Towards Rigorous Derivation of Quantum Kinetic Equations

We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator the equivalence of the description of the evolution of quantum many-particle states by the Cauchy problem of the quantum BBGKY hierarchy and by the Cauchy problem of the generalized quantum kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is established in the space of trace class operators. The links of the specific quantum kinetic equations with the generalized quantum kinetic equation are discussed.Comment: 25 page

Approximations of singular vertex couplings in quantum graphs

We discuss approximations of the vertex coupling on a star-shaped quantum graph of $n$ edges in the singular case when the wave functions are not continuous at the vertex and no edge-permutation symmetry is present. It is shown that the Cheon-Shigehara technique using $\delta$ interactions with nonlinearly scaled couplings yields a $2n$-parameter family of boundary conditions in the sense of norm resolvent topology. Moreover, using graphs with additional edges one can approximate the ${n+1\choose 2}$-parameter family of all time-reversal invariant couplings.Comment: LaTeX source file, 33 pages, with 3 eps figure

The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems

The Cauchy problem for the von Neumann hierarchy of nonlinear equations is investigated. One describes the evolution of all possible states of quantum many-particle systems by the correlation operators. A solution of such nonlinear equations is constructed in the form of an expansion over particle clusters whose evolution is described by the corresponding order cumulant (semi-invariant) of evolution operators for the von Neumann equations. For the initial data from the space of sequences of trace class operators the existence of a strong and a weak solution of the Cauchy problem is proved. We discuss the relationships of this solution both with the $s$-particle statistical operators, which are solutions of the BBGKY hierarchy, and with the $s$-particle correlation operators of quantum systems.Comment: 26 page

On the spectrum of a bent chain graph

We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever $\alpha\ne 0$. We consider a "bending" deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling $\alpha$ and the "bending angle" as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands.Comment: LaTeX, 23 pages with 7 figures; minor changes, references added; to appear in J. Phys. A: Math. Theo

Parents and Children: Way to Choice of Profession

It is reported the monograph “Parent assistance in professional self-determination of senior pupils” (2016), prepared by T. D. Zelenkina, E. Yu. Pryazhnikova and M. G. Sergeyeva, touches upon the problem of effective vocational guidance. The value of the edition is based on the fact that problems of choosing the profession do not lose its relevance. The views of the authors of the monograph on parental involvement in career choice of their children are characterized. For example, it is noted that the family may not only contribute to the process of professional self-determination, but also prevent correct choice. Model of training parents to help in professional self-determination of senior pupils proposed by the authors is briefly described

The efficiency of using case-method for training staff of the higher qualification

В статье отмечено значение применения кейс-технологий для подготовки инженерных кадров высшей квалификации. Обозначено, что кейсовые чемпионаты являются эффективным инструментом для передачи будущим специалистам-инженерам практических знаний, опыта и новых компетенций. Приведены доказательства, что метод с использованием кейсов, имеет актуальность, эффективность и востребованность по сравнению с традиционными методами обучения, так как реализует главные образовательные аспекты: практическую направленность, интерактивный формат и конкретные навыки.The article notes the importance of using case technologies for the training of highly qualified engineering personnel. It is indicated that case championships are an effective tool for transferring practical knowledge, experience and new competencies to future engineers. Evidence is given that the method using cases is relevant, effective and in demand in comparison with traditional teaching methods, as it implements the main educational aspects: practical orientation, interactive format and Soft skills

The Reference System in Determining the Parameters of Horizontal Deformations of the Earth's Crust on Geodynamic Polygons

The article is devoted to the choice of the reference system and the related problem of initial data errors while determining the features of the earth's crustal deformations, determined at the geodynamic polygons (GDP) by the differences of the equalized coordinates of network points between the geodetic measurements epochs. It is shown that the problem is not eliminated in the transition to satellite measuring instruments. In determining the geometric component of the earth's crust deformations, it is recommended to take into account the physical nature of its origin. To ensure the uniformity of the reference system for all geodesic measurements epochs on the local GDPs it is recommended to use the free geodetic networks equalization device without reference points. The deformation components obtained according to the theory of elasticity should be recognized the priority features of the earth's crust deformations on such GDPs

Periodic Pattern in the Residual-Velocity Field of OB Associations

An analysis of the residual-velocity field of OB associations within 3 kpc of the Sun has revealed periodic variations in the radial residual velocities along the Galactic radius vector with a typical scale length of lambda=2.0(+/-0.2) kpc and a mean amplitude of fR=7(+/-1) km/s. The fact that the radial residual velocities of almost all OB-associations in rich stellar-gas complexes are directed toward the Galactic center suggests that the solar neighborhood under consideration is within the corotation radius. The azimuthal-velocity field exhibits a distinct periodic pattern in the region 0<l<180 degrees, where the mean azimuthal-velocity amplitude is ft=6(+/-2) km/s. There is no periodic pattern of the azimuthal-velocity field in the region 180<l<360 degrees. The locations of the Cygnus arm, as well as the Perseus arm, inferred from an analysis of the radial- and azimuthal-velocity fields coincide. The periodic patterns of the residual-velocity fields of Cepheids and OB associations share many common features.Comment: 21 page

EPIDEMIOLOGICAL FEATURES OF MYASTHENIA GRAVIS

Aim. To assess the main epidemiological indicators of myasthenia gravis in various countries of the world, as well as in the territory of the Russian Federation.Materials and methods. Materials of publications on the study of epidemiological and population characteristics of myasthenia gravis of native and foreign authors are studied.Results. The indicator of the prevalence of myasthenia in the world varies from 0.5 to 20.0 per 100,000. The average primary morbidity of myasthenia gravis in the world is 0.53 per 100,000 population. The indicator varies from 0.17 to 2.13 per 100 thousand of the population.Conclusion. A fairly large range of epidemiological characteristics of myasthenia gravis in the world is revealed. The high prevalence of this pathology in the territory of the Russian Federation is established, which causes further interest in this type of research