Riemann-Hilbert Formalism in the Study of Crack Propagation in Domains with a Boundary

The Wiener-Hopf technique is a powerful tool for constructing analytic solutions for a wide range of problems in physics and engineering. The key step in its application is solution of the Riemann-Hilbert problem, which consists of finding a piece-wise analytic (vector-) function in the complex plane for a specified behavior of its discontinuities. In this dissertation, the applied theory of vector Riemann-Hilbert problems is reviewed. The analytical solution representing the problem on a Riemann surface, and a numerical solution that reduces the problem to singular integral equations, are considered, as well as a combination of the numerical and analytical techniques (partial Wiener-Hopf factorization) is proposed. In this work, we begin with a brief survey of the Riemann-Hilbert problem: constructing solution of the scalar Riemann-Hilbert problem for a class of Holder continuous functions; considering classes of matrices that admit the closed-form solution of the vector Riemann-Hilbert problem; discussing numerical and analytical techniques of constructing solutions of vector Riemann-Hilbert problems. We continue with applications of the Wiener-Hopf technique to problems of Dynamic fracture mechanics: reviewing well-known solutions to problems on propagation of a semi-infinite crack in an unbounded plane in the cases of a stationary crack, a crack propagating at a constant speed, and a crack propagating at a non-uniform arbitrary speed. Based on those, we derive solutions to new problems on a semi-infinite crack propagation in a half-plane (steady-state and transient problems for subsonic speeds) as well as in a composite strip (for intersonic speeds). These latter results are new and were first derived by Y. Antipov and the author

The Implementation of Energy-Saving Lighting Systems for Poultry Houses

The provision of lighting in poultry shelters is an energy-intensive process in poultry farming, due to a lack of sunlight in closed facilities. Lighting plays an important role in the majority of organism biorhythms and it clocks the processes of vital activities of the birds. Lighting directly influences productivity, growth and sexual maturation of birds. A determining factor for the lifetime of an LED is the crystal heating temperature during its operation. It may be assumed that the LED lifetime is largely independent of the variation in the current passing through the LED (within the limits of its design values). The research objective was to conduct laboratory testing to compare the electricity consumption between the existing and a newly developed lighting system for poultry house no. 19 of the Kuchinsky Poultry Breeding Plant. In order to conduct the laboratory testing, the authors developed lighting fixtures consisting of sealed plastic bodies with an LED-carrying PCB inside. The testing continued for 113 days. The new system consumed 662 kWh, while the previous system consumed 783 kWh. Energy savings through the testing period amounted to 15%. During the testing, the new equipment was reliable; no failures of LED fixtures were recorded. Keywords: LED lighting, energy conservation, poultry farming, microclimat

Comparison of Sex Determination in Vertebrates (Nonmammals)

The chapter is devoted to the consideration of sex determination in vertebrate groups of nonmammalians: fish, amphibians, reptiles, and birds. Attention is drawn to the fact that all these groups of animals, unlike mammals, are implemented hormonal control options for primary sex determination, and there is a possibility of sex reversion. Determination of gonadal development in vertebrates like testis or ovary was initially controlled mainly by sex hormones (fish and amphibians). Later, various sex determining genes were involved in this process. The system was quite plastic and was able to respond to changes in external conditions (reptiles). The appearance of heteromorphic sex chromosomes (birds) has led to the emergence of some specific W chromosomal signal, which provides estrogen control of the development of a heterogametic sex. In mammals, the control of the primary determination of sex (the appearance of the gonad) becomes purely genetic, and the role of sex hormones is reduced to the differentiation of testis or ovaries

The vector form of Kundu-Eckhaus equation and its simplest solutions

In our work a hierarchy of integrable vector nonlinear differential equations depending on the functional parameter $r$ is constructed using a monodromy matrix. The first equation of this hierarchy for $r=\alpha(\mathbf{p}^t\mathbf{q})$ is vector analogue of the Kundu-Eckhaus equation. When $\alpha=0$, the equations of this hierarchy turn into equations of the Manakov system hierarchy. New elliptic solutions to vector analogue of the Kundu-Eckhaus and Manakov system are presented. In conclusion, it is shown that there exist linear transformations of solutions to vector integrable nonlinear equations into other solutions to the same equations.Comment: 20 pages, 3 figure

Specific Features of Sex Determination in Birds on the Example of <em>Gallus gallus</em> domesticus

The chapter is devoted to the consideration of sex determination in birds. The appearance of heteromorphic sex chromosomes (birds) has led to the emergence of some specific W chromosomal signal, which provides estrogen control of the development of a heterogametic sex. At present, two hypotheses about sex determination in birds compete. One of these hypotheses considers the number of Z chromosomes as a key sex-determining factor, while the other hypothesis supposes the presence in W chromosome of the key gene controlling ovarian development or suppressing the appearance of testes. Into the modern scheme of the genetic control of sex determination in birds (practically within the hypothesis of dose compensation), an epigenetic mechanism was added. The appearance of gonads in birds is most likely determined by sex hormones and to the greatest extent by estrogen under the control of W chromosome. It is desirable to pay attention to noncoding RNAs, their connection with the W chromosome and their role in bird sex determination

Дворцовое землевладение в Казанском уезде во второй половине xvi - начале xvii века

The research is devoted to the analysis of the landownership system of palace in Kazan district in the second half of the 16th century. The author dwells upon the features of palace village such as the granary or the Orthodox church. The church was mandatory attribute for villages with the local population professing the Orthodox religion. The next passage covers the information on the legal status of the land of the palace in the legislation and the cadasters. Further we can learn the ways of forming land of the palace in the district. The composition of the lands of palace was not permanent. Firstly, the formation of the fund land of the palace administration occurred as a result of seizures of other forms of ownership with the change of their status. Secondly, the peasant land was transferred to the category of palace. Land of the palace administration was actively transferred into the possession of the temporal and monasteries landowners. The next part contains the data on documentation of land ownership in the cadasters. The author reconstructs the composition of palace settlements in the 1560s and reviews the domains at the end of the 16th - early 17th century. In the end, overview of this type of land tenure shows an important role in the integration of multinational region in Moscow State and the economic development of the region. (author's abstract

Additional education in the system of professional training of university students

The article reflects the results of the implementation of a theoretical and experimental approach to understanding the role of additional education in the professional development of university students. Considering additional education as an element of the continuing education system, we believe that it is the activation of the development of additional education programs for university students, as well as the creation of conditions for effective implementation in the educational process, that will allow us to realize the main task of further education, as defined in the Law of the Russian Federation “On Education”, - education of a creative person, ready for self-development and self-determination. At the same time, the study we organized showed that only a little more than 50% of the students who took part in our study are positively oriented towards receiving additional education. In order to stimulate students' interest in obtaining additional education, including, within the framework of optimizing their professional development, we propose to focus on “immersing” students in research activities

X-RAY DIAGNOSIS OF PRIMARY OSTEOPOROSIS

The prevalence of bone demineralization is a distinguishing characteristic of primary osteoporosis (OP). The paper describes in detail the Xray symptoms of OP in different parts of the skeleton and in spongy and cortical bone tissues. It gives the calculation of the cortical index and the index of vertebral bodies on the basis of X-ray morphometry of the vertebral column, as well as the Singh semiquantitative method for the assessment of the trabecular bone structure of the proximal femur. Dual-energy X-ray absorptiometry is a method for the early diagnosis of OP. The main determinants of bone mineralization are described and the approaches to correctly interpreting the results of densitometry and to assessing the risk of bone fractures are presented