MATHEMATICS IN HIGHER SCHOOL

Mathematics In Higher School

N:1

2016

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Guidance collection «Mathematics in high school» covers modern basic questions of teaching mathematics in general educational and high school. Results received nowadays in different fields of mathematics as well as researches in this direction made by specialists, lecturers of Higher Educational Institutions of the republic and teachers of general educational schools are published here. The collection is designed for students, post-graduate students, competitors, teachers, lecturers.

Headings

  • группы Шоттки

  • декартова конфигурация окружностей

  • клейновые группы

  • ковер Аполлония

  • преобразования Мебиуса

The different ways for the construction of Apollonian gasket was introduced. Apart from the geometric construction, two difeerent but closely related Kleinian groups that produce the same gasket were examined and some of their connections were revealed. However, there is still left to discover an explicit relation between them in order to explain this coincidence.

  • емкость множества

  • классы Карлесона и Джрбашяна

  • коэффициенты Тейлора

  • произведения Бляшке и М.М. Джрбашяна

  • конусы

  • риччи-полусимметрические подмногообразия

  • эйнштейновы подмногообразия

A geometric description of a class of normally flat Ricci semi-symmetric submanifolds of codimension two with zero singularity index and regularity index two in Euclidean spaces is done. The class of Einstein submanifolds which are canal submanifolds is investigated in detail.

  • геодезические линии

  • кривизна

  • метрика

  • погружение

  • производная

Infinite polygonals belonging to sertain slass in ds2 = dx2+(e-x+b(y))2dy2 complete metrie of negative curvature is considered. The existence of polnonals of thrse tuo ckasses in a more general metric than the one being observed is proved in the work (1). The general result of this work is the following theorem. In the obove mentioned metric any infinite polonal belonging bo class M1 immerses info E3 in regular, isometrie way.

  • множество точек Жюлиа

  • нормальные эквиморфные функции

  • предельные множества

For normal [1] and equimorphic [3] functions in the unit disc it is proven theorem of Julias points JA (f) [4].

  • аменабельная группа

  • нильпотентная группа

  • разрешимая группа

  • случайное блуждание

  • спектральный радиус

For symmetric random walks on countable groups sufficient conditions for equality of the spectral radius of unit are obtained.

  • прямые произведения

  • риччи-полусимметрические подмногообразия

  • цилиндры и конусы над римановыми многообразиями

A geometric description of normally flat Ricci-semisymmetric submanifolds in euclidean space of codimension two with two nonzero eigenvalues of the Ricci tensor is given. Normally flat Ricci semisymmetric submanifolds with one regular and one nonzero singular principal curvature vectors are also considered.

  • аналитические

  • гармонические

  • субгармонические функции

It was studied some famous theorems for harmonic and subharmonic functions and their connection with analytical functions in a “Complex analysis” course.

Council

V.S. ZAKARYAN (editor-in-chief), H.S. Mikaelyan (editor-in-chief deputy), A.H. Arakelyan (responsible secretary), H.M. Hayrapetyan, A. O. Babayan, L.Z. Gevorkyan, V.A. Mirzoyan, A.Kh. Khachatryan, M. Muradyan, Ye.A. Harutyunyan, L.G. Arabajyan, G.M. Grigoryan, G.A. Karapetyan, A.M. Jerbashian, S.M. Mkhtitaryan, A.A. Mitoyan