#2 / 2013

This paper fins the necessary and sufficient conditions which give the existence of all the regular solutions, or tendency of the solution component to infinity (zero) on a positive half-axis of oscillation property for the Emden-Fowler system of differential equations.

gazieva2013_2.pdf

(4 Mb)

The paper deals with the operation of repeated commutation of linear differential operators and zero curvature equation generated by commuting linear operators.

kuizheva2013_2.pdf

(5 Mb)

Physics

The paper considers the method of analytical solution of systems of the first order ordinary differential equations with cubic nonlinearities. This method is generalized for such systems of the most common form. The criteria are found for the existence of an analytical solution at such systems. Application of the method is illustrated by the specific problem of nonlinear plasma electrodynamics.

bobylev2013_2.pdf

(1 Mb)

Natural Sciences

The paper provides the results of inventory and floristic analysis of woody plants in Maikop, the capital of the Adyghea Republic. An assessment of the prospects of using the exotic plants in gardening is given.

tolstikova2013_2.pdf

(927 Kb)

Dorsoventral mesophill consists of 2-3 layers of palisade and 6-10 layers of spongy tissues. In palisade tissue there are large unicellular etheric olive cavities. Anamozit stoma. There are more simple unicellular and tiny glandular hair on the lower epiderma than on the upper one. Correlation indices between the parameters of the compound leaf and leaflets are defined.

menknasunova2013_2.pdf

(2 Mb)

This paper presents a modern picture of the number and spatial distribution of the Caucasian population of brown bear living in the conditions of the Kabardino-Balkariya experimental hunting farms.

mashukov2013_2.pdf

(2 Mb)

The paper gives an ecological justification for concept of flooding and remoistening of lands of agricultural grounds and the technique to assess them. Attention is focused on researches of flooded and remoistened lands of the Adyghea Republic.

khamerzokova2013_2.pdf

(974 Kb)

The paper gives a characteristic of the museum’s rock traces of the Archean - late Phanerozoic bacterial biosphere and the remains of Phanerozoic skeletal fauna: from the Wend and early Cambrian to the Holocene.

volkodav2013_2.pdf

(864 Kb)

A geoinformation model of the Adyghea recreational system is developed. Areas of recreational specialization are distinguished. An inventory of recreation objects and criteria for their cadastral assessment is made.

shtelmakh2013_2.pdf

(3 Mb)

A group of comparison shows a statistically significant excess of cholesterol in blood serum. Simultaneously persons with heterozygotic Leu28/28Pro AROE genotype show increase in the content of cholesterol (> 7,5 mmol/l) compared to those with «homozygous» Leu28Leu. Football and basketball players have no 28Pro allele and Leu28Pro AROE genotype. In a group of athletes, the predictively adverse heterozygotic Leu28Pro genotype associated with increased risk of violation of a lipidic exchange (OR=3,85; CI (0,94-88,5)) is marked out in 27,3% of cases.

muzhenya2013_2.pdf

(881 Kb)

The paper gives the results of surgical treatment and prevention of venous thromboembolism in a multidisciplinary hospital. Clinical effectiveness, cost-effectiveness and safety of a comprehensive program and surgical prophylaxis of venous thromboembolism were studied in 125501 hospitalized patients. The effectiveness of surgical treatment and prevention of venous thromboembolism over the study period (2001-2007) showed a reduction in the overall incidence of venous thromboembolism from 2,9% to 0,8%. At the same time in-hospital mortality and perioperative lethality from pulmonary embolism (PE) were significantly reduced. Clinical efficacy associated with a reduction in venous thromboembolism and death from pulmonary embolism in the group of operated patients was almost 2 times higher.

zhane2013_2.pdf

(2 Mb)

An analysis is made of data of the international researches on distribution of the most studied -1082G/A, -819C/T, -592C/A of polymorphisms in the IL-10 gene of the promotor region at malignant new growths of female reproductive organs. Association of polymorphic gene variants of the main anti-inflammatory IL-10 cytokine revealed at women of the Adyghea Republic is confirmed by similar results in world populations.

anokhina2013_2.pdf

(729 Kb)

Frequencies of the DD genotypes (%) and D alleles of ACE gene at highly skilled athletes of the Adyghea Republic (football players, basketball players and athletes) authentically exceed indicators for the control group (84,8%, χ2=12,19, р=0,005 and 0,894, χ2=11,75, р=0,0006) and differ from data of the world researches. Depending on sports specialization of athletes reliable distinctions in distribution of genotypes and alleles of ACE polymorphic locus have not been revealed.

muzhenya2013_2.pdf

(826 Kb)

Technical Sciences

Development of plans on management of transport infrastructure in the conditions of limited resources and the emergency situation (ES) is very labor-consuming and not up to the end formalized process. Efficiency increase in activity of the governing bodies providing mathematical support to introduce modern transport planning methods on a basis of geoinformation technologies is extremely relevant. In this regard we examine characteristics of evacuation – a set of basic data and the objects participating in this process. A statement of a twostage mathematical problem of transport actions and the optimized model of evacuation are proposed.

kucher2013_2.pdf

(1006 Kb)

The paper deals with creation of the program rated theoretical module to determine the possible volume of renewable energy involved in a regional energy balance. Its structure is proposed. Design of relational structure of the database (D) is executed taking into account requirements of data integrity of subject domain and integration with geoinformation systems (GIS). An application of a program complex to assess the use of renewables in power supply systems of Krasnodar Territory and the Adyghea Republic is shown as an example.

simankov2013_2.pdf

(6 Mb)

Summaries of the New Books on the Natural and Exact sciences Published by Teachers of Adyghe State University

This book addresses the problems of stabilization of controllable linear dynamic systems. Interest to a problem of stabilization is based both on inquiries of practice of control and on the open problems existing in the control theory. Stabilization questions, as well as the related questions were very intensively studied in the last decades and in the present they remain in the center of attention of researchers. In the monograph, modern methods of stabilization of controllable linear systems are described. The first two chapters are introduction. In these chapters, the main concepts of the linear control theory are stated: transfer function, frequency characteristic, controllability, observability and stabilizability. In chapter 3, methods of stationary stabilization of linear controllable systems are described. The pole assignment problem with full and incomplete feedback is considered. In chapter 4, methods of low-frequency stabilization are described. Here estimates of solutions of linear systems on steady and unstable varieties are used and the Poincare's reflections which are carrying out enclosures of unstable varieties into steady varieties are synthesized. Existence of such reflections is a basis for low-frequency stabilizability of linear controllable systems. Necessary conditions for stabilizability are obtained similarly to Chetayev's theorems. Necessary and sufficient conditions of stabilizability are given for two-dimensional and for a number of standard three-dimensional systems with scalar entrances and exits. In chapter 5, methods of high-frequency stabilization are considered. They are based on a widely known method of averaging and special non-stationary linear transformations. Here the results obtained by the Belgian mathematicians L. Moreau and D. Aeyels are presented. The results stated in the fourth and fifth chapters give a solution of Brockett's problem on synthesis of non-stationary feedback for stabilization of stationary linear system. This is important for practice in a number of cases. In chapter 6, the methods stated in the third, fourth and fifth chapters are generalized for discrete controllable systems. The material statement in the book is closed. The used mathematical data are proved in detail. The book is intended for specialists in the control theory, the theory of the differential equations and dynamic systems and in theoretical and applied mechanics. Certain chapters and paragraphs of the book can serve as good introduction in the mathematical control theory for students and post-graduate students of mathematical specialties.

leonov1_2013_2.pdf

(182 Kb)

The book addresses the problems of stability and stabilization of dynamic systems with hysteresis nonlinearities. Mathematical models of many processes and systems from physics, biology, economy, the theory of automatic control, etc. are reduced to the systems of the differential equations containing nonlinearities of the hysteresis nature, for example, electromagnetic fluctuations in a contour containing ferroelectric condensers, economic cycles in the conditions of «hysteresis» behavior of economic agents, the control systems containing hysteresis links, etc. in addition to usual functional nonlinearities. The most important aspects of studying such models are research of their stability and stabilization of such systems. In introduction, relevance of a subject is proved and the review of the classical and modern works devoted to stability of systems with a hysteresis is given. In chapter 1, the main definitions, the data and provisions of the theory of stability of systems of the differential equations with hysteresis functions are given. Chapter 2 examines stability of systems with a hysteresis for a case, when a matrix of linear part of system is gurvitsev. Frequency criteria for stability have been obtained. Theorems of a global asymptotics, absolute stability and dichotomy of systems with hysteresis nonlinearities are proved. In chapter 3, the critical case is considered, when a matrix of linear part of system is the special. Here the corresponding frequency criteria for a global asymptotics, absolute stability and dichotomy have been obtained. The results obtained in the second and third chapters are applied to study stability of two-dimensional differential systems with a hysteresis. Chapter 4 deals with the harmonious stabilization of systems with a hysteresis. The frequency criterion for harmonious stabilization of nonlinear systems has been obtained, which can be applied both to analyze capture of self-oscillations by the frequency of external harmonious influence, and to stabilize systems with chaotic behavior. In chapter 5, stabilization of nonlinear system by any periodic external influence is considered. Existence of steady, as a whole, periodic solution with the period of external influence is proved. The book is intended for specialists in dynamic systems, the differential equations and their appendices, theoretical and applied mechanics, as well as for students and post-graduate students of mathematical specialties.

leonov2_2013_2.pdf

(139 Kb)

The book deals with the problems of topological behavior of solutions of the dynamic systems the right parts of which are the second- and third-order polynomials. Straight line-isoclines, Poincare's transformations and Poincare's sphere are used as the main tools. The book is composed of the authors’ original works published in journals. The book contains a detailed statement of theoretical questions and a big illustrative material in the form of phase portraits of specific polynomial differential systems. The statement is very laconic and transparent. The monograph is intended for students, teachers and the scientists who are engaged in the theory of the differential equations. It can be used when reading a special course on the qualitative theory of the differential equations. Chapter 1 «Straight line-isoclines of polynomial differential systems on the plane. The main concepts, definitions, theorems» includes eight paragraphs. Here you will find the used definitions, proofs of the theorems relating to isoclines of polynomial differential systems with polynomials of any order n>2 in the right parts, estimates of number of straight line-isoclines and classification of the systems possessing the maximum number among themselves of straight line-isoclines. Chapter 2 «Axes of symmetry of a field of the directions of quadratic and cubic differential systems on the plane» consists of four paragraphs in which the author's original theory of symmetry axes of N and S-types is considered and full research of autonomous systems for N and S-symmetry is carried out. Chapter 3 «Special points of cubic differential system on the equator of Poincare's sphere» consists of two paragraphs. Here behavior of trajectories of dynamic systems in infinitely remote parts of the phase plane is considered, as well as the full qualitative analysis is given for a number of cases.

tlyachev2013_2.pdf

(153 Kb)