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#4 / 2012
Mathematics
M.M. Shumafov
Stabilization of systems with hysteresis nonlinearities by harmonic external action
A problem of stabilization of systems of differential equations with hysteresis nonlinearities by harmonic external action is considered. A frequency criterion of stabilization by using harmonic external action is obtained for a class of the dynamical systems with hysteresis elements. This criterion can also be applied for stabilization of the nonlinear systems which may behave chaotically.
M.M. Shumafov
Stability of systems of differential equations with hysteresis nonlinearities
Problems of the stability of differential systems with hysteresis nonlinearities are considered. New frequency criteria for global asymptotics, absolute stability and dichotomy of systems with hysteresis in critical and noncritical cases are obtained. Here hysteresis functions may contain several loops which may be bypassed in arbitrary directions. The results of the present paper are a generalization of the results of papers [13].
V.B. Tlyachev, A.D. Ushkho, D.S. Ushkho
On absence of the isolated periodic solutions for the quadratic system with axis of symmetry
This paper considers an example of a quadratic dynamical system, which has an invariant straight line and at least one limit cycle with very close to zero positive different values of the parameter. The phase portraits of the system under different conditions of this parameter in terms of the Poincare circle are constructed. As a result of a generalization two theorems are proved. One theorem is on the absence of limit cycles in the quadratic system with four singular points and the other is also on the absence of limit cycles in the system, if the vector field is symmetric with respect to at least one axis of symmetry.
V.I. Paranuk
Macdonald functions from two variables
Unitary representations of group of cellular and triangular matrices of order 4, equivalent to earlier considered representations of the same group [1] are under construction. The type of the operator of representation for some subgroups of the considered group is established. In particular, operators of representation are integral transformations with a kernel. Macdonald generalized functions from two variables are entered into consideration, kernels of operators of representations are expressed through these functions. Some functional ratios for Macdonald generalized functions are established.
V.N. Lesev, A.O. Zheldasheva
The nonlocal boundary value problem for second order equations of the mixed type in the characteristic region
The work studies the unique solvability of boundary value problem with the shift to parabolichyperbolic equation of the second order. A question of existence of the problem solution is reduced to the equivalent of the Fredholm integral equation solvability and uniqueness of the solution is established on the basis of the energy integrals method.
M.M. Shumafov
On the conditions of stabilizability of threedimensional linear systems
The problem of stabilization of threedimensional linear timeinvariant controllable systems by means of static timeinvariant delayed output feedback is considered. Sufficient/necessary conditions for stabilizability of threedimensional linear systems are given. The potential of delayed feedback is shown. The obtained results illustrate very well the efficiency of introduction of delayed feedback for stabilization of unstable threedimensional linear systems.
Physics
Y.F. Golovnev, D.A. Nurguleev, I.G. Sidorova
Types of excitons in nanodimensional heterosystems EuOSrO
The paper studies the outbarriers and outdots excitons in nanodimensional heterosystems EuOSrO. The effect of spin on the exciton state was analyzed. An expression for the exciton Hamiltonian and the dispersion law for exciton excitement in ferromagnetic semiconductor were obtained.
E.R. Shchukin, N.V. Malay, Z.L. Shulimanova
On onedimensional movement of spherical aerosol particles at their braking at Reynolds large numbers
The analytical expression is found on the basis of experimental data. This expression describes, in the interval of Reynolds numbers 0 < Re < 10^3 with accuracy up to 5%, the dependence of the coefficient of resistance of gaseous environment to the motion of a spherical aerosol particle upon the Reynolds number. The analytical expression is used to carry out the integration in the explicit form of the onedimensional nonlinear equation of motion of a spherical particle taking into account the inertia of the particle and the force of resistance. The formula to directly assess the time of transition of a particle from the state with the initial Reynolds number into the state with finite Reynolds number as well as the distance, travelled by the particle were obtained. The analysis of the obtained results is carried out.
Natural Sciences
E.A. Sirotyuk
Highaltitude distribution and ecologicalphitocenotic features of gentians in the Western Caucasus
The paper discusses the results of studying the vertical distribution of gentians in the Western Caucasus and their tolerance in relation to the major directaction environmental factors. The obtained data expand knowledge of adaptive potentialities of species and can become a scientific basis for their protection and rational use.
T.S. Uligova, F.V. Khezheva, O.N. Gorobtsova, R.Kh. Tembotov
Profile and genetic peculiarities of enzymatic activity in semihydromorphic soils of the steppe zone of the Central Caucasus (within the KabardinoBalkaria)
The profile and genetic assessment and a comparative analysis are made of enzymatic activity (invertase, urease, phosphatase, dehydrogenase and catalase) in the subtypes of meadow chernozem soil from the steppe zone under conditions of the terski and elbrusskiy variants of vertical zonation within KabardinoBalkaria. The peculiarities in profile changes of biological activity in the subtypes of meadow chernozem soil, formed in the abovespecified variants of vertical zonation, are revealed.
A.V. Yakimov, M.I. Shapovalov, Kh.Kh. Shekikhachev, T.N. Efimova, O.T. Gladkaya
Environmental assessment of anthropogenic influence on the benthic fauna of the Baksan river (KabardinoBalkarian Republic, Central Caucasus)
The paper presents the evaluation of the current anthropogenic influence on communities of benthic organisms in the river. Class of quality and instream water saprobity were defined using the index of water pollution (WPI) and bioindication method. Changes in ecological conditions are observed in different highaltitude parts of the Baksan river. Reasons for the deterioration of the environmental situation of this water body are examined.
A.A. Guchetl
The individual profile of the asymmetry of elder preschool aged children
The cubic system of classification of functional asymmetries was developed. Of all the possible combinations of asymmetries according to three analyzer systems 17 individual combinations of profile asymmetry of 5–6yearold children were identified. The level of manual asymmetry is characerized by the increasing dextromanual dominance and by the gradual decrease of groups of lefthanded and ambidexters. This testifies to the influence of «the righthanded culture».
G.S. Boleeva
The disturbance of sympathetic neurotransmission in saphenous artery of rats with insulindependent diabetes mellitus
The prejunctional mechanisms of sympathetic neurovascular transmission are impaired in saphenous artery of rats 10–12 weeks after treatment with streptozotocin. This is manifested in reduced constrictor response to electrical nerve stimulation without alteration of smooth muscle cell sensitivity to noradrenaline. Morphological changes of periarterial nerve plexus are not observed at that stage of diabetes development.
A.R. Tuguz, E.N. Anokhina, D.V. Muzhenya, L.D. Aldonina, K.A. Rudenko, T.M. Ashkanova, A.F. Kizyanov
Gene allele association G197/197A of proinflammatory cytokine IL17A with the lowdifferentiated adenocarcinoma at malignant new growths of the female reproductive organs in ethnic groups of the population of the Adygheya Republic
Distribution of G197/197A of polymorphisms in proinflammatory cytokine IL17A gene is investigated by SNP (single nucleotide polymorphism) method in ethnic groups (Russian and Adyghes) of the population of the Adygheya Republic: donors and patients with different malignant new growths of female reproductive organs. «Normal» G197 allele IL17A, which is most widespread in populations, is associated with risks of development of an oncopathology (đ=0,04; OR=1,5; 95%CI) and tumoral progression (đ=0,008; χ2=6,05). Presence of G197 of polymorphism of proinflammatory IL17A can be used for inhabitants of the Adygheya Republic as a marker of system inflammatory reactions of the organism involved in pathogeny of malignant new growhs in Russian women.
Technical Sciences
M.A. Meretukov
The organization of system of body repair at stations of technical service in modern conditions
The paper discusses the organization of body repair at stations of technical service. It is suggested to use the combined station departments to carry out disassembling works, repair of a body and preparation for coloring. Then the car moves to a painting site. Recommendations are given to select the equipment of the combined station department. Features of station design for body repair are presented.
V.V. Buchatskaya
Technique to define the interval estimates when forecasting by extrapolation methods
Definition of confidential intervals of a forecast is one of the main objectives arising at extrapolation. On the basis of data from literature sources a connection is established between the size of a confidential interval and the length of a temporary row, as well as the period of anticipation of a forecast. Results of calculation of the size of a confidential interval for the set temporary row are analyzed.
M.S. Akopov, E.V. Khekert
Analysis of a problem of oil shipping arising due to a vetting
The paper deals with oil shipping problems arising due to a vetting of the vessels carried out by the international oil companies. Analysis of ship’s vetting which is conducted nowadays is presented. The necessity of factors influencing navigational safety is substantiated.
