Журнал Сибирского федерального университета
Journal of Siberian Federal University
Математика и Физика
Mathematics & Physics
Редакционный совет:
академик РАН
Е.А. Ваганов
академик РАН
И.И. Гительзон
академик РАН
А.Г. Дегерменджи
академик РАН
В.Ф.Шабанов
чл.-корр. РАН,
д-р физ.-мат. наук
В.В. Зуев
чл.-корр. РАН,
д-р физ.-мат. наук
В.Л. Миронов
чл.-корр. РАН,
д-р техн. наук
Г.Л. Пашков
чл.-корр. РАН,
д-р физ.-мат. наук
В.В.Шайдуров
Editorial Advisory Board
Chairman:
Eugene A. Vaganov
Members:
Josef J. Gitelzon
Vasily F. Shabanov
Andrey G. Degermendzhy
Vladimir V. Zuev
Valery L. Mironov
Gennady L. Pashkov
Vladimir V. Shaidurov
Свидетельство
о регистрации СМИ
ПИ №ФС77 - 28724
от 29.06.2007 г.
B.I.Abdullaev
S.I.Burkov,
O.P.Zolotova,
B.P. Sorokin
N.S.Chernikov
CONTENTS
P-Measure in the Class of m−wsh Functions
3–9
The
Influence of Uniform Pressure
on Propagation of Acoustic Waves in
Piezoelectric Layered Structures
10-21
Groups Satisfying the Minimal Condition
for Non-abelian Non-normal Subgroups
22-34
I.A.Denisov,
A.A.Zimin,
L.A.Bursill,
P.I.
Belobrov
A.A.Gavrilov,
V.Ya.Rudyak
D.A. Krasnova
Nanodiamond Collective Electron States
and its Localization
35-45
A Model of Averaged Molecular Viscosity
for Turbulent Flow of Non-Newtonian
Fluids
46-57
Group Analysis of Three-dimensional
Equations of an Ideal Fluid in Terms of
Trajectories and Weber Potential
58-67
Редакторы: В.Е.Зализняк, А.В.Щуплев
Компьютерная верстка: Г.В.Хрусталева
Подписано в печать 10.01.14 г. Формат 84×108/16. Усл.печ. л. 12,1.
Уч.-изд. л. 11,7. Бумага тип. Печать офсетная.
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Отпечатано ПЦ БИК СФУ. 660041 Красноярск, пр. Свободный, 82.
2014 7(1)
Стр.1
Editorial Board:
Editor-in-Chief :
Michail I. Gladyshev
Founding Editor:
Vladimir I. Kolmakov
Managing Editor:
Olga F. Aleksandrova
Subject Editor for
Mathematics & Physics:
Prof. Alexander M. Kytmanov
(SibFU, Krasnoyarsk, Russia)
Consulting Editors
Mathematics & Physics:
Prof. Lev Aizenberg
(Bar-Ilan Univ., Tel-Aviv, Israel)
Prof. Viktor K. Andreev
(ICM, Krasnoyarsk, Russia)
Prof. Alexander M. Baranov
(KSP Univ., Krasnoyarsk, Russia)
Prof. Yury Ya. Belov
(SibFU, Krasnoyarsk, Russia)
Prof. Sergey S. Goncharov
(IM, Novosibirsk, Russia)
Prof. Vladimir M. Levchuk
(SibFU, Krasnoyarsk, Russia)
Prof. Yury Yu. Loginov
(SibSASU, Krasnoyarsk, Russia)
Prof. Mikhail V. Noskov
(SibFU, Krasnoyarsk, Russia)
Prof. Sergey G. Ovchinnikov
(IPh., Krasnoyarsk, Russia)
Prof. Gennady S. Patrin
(SibFU, Krasnoyarsk)
Prof. Azimbay Sadullaev
(NUUz., Tashkent, Uzbekistan)
Prof. Nikolai Tarkhanov
(Potsdam Univ., Germany)
Prof. Avgust K. Tsikh
(SibFU, Krasnoyarsk, Russia)
Prof. Valery V. Val’kov
(IPh., Krasnoyarsk, Russia)
Prof. Yury V. Zakharov
(SibSTU, Krasnoyarsk, Russia)
N.M.Zhabborov,
Kh.Kh. Imomnazarov
S.V.Smolin
M.G. Sadovsky,
I.Borovikov
G.V. Romanenko
L.N.Krivonosov,
V.A.Luk’yanov,
L.V.Voloskova
O. Makhmudov,
N.Tarkhanov
E.K.Myshkina
Extremal Curves in the Conformal
Space and in an Associated Bundle
68-78
An Extremal Problem Related to
Analytic Continuation
79-90
On One Condition for the Decomposition
of an Entire Function into an
Infinite Product
91-94
C.W.Parker,
A.A.C. Kanchana
Examples of Groups with the Same
Number of Subgroups of Every Index
95-99
A Representation of Solution of
the Identification Problem of
the Coefficients at Second Order
Operator in the Multi-Dimensional
Parabolic Equations System
100-111
Analysis of Financial Time Series
with Binary N-Grams Frequency Dictionaries
112-123
Three-dimensional
Dynamics of the
Earth’s Radiation Belt Protons During
the Magnetic Storm
124-131
Mean Value Theorem for a System of
Differential Equations for the Stress
Tensor and Pore Pressure
132-138
Стр.2
Journal of Siberian Federal University. Mathematics & Physics 2014, 7(1), 3–9
УДК 517.55+517.947.42
P-Measure in the Class of m−wsh Functions
Bakhrom I.Abdullaev∗
Urgench State University,
H.Olimjan, 14, Urgench, 220100
Uzbekistan
Received 04.10.2013, received in revised form 16.11.2013, accepted 09.01.2014
In this work we study the P-measure and P-capacity in the class of m−wsh functions and prove a number
of their properties.
Keywords: m−wsh function, P-measure, P-capacity, mw-regular point.
Introduction
The classical potential theory (see [1, 2]) works with classes of harmonic and subharmonic
functions and involves such concepts like the condenser capacity, harmonic measures of the sets,
polar sets and others. The pluripotential theory, as is known, deals with the class of psh functions
and the Monge-Ampere operator (ddcu)n = 0 (see [3, 4]), where as usual
d = ∂ +∂, dc =
∂ −∂
4i .
In the recent work [5] the author has studied the class of m−wsh functions, introduced the
concept of mw-polarity of sets and proved several of their properties. In this paper we study
the P-measure and P-capacity in the class of m−wsh functions. In section 1 we briefly give
the definition of m−wsh functions and some results, which we use below. In section 2 we give
the definition of P-measure and we prove some of its properties. Section 3 is dedicated to the
P-capacity and its properties.
We note that m−sh and m−wsh functions are related to the Hessians of function u (see
[3, 6]). They can be used in different problems of multidimentional complex analysis. One of
such application is shown in the work [6] (see also [7, 8]) where the characteristic functions of
Nevalinna of higher order are estimated.
function (subharmonic function on (n−m+1)-dimensional complex surfaces) in D, 1 m n,
if:
1. m−wsh functions
Definition 1. A function u(z) ∈ L1
1) it is upper semicontinuous in D, i.e.
lim
∗abakhrom1968@mail.ru
- Siberian Federal University. All rights reserved
c
– 3 –
z→z0 u(z) = limε→0 sup u(z) u(z0);
B(z0,ε)
loc(D) given in a domain D ⊂ Cn is called an m − wsh
Стр.3