We consider algebraic properties of prosymmetric, almost symmetric and
antisymmetric of affinely connected manifolds, close to symmetric spaces.

The polypolar system of coordinates formed by a family of multifocal lemniscates
is introduced, the full gang of which focuses forms its structural beginning. The arbitrary
point of a plane has, as well as in a classical polar system of coordinates, polypolar
coordinates: metric ¥, and angular ϕ, being functions of polar coordinates of rather
each of focuses. The focal representation of the curve form by multifocal lemniscates allows
to adjust a polypolar system of coordinates so that a metric component corresponded
to the form of the given curve. Lemniscate and its focal structure have the same group of
symmetries. The symmetries of polypolar coordination, and also curvilinear symmetries
on multifocal lemniscates are considered

Some problems of both physical and chemical regeneration of high purity silicon
using manufactories are observed. Possibilities of wastes separation of silicon and
silicon carbide, mineral oil and polyethylenglycole (PEG) are discussed. This allows decreasing
ecological problems of solar batteries and electronic components production.

The technique of research of anisotropy of speed of ultrasound in nematic Н-37 in
a temperature interval from 25 to 70 0С is presented at various pressure. In all investigated
temperature intervals of existence of a nematic mesophase, speed of ultrasound is more in
case of parallel orientation of a vector of a magnetic induction and a wave vector in comparison
with perpendicular orientation. In the distance (Т≥10К) from phase transition relative
anisotropy of speed of ultrasound practically doesn't depend on temperature and has
small value. The maximum influence of a magnetic field on speed of ultrasound takes place
for Т=5 to from enlightenment temperature.

This article provides information on substances with a record high temperature
superconductivity transition, a brief overview of the use of superconducting substances in
the field of power electronics and microelectronics. Based on the identity of the superconducting
properties of a new class of iron superconducting materials and perform prediction
of compositions of these substances with temperature superconducting transition
from 55 to 62.5 k.

A method to indirectly estimate the signal-to-noise ratio is described in this article
for various low-frequency controlled source electroprospecting methods. The problem
of the determination of the signal-to-noise ratio is important during the field work and in
the subsequent processing. However it cannot be calculated directly as the true signal is
not known. It is the antiperiodicity property of the signal that gives rise to the proposed
method. All controlled source electroprospecting signals possess this property. A description
of the proposed indirect estimation method is presented here as well as its relation to
the direct signal-to-noise ratio formula.

To take care of variability involved in the writing style of different individuals
in this paper we propose a robust scheme to segment unconstrained handwritten texts into
primitives, which can be easily recognized later. While most similar works concentrated
on searching for middle line of the character we decided to extract an outer line. This approach
leads to much simpler implementation and acceptable quality of segmentation.

The article introduces the concept of intrinsic relativistic kinetic energy. Its fundamental
significance in kinetics of nuclear reaction and the process of elementary particles
collisions were shown. The necessity of introduction of this concept in teaching the
basics of the theory of relativity in theoretical physics courses in both classical and pedagogical
universities was methodically substantiated.

In the article for the problem of pursuit a comparison made of two approaches
to the study of this topic, aimed at improving the cognitive activity of students in the
study of dynamical systems: first with using differential equations and second with the
use of a simulation model. Graphic illustrations are made in the environment MathCad
and NetLOGO.

Process of mathematical tasks system construction for schoolchild is considered.
In the tasks of the offered system the sum of distances from the point to polygon
sides and similar value in volume for point and polyhedron are examined.

In the present article the problem of change of the status of research activity in
professional education of the mathematics teacher is considered. The author formulates
priority problems in the organization of research activity of students and assumes that
their successful solution is possible within the limits of realization of model of formation
of research competency. In article the model of formation of research competency of the
future mathematics teacher is presented, organizational-pedagogical conditions of its realization
are specified, levels of progress of research competency are described, forms of
development of research competences are considered.