Учредитель Федеральное государственное автономное образовательное
учреждение высшего образования
Южно-Уральский государственный университет
(национальный исследовательский университет)≫
≪
Основной целью издания является пропаганда союза качественных и численных исследований
математических моделей. Предпочтение при публикации будут иметь статьи, посвященные
результатам качественных исследований математических моделей, выявляющих
какие-либо неочевидные их свойства; результатам численных исследований, содержащих
разработки новых вычислительных алгоритмов применительно к математическим моделям;
и комплексам программ, созданным для постановки вычислительных экспериментов.
Редакционная коллегия
ê.ô.-ì.í., ïðîô. Заляпин Â.È.,
ä.ô.-ì.í., äîö. Замышляева À.À.,
ä.ô.-ì.í., äîö. Келлер À.Â.,
ä.ô.-ì.í., äîö. Манакова Í.À.
(отв. секретарь),
ä.ô.-ì.í., ïðîô. Свиридюк Ã.À.
(гл. редактор)
Редакционный совет
ïðîô., ä-ð Аббас Ñ.,
ä.ô.-ì.í., ïðîô. Банасяк ß.,
ä.ò.í., ïðîô. Богомолов À.Â.,
ä.ô.-ì.í. Бржезинская Ì.Ì.,
ä.ò.í., ïðîô. Володарский Å.Ò.,
ïðîô., ä-ð Вонг Ï.,
ïðîô., ä-ð Йонг Ëè,
ä.ô.-ì.í., ïðîô. Кадченко Ñ.È.,
ä.ô.-ì.í., àêàä. НАН Республики
Казахстан Кальменов Т.Ш.,
ä.ô.-ì.í., äîö. Корпусов Ì.Î.,
ä.ò.í., ÷ë.-êîð. РАН Новиков Ä.À.
(председатель),
ä.ò.í., ñ.í.ñ. Поляк Á.Ò.,
ä.ô.-ì.í., ïðîô. Пятков Ñ.Ã.,
ä.ò.í., ïðîô. Радев Õ.Ê.,
ïðîô., ä-ð Ривера Æ.Å.Ì.,
ä.ô.-ì.í., ïðîô. Сапронов Þ.È.,
ïðîô., ä-ð Tà Зуй Ôûîíã,
ïðîô., ä-ð Тиба Ä.,
ä.ò.í., ïðîô. Уткин Ë.Â.,
ïðîô., ä-ð Фавини À.,
ä.ô.-ì.í., ïðîô. Фурсиков À.Â.,
ä.ô.-ì.í., ÷ë.-êîð. РАН Ченцов À.Ã.
⃝c Издательский центр ÞÓðÃÓ, 2017
Стр.1
South Ural State University
Main purpose of the publication is to promote the union of the qualitative of numerical studies of
mathematical models. Articles, devoted to the results of qualitative studies of mathematical models, that
identify any non-obvious properties, the results of numerical studies that contain the development of
new computational algorithms applied for the computational experiments, will have the preference for
publication.
Editorial Board
A.V. Keller, South Ural State University, Chelyabinsk, Russian Federation
N.A. Manakova, South Ural State University, Chelyabinsk, Russian Federation
G.A. Sviridyuk, South Ural State University, Chelyabinsk, Russian Federation
V.I. Zalyapin, South Ural State University, Chelyabinsk, Russian Federation
A.A. Zamyshlyaeva, South Ural State University, Chelyabinsk, Russian Federation
Editorial Council
S. Abbas, Indian Institute of Technology Mandi, Mandi, India
J. Banasiak, University of Pretoria, Pretoria, Republic of South Africa
A.V. Bogomolov, Military Academy of the General Sta of the RF Armed Forces, Moscow,
Russian Federation
M.M. Brzhezinskaya, Helmholtz-Zentrum Berlin for Materials and Energy, Berlin, Germany
A.G. Chentsov, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the RAS,
Yekaterinburg, Russian Federation
A.V. Fursikov, Lomonosov Moscow State University, Moscow, Russian Federation
A. Favini, University of Bologna, Bologna, Italy
S.I. Kadchenko, Nosov Magnitogorsk State Technical University, Magnitogorsk, Russian Federation
T.Sh. Kal'menov, Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan
M.O. Korpusov, Lomonosov Moscow State University, Moscow, Russian Federation
D.A. Novikov, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation
B.T. Polyak, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation
S.G. Pyatkov, Sobolev Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk,
Russian Federation
H.K. Radev, Technical University of So a, So a, Bulgaria
J.E.M. Rivera, Federal University of Rio de Janeiro, Institute of Mathematic, Rio de Janeiro, Brazil
Yu.I. Sapronov, Voronezh State University, Voronezh, Russian Federation
Ta Duy Phuong, Hanoi Institute of Mathematics, Hanoi, Vietnam
D. Tiba, Institute of Mathematics Romanian Academy, Bucharest, Romania
E.T. Volodarskiy, National Technical University, Kiev, Ukraine
L.V. Utkin, Peter the Great Saint-Petersburg Polytechnic University, Saint Petersburg,
Russian Federation
P.J.Y. Wong, Nanyang Technological University, School of Electrical and Electronic Engineering,
Singapore, Singapore
Yong Li, College of Electrical and Information Engineering, Hunan University, Changsha, China
76, Lenin ave, Chelyabinsk, 454080, Russian Federation, vestnik@susu.ru, mmp.vestnik.susu.ru
Стр.2
Содержание
Математическое моделирование
SOME MATHEMATICAL MODELS WITH A RELATIVELY BOUNDED OPERATOR
AND ADDITIVE "WHITE NOISE" IN SPACES OF SEQUENCES
K.V. Vasyuchkova, N.A. Manakova, G.A. Sviridyuk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
STATIONARY ELECTROCHEMICAL MACHINING SIMULATION APPLYING
TO PRECISION TECHNOLOGIES
V.P. Zhitnikov, N.M. Sherykhalina, S.S. Porechny . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
ITERATIVE EQUITABLE PARTITION OF GRAPH AS A MODEL OF CONSTANT
STRUCTURE DISCRETE TIME CLOSED SEMANTIC SYSTEM
E.E. Ivanko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
ОСЛАБЛЕНИЕ СФЕРИЧЕСКИХ УДАРНЫХ ВОЛН В ГЕТЕРОГЕННЫХ СРЕДАХ
Í.Ë. Клиначева, Þ.Ì. Ковалев . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
О ФОКУСИРОВКЕ ЦИЛИНДРИЧЕСКИ СИММЕТРИЧНОЙ УДАРНОЙ ВОЛНЫ В ГАЗЕ
Â.Ô. Куропатенко , Ô.Ã. Ìàãàçîâ, Å.Ñ. Шестаковская . . . . . . . . . . . . . . . . . . . . . . . 46
РАСЧЕТ ДИНАМИКИ БАЛЛИСТИЧЕСКОЙ МОДЕЛИ РАКЕТ
Â.È. Ïåãîâ, È.Þ. Мошкин . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
MODEL OF CONVEYER WITH THE REGULABLE SPEED
Î.Ì. Pihnastyi, V.D. Khodusov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Программирование
MODELS AND METHODS FOR THREE EXTERNAL BALLISTICS INVERSE PROBLEMS
N.K. Arutyunova, A.M. Dulliev, V.I. Zabotin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
МЕТОД МАТРИЧНЫХ ПУЧКОВ ДЛЯ ОЦЕНКИ ПАРАМЕТРОВ ВЕКТОРНЫХ ПРОЦЕССОВ
Ì.Ï. Ãåíðè, Î.Ë. Èáðÿåâà, Ä.Ä. Ñàëîâ, À.Ñ. Семенов . . . . . . . . . . . . . . . . . . . . . . . . 92
THE DEVELOPMENT OF FREE ENGINEERING SOFTWARE PACKAGE
FOR NUMERICAL SIMULATION OF HYDRODYNAMICS, HEAT TRANSFER,
AND CHEMICAL REACTION PROCESSES
A.A. Dekterev, K.Yu. Litvintsev, A.A. Gavrilov, E.B. Kharlamov, S.A. Filimonov . . . . . . . 105
MATHEMATICAL AND SOFTWARE SUPPORT FOR 3D MATHEMATICAL MODELLING
OF THE AIRFLOW IMPACT ON THE OPTICAL-MECHANICAL UNIT MOUNTED
IN THE AIRCRAFT UNPRESSURIZED COMPARTMENT
I.E. Ivanov, I.A. Kryukov, E.V. Larina, V.L. Miroshkin . . . . . . . . . . . . . . . . . . . . . . . . 113
MATHEMATICAL MODEL OF METHANE REPLACEMENT PROCESS IN GAS HYDRATE
WITH CARBON DIOXIDE IN A POROUS LAYER
M.Ê. Khasanov, M.V. Stolpovsky, S.R. Kildibaeva . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
ДИНАМИКА ВЗАИМОДЕЙСТВИЯ БЛОХОВСКИХ ДОМЕННЫХ ГРАНИЦ
В ДВУМЕРНОЙ НЕЛИНЕЙНОЙ СИГМА-МОДЕЛИ
Ô.Ø. Шокиров . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Краткие сообщения
APPROXIMATION OF SOLUTIONS TO THE BOUNDARY VALUE PROBLEMS
FOR THE GENERALIZED BUSSINESK EQUATION
V.Z. Furaev, A.I. Antonenko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Персоналии
ВАЛЕНТИН ФЕДОРОВИЧ КУРОПАТЕНКО (1933 2017) . . . . . . . . . . . . . . . . . . . . . 151
Математическая деятельность
ЭЛИТНАЯ МАТЕМАТИЧЕСКАЯ ПОДГОТОВКА СТУДЕНТОВ
ЭНЕРГЕТИЧЕСКОГО ФАКУЛЬТЕТА ЮУрГУ
Ì.À. Êîðûòîâà, À.Á. Самаров . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Вестник ЮУрГУ. Серия ≪
и программирование≫
Математическое моделирование
(Âåñòíèê ЮУрГУ ÌÌÏ). 2017. Ò. 10, 4
Стр.3
Contents
Mathematical Modelling
SOME MATHEMATICAL MODELS WITH A RELATIVELY BOUNDED OPERATOR
AND ADDITIVE "WHITE NOISE" IN SPACES OF SEQUENCES
K.V. Vasyuchkova, N.A. Manakova, G.A. Sviridyuk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
STATIONARY ELECTROCHEMICAL MACHINING SIMULATION APPLYING
TO PRECISION TECHNOLOGIES
V.P. Zhitnikov, N.M. Sherykhalina, S.S. Porechny . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
ITERATIVE EQUITABLE PARTITION OF GRAPH AS A MODEL OF CONSTANT
STRUCTURE DISCRETE TIME CLOSED SEMANTIC SYSTEM
E.E. Ivanko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
THE ATTENUATION OF SPHERICAL SHOCK WAVES IN HETEROGENEOUS MEDIA
N.L. Klinacheva, Y.M. Kovalev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
FOCUSING OF CYLINDRICALLY SYMMETRIC SHOCK IN A GAS
V.F. Kuropatenko , F.G. Magazov, E.S. Shestakovskaya . . . . . . . . . . . . . . . . . . . . . . . . 46
DYNAMIC ANALYSIS OF A BALLISTIC MISSIBLE MODEL
V.I. Pegov, I.Yu. Moshkin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
MODEL OF CONVEYER WITH THE REGULABLE SPEED
Î.Ì. Pihnastyi, V.D. Khodusov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Programming & Computer Software
MODELS AND METHODS FOR THREE EXTERNAL BALLISTICS INVERSE PROBLEMS
N.K. Arutyunova, A.M. Dulliev, V.I. Zabotin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
MATRIX PENCIL METHOD FOR ESTIMATION OF PARAMETERS OF VECTOR PROCESSES
M.P. Henry, O.L. Ibryaeva, D.D. Salov, A.S. Semenov . . . . . . . . . . . . . . . . . . . . . . . . . . 92
THE DEVELOPMENT OF FREE ENGINEERING SOFTWARE PACKAGE
FOR NUMERICAL SIMULATION OF HYDRODYNAMICS, HEAT TRANSFER,
AND CHEMICAL REACTION PROCESSES
A.A. Dekterev, K.Yu. Litvintsev, A.A. Gavrilov, E.B. Kharlamov, S.A. Filimonov . . . . . . . 105
MATHEMATICAL AND SOFTWARE SUPPORT FOR 3D MATHEMATICAL MODELLING
OF THE AIRFLOW IMPACT ON THE OPTICAL-MECHANICAL UNIT MOUNTED
IN THE AIRCRAFT UNPRESSURIZED COMPARTMENT
I.E. Ivanov, I.A. Kryukov, E.V. Larina, V.L. Miroshkin . . . . . . . . . . . . . . . . . . . . . . . . 113
MATHEMATICAL MODEL OF METHANE REPLACEMENT PROCESS IN GAS HYDRATE
WITH CARBON DIOXIDE IN A POROUS LAYER
M.Ê. Khasanov, M.V. Stolpovsky, S.R. Kildibaeva . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
DYNAMICS OF INTERACTION OF BLOCH TYPE DOMAIN WALLS
IN A TWO-DIMENSIONAL NONLINEAR SIGMA MODEL
F.Sh. Shokirov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Short Notes
APPROXIMATION OF SOLUTIONS TO THE BOUNDARY VALUE PROBLEMS
FOR THE GENERALIZED BOUSSINESQ EQUATION
V.Z. Furaev, A.I. Antonenko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Personalia
VALENTIN FEDOROVICH KUROPATENKO (1933 2017) . . . . . . . . . . . . . . . . . . . . . . 151
Mathematical Activity
ELITE MATHEMATICAL PREPARATION OF STUDENTS
OF THE POWER FACULTY OF THE SUSU
M.A. Korytova, A.B. Samarov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming
& Computer Software (Bulletin SUSU MMCS), 2017, vol. 10, no. 4
Стр.4