Vol 17, No 2 (2011)

A nonlocal boundary value problem for degenerate elliptic equation is con
sidered. Boundary value of this problem considerably depend on low derivative
coefficient changes. Existence and uniqueness of a solution are proved.

This paper is the first systematic step to obtain the birational classification
of 4-dimensional tori. All the cohomological birational invariants of this tori are
calculated. All the 4-dimensional tori with nontrivial invariants are described.

In this paper, the initial-boundary value problems for hyperbolic equation
with nonlinear boundary conditions are considered. Existence and uniqueness of
generalized solution are proved.

In the article the unique algorithm of construction of the system of orthog
onal compact V.L. Leontev’s type functions for the nonlinear spatial equation
of viscous transonic flow is described by the method of Galerkin. The result of
designing on corresponding subspaces is system of ordinary differential equations
with a diagonal matrix.

In the work the problem about monoaxial and triaxial orientations of a
two-body system concerning Kenigov and random not inertial coordinate system
is put. The solution is gained by construction of active control which is realized
by a feedback principle. Stabilizing controls are synthesized and conditions under
which the desirable asymptotically stable orientation is possible. The assigned
task is solved on the basis of modified method of Lyupanov’s functions, which
allows to use Lyupanov’s functions with sign fixed derivatives.

The article is devoted to the fatigue growing crack problems in damaged
media and mutual effects of damage on the evolution of the stress-strain state
near the crack tip and vice versa. The new asymptotic study of fatigue crack
growth in an isotropic linear elastic material based on the continuum damage
mechanics in the coupled (elasticity damage) formulation under plane strain
and plane stress conditions is proposed. 1) The new numerical solution of the
two-point boundary value problem for non-linear ordinary differential equations
to which the fatigue crack growing problem reduces is obtained; 2) The new
analytical presentation of stress, strain and continuity fields both for plane strain
and plane stress conditions is given. The results obtained differ from Zhao and
Zhang’s solution where the original formulation of the problem for plane stress
conditions has been proposed.

Results of researches on modeling of dynamics of difficult systems contain
ing different physical elements, solving dynamics problems and control of a rigid
body and robotics systems are stated. Necessary conditions for stability of de
cisions of dynamics equations are defined, and the algorithm of the constraints
perturbations equations construction, guaranteeing constraint stabilization is of
fered at the numerical solution. Some results of the applied problems solution
illustrate efficiency of the described methods

Mean-square radii and electromagnetic form factors of light mesons are ob
tained in the framework of Poincare covariant quark model, which is based
on the point form of Poincare invariant quantum mechanics. Calculations are
performed with the use of the requirement of self-consistent description of elec
troweak properties and masses of pseudoscalar and vector mesons.

The work is devoted to applications of group-theoretic coherent states to
describe the nonlinear optical effects. Important in modern quantum information
process of parametric down conversion is studied. It is shown that the use
of superpositions of coherent states of SU(1; 1) allows to increase the squeezing
of generated photon pairs.

The results of quantum chemical computations of isolated molecules
(derivatives of 1,4-quinone) performed by using restricted Hartree-Fock (RHF)
method with the aid of Gaussian94 software in 3-21G basis set, are reported.
Correlation coefficients between quantum chemical characteristics (QCC) of the
molecules of inhibitors of corrosion and hydrogen absorption of steel St3 and
experimentally measured efficiencies of such species as the inhibitors in SRB
containing media, have been calculated.

For the first time a high efficiency of the technical alkylsalicylic acids as
a basis of the lubricity additive to low-sulfur diesel fuel is established. The
optimum compounding and method of obtaining the lubricity additive is devel
oped. A representative sample of the lubricity additive obtained in the labora
tory conditions. This the lubricity additive has passed tests for compliance with
the requirements of European safety criteria, according to GOST R 52368-2005
(EN 590:2004), and in the frameworks of the Complex of qualifying estimation
methods for high-speed diesel engines.

Solonetz meadow and artificial pinery ground cover lichen were explored in
detail. In artificial pinery we have found Cladonia fimbriata, C. carioza, C. cor
nuta, C. coniocraea. In solonetz meadow we have discovered Endocarpon pus
silum, Colemma sp., Corricularia sp., Peltigera lepidophora, Peltigera didactyla,
C. fimbriata, C. carioza. We revealed 10 lichen sinuses.

The results of the survey and assessment with the help of specially developed
questionnaire of external respiration function of 393 students (73 youngsters and
320 girls) at the age of 16–22 years from Samara universities are presented in
this work. The early beginning of familiarization with smoking is shown. It
was detected that smoking youngsters and girls more often use other psychoac
tive substances (alcohol, drugs), in 18,8 % preference is given to strong alcohol
drinks. The incipient character of abnormalities in external respiration functions
for smoking youth were identified.

Somatostatin is a hypothalamic neuropeptide suppressing the secretion of
somatotropin-releasing-factor, somatotropin and some other physiologically active
peptides. Somatostatin and its receptors are widely distributed in many CNS
structures and peripheral organs; it suggests the involvement of somatostatin in
regulation of different physiological functions. Presence of somatostatin and its
receptors in respiratory-related nuclei of the brain stem suggests the involvement
of the peptide in the respiratory control. In the paper, data about different
physiological effects of somatostatin, particularly regarding the involvement in
central mechanisms of the respiratory control, are summarized.

New data concerning role of reticular gigantocellular nucleus respiratory areas
in respiratory pattern forming is discussed. Based on electrical stimulation of
nucleus inspiratory and expiratory points results, authors suggest that reticular
gigantocellular nucleus plays a considerable role in central respiration control
mechanisms.