The analytical continuation problem and Cauchy problem for the elliptic equations,
a so-called Adamar example, have appeared important problems in geophysics in
connection with questions of potential fields continuation. Bavrin I.I. has offered the formulas
restoring analytical or harmonious function on its values on an internal circle for
areas with circular symmetry of E2 . The analytical decision of a problem of harmonious
function continuation in an individual-dimensional sphere on its known values on internal
sphere is found. The decision of a similar continuation problem in case of the task on
sphere not the function, and its some operational transformations is received.

Analysis of medical database is described. Noise detection algorithm based on
equivalent special methodics is used. Effectiveness of algorithms is numerically proven.
This methodic is used in combination with traditional statistic methods. Analysis of database
using given algorithm is implemented and some classification results are presented.

The development of the possibilities of the analytical method of investigating
the structure of shock wave front with the progressively nonequilibrium chemical reactions
is considered. The method is based on the Tamm-Mott- Smith's bimodal approxi
mation of the function of the molecules distribution in connection with to the analysis of
the barrier chemical processes rates.

Features of reflexion of waves from sites of wave guides and environments
with evanescent parametres are used by working out of generators of high-frequency fluctuations,
however are considered only for dissipative isotropic environments. In this
work reflexion of electromagnetic waves from evanescent sites disperse gyrotropy. Environments
with strengthening is considered. It is established, that strengthening essentially
changes conditions of reflexion and passage of waves through borders of section of environments.

We report an X-ray diffraction study of some liquid crystalline nitro derivatives.
The influence of the molecular structure of these compounds on the formation of
layered structures of different types is discussed.

In this paper, we present robust scheme of controlled source electromagnetic data
processing. We specify various types of noise that affect measurements and show how
these noise components can be suppressed. We promote an improved algorithm to process
noisy data. We demonstrate that our method can recover response functions from extremely
noisy field data. The proposed software can be adapted to new data sets and noisy
environments. We apply our processing method to field data from Komi, Norilsk region,
Pechora province and other areas in Russia. In this article we present processing data results,
obtained at Magadan region in 2009.

Is determined invariant of a plane shock wave pulse of the sawtooth form.

Oxide glasses were implanted with Co+ ions at nominal fluences (F) ranging
from 2?e1015 to 3?e1017 cm-2 at energy E = 150 keV. The lines of EPR with g ~ 4 were observed
at 4.2 K for the samples implanted to F = (2?i8)×1015 cm-2 and were attributed to
Co2+ ions in distorted octahedral or tetrahedral environment depending on substrate. Results
of TEM, optical spectroscopy and EPR indicate the formation of Co metallic nanoparticles
at F >1016 cm-2. FMR line with g ~ 2.2 was observed in temperature region 4.2
?i77 K and even at 295 K for silicate glass.

Orientation of hydrocarbon molecules towards the surface of graphite and
polyethylene crystals has been simulated. The dependence of the interaction energy
of hydrocarbon molecules with the surface on angles characterizing their orientation
relatively to crystal surface is calculated. The dependences of the probability
of various orientational states on orientation angles are found. The average
values of the degree of orientation of molecules towards the crystal surface and of
the orientation factor are calculated. The dependence of the minimal value of the
energy of hydrocarbons interaction with surfaces on the number of atoms in a
molecule is found.

Statistical functions of distribution for oscillating fine-dispersed particles
in the quasicontinuous condensed medium were found from Liouville - Gibbs
equation. The main physical laws of the evolution of distributions were revealed
and their dependence from the task parameters was explored.

In this article, extension of some temporal CTL logics operators is proposed,
which enables explicit indication of the number of system states or the number of ways
wherein the preset feature of the system is realized. Semantics, formal grammar, as well
as relevant Kripke structure and extended temporal operators based feasibility check algorithms
are given.

The interconnection of teaching schoolboys to solve mathematical problems and
programming is being considered. Demands to the system of programming problems are
formulated.

The problem of formation the teaching and educational Internet system assisting
training to computer science and providing positive educational influence, focused on historical
and cultural values traditional for Russia is put. Features of becoming of an information
society in Russia are taken into account. Recommendations to such system are
formulated. Variants of system educational functions and pedagogical HIGH SCHOOLS
students participation in its functioning maintenance realization are considered

Article is devoted possibility of training of students with case-method
use. In particular, the problem of a highest level of complexity from a case is considered
- the problem of optimum formation of group of the people allocated with
a certain set of qualities, for the decision of the problems demanding qualities of
persons in certain volume is put. The device of linear algebra is necessary for the
decision of the given problem for students, and bases of linear programming
should be known. In article, as an example, process of formation of chair of four
classes of people is considered: assistants, the senior teachers, senior lecturers,
professors. Thus the circle of problems which is necessary for solving to the generated
group, is defined in advance.

Some problems сonnected with sequence of studying mathematical concepts in
school cource of math are considered in this article. School program made in such manner
that using some mathematical concepts begin more earlier in computer science then in
math. That's why teacher has some difficulties in the explaining of material and pupils has
some difficulties in it's mastering.

This article is devoted modernization and optimization of educational
process. The author by means of examples explains necessity of use modern technologies
for an education system, including programs for work with databases in
the multiuser mode and Internet decisions for education process. In particular, relational
databases which are widely used in the information environment are considered.

On an example of two tasks the application of computer system Mathematica on
employment on geometry is demonstrated, the opportunities of development of spatial
perception are demonstrated. These two moments are represented by the important factor
of increase of pedagogical competence of the future teachers of mathematics

In present work main ideas of the string theory is presented. The results
on fundamental issues of elementary particle physics give grounds to consider it
as the main candidate for the role of a unified theory. The possibilities of its experimental
confirmation are given.