Статьи

There are two main approaches to the numerical solution of the eikonal equation: reducing it to a system of ODES (method of characteristics) and constructing specialized methods for the numerical solution of this equation in the form of a partial differential equation. The latter approach includes the FSM (Fast sweeping method) method. It is reasonable to assume that a specialized method should have greater versatility. The purpose of this work is to evaluate the applicability of the FSM method for constructing beams and fronts. The implementation of the FSM method in the Eikonal library of the Julia programming language was used. The method was used for numerical simulation of spherical lenses by Maxwell, Luneburg and Eaton. These lenses were chosen because their optical properties have been well studied. A special case of flat lenses was chosen as the easiest to visualize and interpret the results. The results of the calculations are presented in the form of images of fronts and rays for each of the lenses. From the analysis of the obtained images, it is concluded that the FSM method is well suited for constructing electromagnetic wave fronts. An attempt to visualize ray trajectories based on the results of his work encounters a number of difficulties and in some cases gives an incorrect visual picture.

In this paper, we study the effect of using the Metropolis–Hastings algorithm for sampling the integrand on the accuracy of calculating the value of the integral with the use of shallow neural network. In addition, a hybrid method for sampling the integrand is proposed, in which part of the training sample is generated by applying the Metropolis–Hastings algorithm, and the other part includes points of a uniform grid. Numerical experiments show that when integrating in high-dimensional domains, sampling of integrands both by the Metropolis–Hastings algorithm and by a hybrid method is more efficient with respect to the use of a uniform grid.

The article presents the results of the evaluation of quartiles of scientific conferences presented by leading rating agencies. The estimates are based on the use of three methods of multivariate statistical analysis: linear regression, discriminant analysis and neural networks. A training sample was used for evaluation, including the following factors: age and frequency of the conference, number of participants and number of reports, publication activity of the conference organizers, citation of reports. As a result of the study, the linear regression model confirmed the correctness of the quartiles exposed for 77% of conferences, while the methods of neural networks and discriminant analysis gave similar results, confirming the correctness of the quartiles exposed for 81 and 85% of conferences, respectively.

The problem of identifying deterministic cause-and-effect relationships, initially hidden in accumulated empirical data, is discussed. Statistical methods were used to identify such relationships. A simple mathematical model of cause-and-effect relationships is proposed, in the framework of which several models of causal dependencies in data are described – for the simplest relationship between cause and effect, for many effects of one cause, as well as for chains of cause-and-effect relationships (so-called transitive causes). Estimates are formulated that allow using the de Moivre–Laplace theorem to determine the parameters of causal dependencies linking events in a polynomial scheme trials. The statements about the unambiguous identification of causeandeffect dependencies that are reconstructed from accumulated data are proved. The possibilities of using such data analysis schemes in medical diagnostics and cybersecurity tasks are discussed.

We introduce a numerical method to solve the two-dimensional time-dependent Schrödinger equation, which characterizes a system of two atoms with a finite-range interaction potential confined within a harmonic oscillator trap. We choose a Gaussian-shaped potential for the interaction potential. Such a system has been previously studied analytically, except that a zero-range interaction potential was used instead. We observe a strong agreement between the results for the two types of interactions. Also, we investigate the one-dimensional time-dependent Schrödinger equation for the relative motion and compute the ground state energy level as a function of the coupling strength.

Our group has been investigating kinetic models for quite a long time. The structure of classical kinetic models is described by rather simple assumptions about the interaction of the entities under study. Also, the construction of kinetic equations (both stochastic and deterministic) is based on simple sequential steps. However, in each step, the researcher must manipulate a large number of elements. And once the differential equations are obtained, the problem of solving or investigating them arises. The use of symbolic-numeric approach methodology is naturally directed. When the input is an information model of the system under study, represented in some diagrammatic form. And as a result, we obtain systems of differential equations (preferably, in all possible variants). Then, as part of this process, we can investigate the resulting equations (by a variety of methods). We have previously taken several steps in this direction, but we found the results somewhat unsatisfactory. At the moment we have settled on the package Catalyst. jl, which belongs to the Julia language ecosystem. The authors of the package declare its relevance to the field of chemical kinetics. Whether it is possible to study more complex systems with this package, we cannot say. Therefore, we decided to investigate the possibility of using this package for our models to begin with standard problems of chemical kinetics. As a result, we can summarize that this package seems to us to be the best solution for the symbolic-numerical study of chemical kinetics problems.

Chronic non-communicable diseases account for more than 70% of global mortality statistics. The main share is made up of diseases of the cardiovascular system. Adequate preventive measures—impact on controllable and conditionally controllable risk factors—can reduce the contribution of these diseases to the structure of mortality. A significant effect can be achieved with an adequately selected level of physical activity, but doctors do not always recommend specific actions to patients. This article describes a prototype of a cognitive assistant for constructing personalized plans for therapeutic physical exercises for relatively healthy people and people suffering from cardiovascular diseases. The developed system consists of two main components: a cardiovascular risk assessment module and an exercise planning module. The risk assessment module consists of a knowledge base and an argumentative reasoning algorithm. Its task is to identify risk factors and levels, which is dual in nature: in the case of monitoring a relatively healthy user, the risk of developing cardiovascular disease is assessed, while in the case of interaction of the system with a user with cardiovascular disease, the risk of complications of a chronic form is assessed—development of a cardiovascular event. The exercise planning module includes an exercise database and a scheduler algorithm. The planning algorithm selects optimal therapeutic physical exercises according to optimal criteria, in order to form a plan that will not harm the patient and will increase his physical performance. The developed mechanism allows you to create training scenarios for users with any level of initial training, taking into account the available sports equipment, the preferred location for training (home, street, gym) and at any level of the cardiovascular continuum.

Superconducting properties of twisted tri-layer graphene (TTG) are studied within the scope of the chiral model based on using the unitary matrix

Earlier we developed a stable fast numerical algorithm for solving ordinary differential equations of the first order. The method based on the Chebyshev collocation allows solving both initial value problems and problems with a fixed condition at an arbitrary point of the interval with equal success. The algorithm for solving the boundary value problem practically implements a single-pass analogue of the shooting method traditionally used in such cases. In this paper, we extend the developed algorithm to the class of linear ODEs of the second order. Active use of the method of integrating factors and the d’Alembert method allows us to reduce the method for solving second-order equations to a sequence of solutions of a pair of first-order equations. The general solution of the initial or boundary value problem for an inhomogeneous equation of the second order is represented as a sum of basic solutions with unknown constant coefficients. This approach ensures numerical stability, clarity, and simplicity of the algorithm.

This research aims to investigate the influence of stock market volatility and liquidity turnover on returns in the emerging markets of Middle East and North Africa (MENA countries) using the interaction of global economic policy uncertainty index and exchange rate as a moderating variable. The paper employs panel quantile regression with daily data from January 1, 2000 to August 30, 2024 and a panel quantile regression sensitivity analysis. The findings suggest that the U. S. economic policy uncertainty index was markedly negative; the negative and significant interaction coefficient between the variables of exchange rate fluctuations and worldwide economic policy uncertainty indicates that stock returns of the MENA markets dropped substantially in response to international economic policy uncertainty; the more extensively the exchange rate fluctuated, the lower were the returns. Empirical evidence reveals shifting dynamics in the impact of short-term interest rate volatility on returns as we move from the period before the pandemic outbreak to the post-pandemic era. The study has notable implications for financial investors. Markets’ response to interest rate volatility cannot be predicted with high degree of certainty because the market reacts spontaneously to adjustments in the short-term interest rate even when market players operate rationally and base their decisions on all available information regarding stock prices. As a result, investors may choose to consider selecting shorter-life alternative equities as a long-term hedge against interest rate volatility risk. The MENA countries’ central monetary authorities and governments should work jointly to maintain stock market stability by enacting measures to make stock exchanges and the equity markets more resilient to the negative effects of uncertainty brought on by foreign economic policy, even as exchange rate volatility rises. Additionally, international business entities and traders could also shield themselves against international economic policy-related risk of uncertainty in the midst of currency volatility given the current research.

Первый раздел настоящей статьи содержит описание оригинальных печатных изданий произведений Г. Ф. Телемана, хранящихся в Российской государственной библиотеке. Собрание насчитывает 15 публикаций, ранее принадлежавших Королевской библиотеке в Берлине (ныне - Берлинская государственная библиотека). Сравнение оригинала Symphonie zur Serenate (шифр МЗ Р-ИН / 3280) с так называемым «факсимиле» Симфонии, изданном в Германии в 1980 г., показывает, что последнее не воспроизводит всех деталей подлинника, но представляет его ретушированную версию. Второй раздел публикации посвящен характеристике источников и особенностям композиции Симфонии и Серенаты. Музыка к юбилею целиком не сохранилась, до нас дошли лишь партитура Симфонии и либретто Серенаты. Изучение либретто позволяет получить представление о типах номеров и структурах некоторых из них. Как либретто Серенаты, так и партитура Симфонии включают другой немаловажный источник - авторский комментарий к частям Симфонии.

В условиях ограниченных возможностей государства в реализации социальных проектов и удовлетворения нематериальных потребностей граждан, все более возрастает роль некоммерческих организаций (далее - НКО), деятельность которых сопряжена с решением социальных проблем и развитием гражданского общества. Однако в условиях цифровой социокультурной реальности НКО сталкиваются с барьерами, препятствующими их продвижению. В статье представлены результаты эмпирического исследования SMM-продвижения НКО в городе Кимры в социальной сети «Вконтакте». На основании результатов проведенного исследования сконструирована модель SMM-продвижения НКО, с учетом их особенностей, которая может способствовать использованию современных методов цифрового пространства, таких как контент, таргетированная реклама, реклама лидеров мнений для повышения потенциала НКО в социальной сфере.