Concept of the course "Numerical methods in object methodology"

The tasks for which computers were created - routine calculations of an industrial, scientific and military nature - required the creation of a whole class of new methods focused not on manual but on machine calculations. The first programming languages did not have convenient means for reflecting such objects often used in computational mathematics as matrices, vectors, polynomials, etc. Further development of programming languages followed the path of embedding mathematical objects into languages as data types, which led to their complication. So, for example, an attempt to make a universal language Ada, in which there are even such data types as dictionaries and queues, led to the fact that the number of keywords in it exceeded 350, making it almost unusable for learning and use. The compromise solution between these two extremes can be the following: let the programmer himself create the data types that he needs in his professional work. Programming languages that implement this approach are called object-oriented. This, on the one hand, makes it possible to make the language quite easy by reducing the number of keywords, and on the other, expandable, adapting to specific tasks by introducing keywords for creating and using new data types.

Theories on the Formation and Evolution of ~2D Planar Celestial Kinematics

The existence of essentially 2-dimensional planar solar systems and galaxies would seem to be a contradiction to the 2nd Law of Thermodynamics relating to the tendency of natural processes toward spatial homogeneity of matter and energy. During the formation process of celestial systems, an equal dispersion of matter throughout 3-dimensional space would have been a more logical result to satisfy entropy/disorder increasing at all times. Conventional belief is that the ~2D planar geometry of galaxies and solar systems is largely due to rotational kinetic forces and matter collapsing due to its own gravity; this project seeks to expand and enhance the potential forces to explain ~2D planar celestial kinematics. Computational mathematics utilizing programming in C# will analyze various potential forces and relative magnitudes to determine proposed force-balances during these formation processes. A better understanding of the formation process (and the forces that govern them) of galaxies and solar systems can help explain their evolutions to steady state; for this, the derived mathematical models will be computed and translated to visual models in 4-D space-time over various time frames.

Preface

The opening of the eleventh International Youth Scientific School-Conference "Theory and Numerical Methods for solving Inverse and ill-posed Problems" was held on August 26, 2019 at Novosibirsk State University. The first ten school-conferences, held from 2009 to 2018, showed the relevance and scientific significance of the chosen subject [1,2,3]. Over the past years, researchers, graduate students and undergraduates from Russia, Belarus, Ukraine, Kazakhstan, Uzbekistan, Kyrgyzstan, as well as from China, the USA, Germany, France, Italy, Japan, the UK, Brazil, Malaysia took part in the school-conferences. For 10 years, representatives of 78 universities, 134 research institutes and more than 20 companies (Total, Baker-Hughes, Schlumberger, Rosneft and others) participated actively at school-conferences. The Conference continued until September 4. The participants were very interested in the reports of academicians S. K. Godunov (Sobolev Institute of Mathematics, Novosibirsk), M. A. Guzev (Institute of Applied Mathematics, Vladivostok), I. A. Taimanov (Sobolev Institute of Mathematics, Novosibirsk), E. E. Tyrtyshnikov (Marchuk Institute of Numerical Mathematics, Moscow), corresponding members of the RAS V.V. Vasin (Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg), S. I. Kabanikhin, G. A. Mikhailov (Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk ), V. G. Romanov (Sobolev Institute of Mathematics, Novosibirsk).

Экстремальная функция интерполяционных формул в пространстве W2(2,0)

One of the main problems of computational mathematics is the optimization of computational methods in functional spaces. Optimization of computational methods are well demonstrated in the problems of the theory of interpolation formulas. In this paper, we study the problem of constructing an optimal interpolation formula in a Hilbert space. Here, using the Sobolev method, the first part of the problem is solved, i.e., an explicit expression of the square of the norm of the error functional of the optimal interpolation formulas in the Hilbert space W2(2,0) is found. Одна из основных проблем вычислительной математики — оптимизация вычислительных методов в функциональных пространствах. Оптимизация вычислительных методов хорошо проявляется в задачах теории интерполяционных формул. В данной статье исследуется проблема построения оптимальной интерполяционной формулы в гильбертовом пространстве. Здесь с помощью метода Соболева решается первая часть задачи — явное выражение квадрата нормы функционала погрешности оптимальных интерполяционных формул в гильбертовом пространстве W2(2,0) .

Применение онтологий для решения задач геофизики

The paper covers an intelligent support system that allows to describe and construct solutions to various scientific problems. In this study, in particular, we consider geophysical problems. This system is being developed at the Institute of Computational Mathematics and Mathematical Geophysics of the Russian Academy of Sciences (ICMMG SB RAS) and Institute of Informatics System of the Russian Academy of Sciences (IIS SB RAS). The system contains a knowledge base, the core of which is a set of several interconnected ontologies such as the ontology of supercomputer architectures, the ontology of algorithms and methods. Ontology can be viewed as a set of concepts and how those concepts are linked. As the result, the authors present an ontological description of two geophysical problems via the means of the intelligent support system: 1) the seismic wavefield simulation and 2) the reconstruction of a seismic image through pre-stack time or depth migration. For a better visual understanding of the system described and the results obtained, the paper also contains several schematic diagrams and images. В статье рассматривается система интеллектуальной поддержки, позволяющая описывать и выстраивать решения различных научных задач. В данной работе рассматриваются геофизические задачи. Система разрабатывается в Институте вычислительной математики и математической геофизики Российской академии наук (ИВМГ СО РАН) и Институте систем информатики Российской академии наук (ИИС СО РАН). Система содержит базу знаний, ядром которой является набор из нескольких взаимосвязанных онтологий, таких как онтология суперкомпьютерных архитектур, онтология алгоритмов и методов. Онтологию можно рассматривать как набор концепций и связей между ними. В результате авторы представляют онтологическое описание двух геофизических задач с помощью средств системы интеллектуальной поддержки: 1) моделирование сейсмического волнового поля и 2) реконструкция сейсмического изображения посредством временной или глубинной миграции до суммирования. Для лучшего визуального понимания описанной системы и полученных результатов в работе также есть несколько схематических диаграмм и изображений.

International Conference «Marchuk Scientific Readings 2021» (MSR-2021)

Preface These Conference Proceedings contain the selected papers of the International Conference «Marchuk Scientific Readings 2021» (MSR-2021) held on October 4 - 8, 2021, in Akademgorodok, Novosibirsk, Russia. The purpose of the «Marchuk Scientific Readings» conference series is to gather specialists in numerical analysis, applied mathematics, mathematical modeling, computational technologies, information systems, artificial intelligence, and machine learning to discuss, identify and systematize current results, applications, and promising directions in computational mathematics and computer science. Due to the risk of spreading coronavirus infection, the meeting took place virtually. The organizers were located in the Institute of Computational Mathematics and Mathematical Geophysics SB RAS (Novosibirsk, Russia). Morning sessions were devoted to the conference sections’ invited oral (20 minutes) and oral (15 minutes) presentations. The Plenary talks (30 minutes) were delivered on the afternoon sessions. Within the timeframe of a talk, there was a possibility to ask and answer several questions from the audience. Technologically, the meeting was carried out on the Zoom platform. Plenary talks were broadcast on youtube.com. This conference was the second one carried out with the help of the Zoom platform, and most of the technical issues were already solved in the previous year. In pandemic conditions, the virtual conference seems to be the most appropriate format to share the research results without exposing the community to the risk of infection. List of Program committee is available in this pdf.

Peer review declaration

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing. • Type of peer review: Single-blind • Conference submission management system: “Conference” Information system (conf.nsc.ru) developed by the Federal Research Center for Information and Computational Technologies (former Institute of Computational Technologies SB RAS). The proceedings papers were submitted via email to the organizing committee. • Number of submissions received: 82 • Number of submissions sent for review: 82 • Number of submissions accepted: 75 • Acceptance Rate (Number of Submissions Accepted/Number of Submissions Received X 100): 91 • Average number of reviews per paper: 1.43 • Total number of reviewers involved: 78 • Any additional info on review process: The submissions were handled by the program committee and redirected to the corresponding conference section chairs. The conference section chairs were sending the initial review requests to the reviewers. The program committee handled the subsequent review process, including sending the papers to the authors for corrections and sending the modified papers to the reviewers for the corrections’ approval. • Contact person for queries: Name : Alexey Penenko Affiliation: Institute of Computational Mathematics and Mathematical Geophysics SB RAS, ICM&MG SB RAS, prospect Akademika Lavrentyeva 6, 630090, Novosibirsk, Russia Email : [email protected]

Professional competence development when teaching computational informatics.

Bachelors and graduate students are offered in the course of teaching computational informatics, the ability to solve non-standard mathematical problems, which, as a rule, are not included in the content of teaching computational informatics. The article aimed to analyze the application effectiveness of non-standard mathematical problems in the course of teaching computational informatics, elaboration of constructive computational solution algorithms of inverse problems for differential equations, during which the bachelors and graduate students develop own professional competencies. The research conducted a review of previous literature on the topic. Formulation of the inverse problem for differential equations for the investigation of which the computational mathematics finite difference methods are applied, is presented. In the course of investigation, it was revealed that at elaborating the constructive computational algorithms of its solution, the bachelors and graduate students develop not only fundamental knowledge in the field of applied and computational mathematics, computational informatics methods, but also develop the professional competences, including computational thinking. Key words: professional competence; computational informatics; computational mathematics methods; non-standard.

The Explicit Formulae of the Determinants of Specific Pentadiagonal Toeplitz Hessenberg Matrices

The pentadiagonal Toeplitz matrix is a special kind of sparse matrix widely used in linear algebra, combinatorics, computational mathematics, and has been attracted much attention. We use the determinants of two specific Hessenberg matrices to represent the recurrence relations to prove two explicit formulae to evaluate the determinants of specific pentadiagonal Toeplitz matrices proposed in a recent paper [3]. Further, four new results are established.

International Journal of Applied Mathematics and Machine Learning

In order to achieve the multi-focus image fusion task, a sparse representation method based on quaternion for multi-focus image fusion is proposed in this paper. Firstly, the RGB color information of each pixel in the color image is represented by quaternion based on the relevant knowledge of computational mathematics, and the color image pixel is processed as a whole vector to maintain the relevant information between the three color channels. Secondly, the dictionary represented by quaternion and the sparse coefficient represented by quaternion are obtained by using the our proposed sparse representation model. Thirdly, the coefficient fusion is carried out by using the “max-L1” rule. Finally, the fused sparse coefficient and dictionary are used for image reconstruction to obtain the quaternion fused image, which is then converted into RGB color multi-focus fused image. Our method belongs to computational mathematics, and uses the relevant knowledge in the field of computational mathematics to help us carry out the experiment. The experimental results show that the method has achieved good results in visual quality and objective evaluation.