Издательский центр ЮУрГУ, 2016 c South Ural State University Main purpose of the publication is to promote the union of the qualitative of numerical studies of mathematical models. <...> 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 Counsil J. Banasiak, University of Pretoria, Pretoria, Republic of South Africa 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 M.T. Dzhenaliev, Institute of Mathematics, Ministry of Education and Science of the Republic of Kazakhstan, Almaty, Kazakhstan A.V. Fursikov, Lomonosov Moscow State University, Moscow, Russian Federation A. Favini, University of Bologna, Bologna, Italy V.V. Jikov, Vladimir State University named after Alexander and Nikolay Stoletovs, Vladimir, Russian Federation S.I. Kadchenko, Magnitogorsk State Technical University named after G.I. Nosov, Magnitogorsk, Russian Federation M.O. Korpusov, Lomonosov Moscow State University, Moscow, Russian Federation A.I. Kozhanov, Sobolev Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk, 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 H.K. Radev, Technical University of So a, So a, Bulgaria Yu. <...> I. Sapronov, Voronezh State University, Voronezh, Russian Federation V.A. Strauss, Simon Bolivar University, Caracas, Venezuela S.N. Vassilyev, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation E.T. Volodarskiy, National Technical University, Kiev, Ukraine B.Ya. <...> Zeldovich, University of Central Florida, Orlando, United States of America P.J.Y. Wong, Nanyang Technological University, School of Electrical and Electronic <...>
Вестник_Южно-Уральского_государственного_университета._Серия_Математическое_моделирование_и_программирование_№1_2016.pdf
Учредитель Федеральное государственное бюджетное образовательное
учреждение высшего профессионального 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;
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.,
ê.ô.-ì.í., äîö. Манакова Í.À.
(отв. секретарь),
ä.ô.-ì.í., ïðîô. Свиридюк Ã.À.
(отв. редактор)
Редакционный совет
ä.ô.-ì.í., ïðîô. Банасяк ß.,
ä.ô.-ì.í. Бржезинская Ì.Ì.,
ä.ô.-ì.í., àêàä. РАН Васильев Ñ.Í.
(председатель),
ä.ò.í., ïðîô. Володарский Å.Ò.,
ïðîô. Вонг Ï.,
ä.ô.-ì.í., ïðîô. Дженалиев Ì.Ò.,
ä.ô.-ì.í., ïðîô. Жиков Â.Â.,
ä.ô.-ì.í., ÷ë.-êîð. РАН Зельдович Á.ß.,
проф. Йонг Ли,
ä.ô.-ì.í., ïðîô. Кадченко Ñ.È.,
ä.ô.-ì.í., ïðîô. Кожанов À.È.,
ä.ô.-ì.í., äîö. Корпусов Ì.Î.,
ä.ò.í., ÷ë.-êîð. РАН Новиков Ä.À.,
ä.ò.í., ñ.í.ñ. Поляк Á.Ò.,
ä.ò.í., ïðîô. Радев Õ.Ê.,
ä.ô.-ì.í., ïðîô. Сапронов Þ.È.,
доктор, проф. Фавини А.,
ä.ô.-ì.í., ïðîô. Фурсиков À.Â.,
ä.ô.-ì.í., ÷ë.-êîð. РАН Ченцов À.Ã.,
ä.ô.-ì.í., ïðîô. Штраус Â.À.
⃝ Издательский центр ÞÓðÃÓ, 2016
c
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 Counsil
J. Banasiak, University of Pretoria, Pretoria, Republic of South Africa
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
M.T. Dzhenaliev, Institute of Mathematics, Ministry of Education and Science of the Republic
of Kazakhstan, Almaty, Kazakhstan
A.V. Fursikov, Lomonosov Moscow State University, Moscow, Russian Federation
A. Favini, University of Bologna, Bologna, Italy
V.V. Jikov, Vladimir State University named after Alexander and Nikolay Stoletovs, Vladimir, Russian
Federation
S.I. Kadchenko, Magnitogorsk State Technical University named after G.I. Nosov, Magnitogorsk,
Russian Federation
M.O. Korpusov, Lomonosov Moscow State University, Moscow, Russian Federation
A.I. Kozhanov, Sobolev Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk,
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
H.K. Radev, Technical University of So a, So a, Bulgaria
Yu.I. Sapronov, Voronezh State University, Voronezh, Russian Federation
V.A. Strauss, Simon Bolivar University, Caracas, Venezuela
S.N. Vassilyev, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation
E.T. Volodarskiy, National Technical University, Kiev, Ukraine
B.Ya. Zeldovich, University of Central Florida, Orlando, United States of America
P.J.Y. Wong, Nanyang Technological University, School of Electrical and Electronic Engineering,
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
УДАРНАЯ ВОЛНА В ГАЗОВОМ ШАРЕ
Â.Ô. Куропатенко, Å.Ñ. Шестаковская, Ì.Í. Якимова . . . . . . . . . . . . . . . . . . . . . . . . 5
ON FIXED POINT THEORY AND ITS APPLICATIONS TO EQUILIBRIUM MODELS
D.A. Serkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
ВРЕМЕНН АЯ ДИНАМИКА ИНДЕКСА ХИРША
Þ.Þ. Тарасевич, Ò.Ñ. Шиняева . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
ОБОБЩЕННАЯ МОДЕЛЬ КУРЬЕРА С ДОПОЛНИТЕЛЬНЫМИ
ОГРАНИЧЕНИЯМИ
À.À. ×åíöîâ, À.Ã. Ченцов . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
INVESTIGATION OF THE UNSTEADY-STATE HYDRAULIC NETWORKS
BY MEANS OF SINGULAR SYSTEMS OF INTEGRAL
DIFFERENTIAL EQUATIONS
E.V. Chistyakova, Nguyen Duc Bang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
ON THE ONE-DIMENSIONAL HARMONIC OSCILLATOR
WITH A SINGULAR PERTURBATION
V.A. Strauss, M.A. Winklmeier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Программирование
ОПРЕДЕЛЕНИЕ ЛОКАЦИИ В КОРПОРАТИВНЫХ WI-FI СЕТЯХ
Ñ.Â. Малодушев, À.À. Рогов . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
STRUCTURAL PARAMETRIC MODELLING
OF AN INFORMATION-ANALYTICAL SYSTEM
V.V. Menshikh, O.V. Pyankov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
OPTIMIZATION OF NOZZLE LAYOUT IN CONTINUOUS CASTING MACHINE
D.S. Safonov, O.S. Logunova, D.V. Chistiakov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Краткие сообщения
THE CRITICAL STATE OF AN INCLINED LAYER IN A SHEET SPECIMEN
WITH NEGATIVE LOADING BIAXIALITY COEFFICIENT
V.L. Dilman, A.N. Dheyab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
SOLVABILITY AND NUMERICAL SOLUTIONS OF SYSTEMS OF NONLINEAR
VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND
WITH PIECEWISE CONTINUOUS KERNELS
I.R. Muftahov, D.N. Sidorov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ДЛЯ НАЗНАЧЕНИЯ СОСТАВОВ
ХЛОРМАГНЕЗИАЛЬНЫХ КОМПОЗИЦИЙ
Ò.Í. ×åðíûõ, Ë.ß. Êðàìàð, Á.ß. Òðîôèìîâ, À.À. Орлов . . . . . . . . . . . . . . . . . . . . . 137
Вестник ЮУрГУ. Серия ≪
и программирование≫
Математическое моделирование
(Âåñòíèê ЮУрГУ ÌÌÏ). 2016. Ò. 9, 1
Стр.3
Contents
Mathematical Modelling
SHOCK WAVES IN GAS SPHERE
V.F. Kuropatenko, E.S. Shestakovskaya, M.N. Yakimova . . . . . . . . . . . . . . . . . . . . . . . . . 5
ON FIXED POINT THEORY AND ITS APPLICATIONS TO EQUILIBRIUM MODELS
D.A. Serkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
TEMPORAL DYNAMICS OF HIRSCH INDEX
Yu.Yu. Tarasevich, T.S. Shinyaeva . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
GENERALIZED MODEL OF COURIER WITH ADDITIONAL RESTRICTIONS
A.A. Chentsov, A.G. Chentsov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
INVESTIGATION OF THE UNSTEADY-STATE HYDRAULIC NETWORKS
BY MEANS OF SINGULAR SYSTEMS OF INTEGRAL
DIFFERENTIAL EQUATIONS
E.V. Chistyakova, Nguyen Duc Bang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
ON THE ONE-DIMENSIONAL HARMONIC OSCILLATOR
WITH A SINGULAR PERTURBATION
V.A. Strauss, M.A. Winklmeier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Programming & Computer Software
DETERMINATION OF LOCATIONS IN CORPORATE Wi-Fi NETWORKS
S.V. Malodushev, A.A. Rogov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
STRUCTURAL PARAMETRIC MODELLING
OF AN INFORMATION-ANALYTICAL SYSTEM
V.V. Menshikh, O.V. Pyankov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
OPTIMIZATION OF NOZZLE LAYOUT IN CONTINUOUS CASTING MACHINE
D.S. Safonov, O.S. Logunova, D.V. Chistiakov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Short Notes
THE CRITICAL STATE OF AN INCLINED LAYER IN A SHEET SPECIMEN
WITH NEGATIVE LOADING BIAXIALITY COEFFICIENT
V.L. Dilman, A.N. Dheyab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
SOLVABILITY AND NUMERICAL SOLUTIONS OF SYSTEMS OF NONLINEAR
VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND
WITH PIECEWISE CONTINUOUS KERNELS
I.R. Muftahov, D.N. Sidorov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
MATHEMATICAL MODELS FOR THE APPOINTMENT
OF THE CHLORINE MAGNESIA COMPOSITION
T.N Chernyh, L.Y. Kramar, B.Y. Tro mov, A.A. Orlov . . . . . . . . . . . . . . . . . . . . . . . . 137
Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming
& Computer Software (Bulletin SUSU MMCS), 2016, vol. 9, no. 1
Стр.4