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, 2018
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, Burnasyan Federal Medical Biophysical Center of Federal Medical Biological
Agency, 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
BOUNDARY INVERSE PROBLEM FOR STAR-SHAPED GRAPH
WITH DIFFERENT DENSITIES STRINGS-EDGES
A.M. Akhtyamov, Kh.R. Mamedov, E.N. Yilmazoglu . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
POPULATION MODELS WITH PROJECTION MATRIX WITH SOME
NEGATIVE ENTRIES A SOLUTION TO THE NATCHEZ PARADOX
J. Banasiak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
LORD KELVIN AND ANDREY ANDREYEVICH MARKOV IN A QUEUE
WITH SINGLE SERVER
A. Bobrowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
STURM LIOUVILLE ABSTRACT PROBLEMS FOR THE SECOND ORDER
DIFFERENTIAL EQUATIONS IN A NON COMMUTATIVE CASE
M. Kaid, K. Ould Melha . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
ВЗАИМОДЕЙСТВИЕ СФЕРИЧЕСКИХ УДАРНЫХ ВОЛН
С ПРИПОВЕРХНОСТНЫМ ГЕТЕРОГЕННЫМ СЛОЕМ
С ХИМИЧЕСКИ АКТИВНОЙ ГАЗОВОЙ ФАЗОЙ
Í.Ë. Клиначева, Þ.Ì. Ковалев . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
DISCRETE MODEL OF PAIRED RELAY-RACE
E.V. Larkin, A.V. Bogomolov, A.N. Privalov, N.N. Dobrovolsky . . . . . . . . . . . . . . . . . . . 72
CAUSAL RELATIONS IN SUPPORT OF IMPLICIT EVOLUTION EQUATIONS
N. Sauer, J. Banasiak, Wha-Suck Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
MULTIPOINT INITIAL-FINAL PROBLEM FOR ONE CLASS
OF SOBOLEV TYPE MODELS OF HIGHER ORDER
WITH ADDITIVE "WHITE NOISE"
G.A. Sviridyuk, A.A. Zamyshlyaeva, S.A. Zagrebina . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Краткие сообщения
ОЦЕНКА ПАРАМЕТРОВ ИГР С ИЕРАРХИЧЕСКИМ ВЕКТОРОМ ИНТЕРЕСОВ
Ò.Â. Меньших . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Персоналии
NOTES ON JAN MARIA KISY NSKI'S LIFE AND SCIENTIFIC WORK
A. Bobrowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Исторические заметки
ON THE TELEGRAPH EQUATION WITH A SMALL PARAMETER
J. Kisy nski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
ON JAN KISY NSKI
K. Goebel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
A TRIBUTE TO JAN KISY NSKI
Jerry Goldstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Вестник ЮУрГУ. Серия ≪
и программирование≫
Математическое моделирование
(Âåñòíèê ЮУрГУ ÌÌÏ). 2018. Ò. 11, 3
Стр.3
Contents
Mathematical Modelling
BOUNDARY INVERSE PROBLEM FOR STAR-SHAPED GRAPH
WITH DIFFERENT DENSITIES STRINGS-EDGES
A.M. Akhtyamov, Kh.R. Mamedov, E.N. Yilmazoglu . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
POPULATION MODELS WITH PROJECTION MATRIX WITH SOME
NEGATIVE ENTRIES A SOLUTION TO THE NATCHEZ PARADOX
J. Banasiak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
LORD KELVIN AND ANDREY ANDREYEVICH MARKOV IN A QUEUE
WITH SINGLE SERVER
A. Bobrowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
STURM LIOUVILLE ABSTRACT PROBLEMS FOR THE SECOND ORDER
DIFFERENTIAL EQUATIONS IN A NON COMMUTATIVE CASE
M. Kaid, K. Ould Melha . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
THE INTERACTION OF SPHERICAL SHOCK WAVES WITH A NEAR-SURFACE
HETEROGENEOUS LAYERS WITH A CHEMICALLY ACTIVE GAS PHASE
N.L. Klinacheva, Yu.M. Kovalev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
DISCRETE MODEL OF PAIRED RELAY-RACE
E.V. Larkin, A.V. Bogomolov, A.N. Privalov, N.N. Dobrovolsky . . . . . . . . . . . . . . . . . . . 72
CAUSAL RELATIONS IN SUPPORT OF IMPLICIT EVOLUTION EQUATIONS
N. Sauer, J. Banasiak, Wha-Suck Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
MULTIPOINT INITIAL-FINAL PROBLEM FOR ONE CLASS
OF SOBOLEV TYPE MODELS OF HIGHER ORDER
WITH ADDITIVE "WHITE NOISE"
G.A. Sviridyuk, A.A. Zamyshlyaeva, S.A. Zagrebina . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Short Notes
ESTIMATION OF PARAMETERS OF GAMES
WITH A HIERARCHICAL VECTOR OF INTERESTS
Ò.V. Menshikh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Personalia
NOTES ON JAN MARIA KISY NSKI'S LIFE AND SCIENTIFIC WORK
A. Bobrowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Historical Notes
ON THE TELEGRAPH EQUATION WITH A SMALL PARAMETER
J. Kisy nski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
ON JAN KISY NSKI
K. Goebel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
A TRIBUTE TO JAN KISY NSKI
Jerry Goldstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming
& Computer Software (Bulletin SUSU MMCS), 2018, vol. 11, no. 3
Стр.4