Scientific Perspectivism and the Methodology of Modern Mathematical Physics

Perspectival realists often appeal to the methodology of science to secure a realist account of the retention and continued success of scientific claims through the progress of science (e.g. Massimi, 2016). However, in the context of modern physics, the retention and continued success of scientific claims is typically only definable within a mathematical framework. In this paper, I argue that this concern leaves the perspectivist open to Cassirer’s (1910) neo-Kantian critique of the applicability of mathematics in the natural sciences. To support this criticism, I present a case study on the conservation of energy in modern physics.

AUTOMATION OF CONSTRUCTION OF A SCHEME FOR SOLVING COMPUTE- INTENSIVE PROBLEMS OF MATHEMATICAL PHYSICS ON SUPERCOMPUTERS

В статье представлен подход к разработке информационно-аналитической системы, помогающей исследователю решать вычислительно сложные задачи математической физики на суперкомпьютерах. Система автоматически строит схему решения задачи по спецификации пользователя, введенной им в режиме диалога. Схема включает наиболее подходящие математические модели для решения задачи, численные методы, алгоритмы и параллельные архитектуры, ссылки на доступные фрагменты параллельного кода, которые пользователь может использовать при разработке собственного кода. Построение схемы осуществляется на основе онтологии проблемной области «Решение вычислительно сложных задач математической физики», онтологии заданной предметной области и экспертных правил, построенных с использованием технологии Semantic Web. The paper presents an approach to the development of an information-analytical system that helps a researcher to solve compute-intensive problems of mathematical physics on supercomputers. The system automatically builds a scheme for solving the problem according to the user's specification entered by him in the dialogue mode. The scheme includes the most suitable mathematical models for solving the problem, numerical methods, algorithms and parallel architectures, links to available fragments of parallel code that the user can use when developing their own code. The construction of the scheme is carried out on the basis of the ontology of the problem area "Solving compute-intensive problems of mathematical physics", the ontology of a given subject area and expert rules built using the Semantic Web technology.

The embedding theorems for anisotropic Nikol’skii-Besov spaces with generalized mixed smoothness

The theory of embedding of spaces of differentiable functions studies the important relations of differential (smoothness) properties of functions in various metrics and has a wide application in the theory of boundary value problems of mathematical physics, approximation theory, and other fields of mathematics. In this article, we prove the embedding theorems for anisotropic spaces Nikol’skii-Besov with a generalized mixed smoothness and mixed metric, and anisotropic Lorentz spaces. The proofs of the obtained results are based on the inequality of different metrics for trigonometric polynomials in Lebesgue spaces with mixed metrics and interpolation properties of the corresponding spaces.

Analytical solutions of the fifth-order time fractional nonlinear evolution equations by the unified method

This key purpose of this study is to investigate soliton solution of the fifth-order Sawada–Kotera and Caudrey–Dodd–Gibbon equations in the sense of time fractional local [Formula: see text]-derivatives. This important goal is achieved by employing the unified method. As a result, a number of dark and rational soliton solutions to the nonlinear model are retrieved. Some of the achieved solutions are illustrated graphically in order to fully understand their physical behavior. The results demonstrate that the presented approach is more effective in solving issues in mathematical physics and other fields.

Deeper properties of the nonlinear Phi-four and Gross-Pitaevskii equations arising mathematical physics

In this paper, the rational sine–cosine and rational sinh–cosh methods are applied in extracting some properties of nonlinear Phi-four and Gross–Pitaevskii equations. The singular periodic wave solutions, dark soliton solutions and hyperbolic function solutions are reported. The solitary waves are observed from the traveling waves under the values of the parameters. Modulation instability analysis is also observed in various simulations. We also plot to observe the wave distributions of parameters of stability in 2D and 3D visuals via package program.

Development of information culture of students when teaching equations of mathematical physics in the conditions of informatization of education

Problem and goal. In modern conditions, specialists in various subject areas who have an information culture and are able to solve complex professional problems using modern information and communication technologies are in demand. Currently, specialists in the field of applied mathematics are required, which plays an important role in the development of human civilization. Therefore, in the process of teaching various academic disciplines of applied mathematics at the university, including the discipline Equations of mathematical physics, attention should be paid to the development of students information culture. Methodology. When teaching students the discipline Equations of mathematical physics, it is extremely important that the teacher knows not only the content of teaching this discipline of applied mathematics, but also has practical experience in solving equations of mathematical physics by computer means. Such qualities of the teacher will allow him to successfully conduct training sessions in the conditions of informatization of teaching mentioned discipline. At the same time, it ought to be clearly understood that the use of computer technologies in teaching the discipline Equations of mathematical physics must be correct. The necessity to develop and implement in practice a variety of methodological approaches that allow students to develop an information culture in training sessions on that discipline is obvious. Results. The use of advanced pedagogical technologies in training sessions on the discipline Equations of mathematical physics, where computer technologies are used, will allow students to develop an information culture. Conclusion. Computer technologies that students use in the process of solving educational problems require them to have certain skills and abilities to identify their broad capabilities. Students are aware of the role of computer technologies in conducting applied scientific research, understand the role of computer modeling methodology and computational experiment in studying the world around them.

Combinatorics of KP hierarchy structural constants

We investigate the structural constants of the KP hierarchy, which appear as universal coefficients in the paper of Natanzon–Zabrodin arXiv:1509.04472. It turns out that these constants have a combinatorial description in terms of transport coefficients in the theory of flow networks. Considering its properties we want to point out three novel directions of KP combinatorial structure research: connection with topological recursion, eigenvalue model for the structural constants and its deformations, possible deformations of KP hierarchy in terms of the structural constants. Firstly, in this paper we study the internal structure of these coefficients which involves: (1) construction of generating functions that have interesting properties by themselves; (2) restrictions on topological recursion initial data; (3) construction of integral representation or matrix model for these coefficients with non-trivial Ward identities. This shows that these coefficients appear in various problems of mathematical physics, which increases their value and significance. Secondly, we discuss their role in integrability of KP hierarchy considering possible deformation of these coefficients without changing the equations on $$\tau $$ τ -function. We consider several plausible deformations. While most failed even very basic checks, one deformation (involving Macdonald polynomials) passes all the simple checks and requires more thorough study.

Mathematical Physics Problem Solving Skills for Secondary School physics Teachers

The aim of the current research is to identify the extent to which secondary school physics teachers possess the skills to solve physical problems and to identify the differences in their physical problem solving skills according to the gender variables. The research identified physics teachers in secondary schools affiliated with the Directorate of Education in Al-Diwaniyah, for the academic year 2020-2021, and the sample size was (160) teachers who were randomly selected, and by reviewing some studies that dealt with physical problem solving skills, such as the study of (Islami et al., 2018). and study (Prasetyo, 2020). It was found that these studies share a number of points with the current research, but they did not provide a tool for measuring physical problem solving skills. Therefore, the researcher designed a scale of physical problem solving skills, which consisted of (32) items. After the exploratory application, the validity and stability of the study tool was confirmed by appropriate methods, and the correlation of the item’s degree with the total score was calculated, and after applying the test to the sample, the data was processed statistically, as the researcher used the equation of the t-test for one sample to verify that physics teachers possess the skills of solving Physical problems, and the results showed that teachers of physics possess the skills to solve physical problems, and the statistical method was used to verify the differences in the skills of solving physical problems according to gender variables (male and female), and the results showed that there are differences in favor of (male) and the researcher recommended in the light of Results Preparing special training programs by the Ministry of Education to develop physical problem solving skills among physics teachers, and suggested the need to focus on the diversity of solving processes based on physical problem solving skills.