiosity, desire to resolve the paradoxes of the title by reading and understanding the content of the book. Paradoxicality, inherent to titles of ironic detective novels, serves as a powerful means of suggestiveness, affecting both readers’ consciousness and the unconscious resources of the psyche. The prospects of this research are to focus on the stra-tegic programs of the communicative influence of titles of popular literature, to conduct experi-mental studies on the index of the title informing properties and on the title predictive value for subsequent texts.

Using Mathematical Equations to Communicate and Think About Karma

Two equations are presented in this article to communicate a particular understanding of karma. The first equation relates future experiences to past and present actions. Although the equation uses variables and mathematical symbols such as the integral sign and summation symbol, it reads more like a literal translation of an English sentence. Based on the key idea in the first equation, a second equation is then created to highlight the viability of using math to communicate concepts that are not readily quantifiable. Analyzing such equations can stimulate thinking, enhance understanding of spiritual concepts, raise issues, and uncover tensions between our ordinary conceptions of external reality and transcendental aspects of spirituality.

ERRORS ANALYSIS OF STUDENTS IN SOLVING VOLUME OF THE SOLID OF REVOLUTION PROBLEM IN TERM OF CRITICAL THINKING ASPECTS

Students of mathematics education need to have a good understanding in solving integral calculus problems, but often have difficulty in understanding the subject material. The difficulties can be seen from the mistakes made by students when solving the problems. This article aims to analyze the errors of students in learning integral calculus especially in the subject of volume of the solid of revolution in terms of critical thinking aspects. This research is a qualitative descriptive study involving twenty-four of 6th-semester students of mathematics education at a private university in Yogyakarta. The research subjects were chosen purposively by considering: student errors in determining the volume of the solid of revolutions with integral techniques in terms of critical thinking aspect. The findings of this study indicate, student errors in determining the function of integrals, write down the rules of integral writing, misunderstanding in algebraic concepts, adding constants, write down limits and sigma notations, determine integration methods, determine boundaries integration, writing in integral sign, and error in determining the radius of the solid of revolution.

Existence of Optimal Control for a Nonlinear Partial Differential Equation of Hyperbolic Type

In this paper, we prove the existence of an optimal control for a nonlinear hyperbolic problem, examined in [3]. An estimation is used which makes it possible to extract from a minimizable sequence of controls and from the sequence of corresponding solutions weakly convergent sub sequences. To prove the passage to the limit in a true equality for every element of the minimizable sequence, Lebesgue’s theorem on the passage to the limit under the integral sign and the theorem of immersion have been used.