The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation

The general construction of quasi-classically concentrated solutions to the Hartree-type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter \h (\h\to0), are constructed with a power accuracy of O(\h^{N/2}), where N is any natural number. In constructing the quasi-classically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for middle or centered moments) is essentially used. The nonlinear superposition principle has been formulated for the class of quasi-classically concentrated solutions of the Hartree-type equations. The results obtained are exemplified by the one-dimensional equation Hartree-type with a Gaussian potential.Comments: 6 pages, 4 figures, LaTeX Report no: Subj-class: Accelerator PhysicsComment: 36 pages, LaTeX-2

Star Formation History in the Galactic Thin Disk

The behavior of the relative magnesium abundances in the thin-disk stars versus their orbital radii suggests that the star formation rate in the thin disk decreases with increasing Galactocentric distance, and there was no star formation for some time outside the solar circle while this process was continuous within the solar circle. The decrease in the star formation rate with increasing Galactocentric distance is responsible for the existence of a negative radial metallicity gradient in the thin disk. At the same time the relative magnesium abundance exhibits no radial gradient. It is in detail considered the influence of selective effects on the form of both age - metallicity and age - relative magnesium abundance diagrams. It is shown that the first several billion years of the formation of the thin disk interstellar medium in it was on the average sufficiently rich in heavy elements ( = -0.22), badly mixed (\sigma_[Fe/H] = 0.21), and the average relative magnesium abundance was comparatively high ( = 0.10). Approximately 5 billion years ago average metallicity began to systematically increase, and its dispersion and the average relative magnesium abundance - to decrease. These properties may be explained by an increase in star formation rate with the simultaneous intensification of the processes of mixing the interstellar medium in the thin disk, provoke possible by interaction the Galaxy with the completely massive by satellite galaxy

The problem of turnover of the psychoactive substance al-cohol: abuse, consequences, countermeasures

The authors made a review of statistical data on the turnover of the psychoactive substance alcohol within the Russian Federation, Ukraine, United States, Moldova, Hungary, Czech Republic, and England. The authors studied the facts of negative consequences caused by the abuse of the psychoactive substance alcohol and dy-namics of alcohol dependence to develop the measures of resistence to the spread of alcoholism among the population. It was revealed that the WHO records only the quantitative indicators of abuse of alcohol. However, it is necessary to consider the qualitative indicators as well (strong or light alcoholic beverages)yesБелгородский госуниверсите

The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration

Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are not obtained by separation of variables for several external electromagnetic fields. We have considered an example of crossed electric and magnetic fields of a special type for which the Dirac equation admits a nonlocal symmetry operato

An application of the Maslov complex germ method to the 1D nonlocal Fisher-KPP equation

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the 1D nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher-Kolmogorov-Petrovskii-Piskunov equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure.Comment: 28 pages, version accepted for publication in Int. J. Geom. Methods Mod. Phy

ORGANIZATIONAL AND LEGAL REGULATION PROCEDURE FOR CIRCULATION OF EXTEMPORAL MEDICINES BASED ON PHARMACEUTICAL LAW

Introduction. The paper studied the situation regarding the production of medicines in pharmacies. Established that the presence of the pharmacy manufacture of medicines, patients entitled to receive medicines made to the needs of individuals. Goal – to study the organizational and legal procedure of regulation of extemporal medicines by developing of the algorithm for determining the legal act used in the event of conflict based on the law pharmaceutical law. Materials and methods. The materials of the study were legal acts of Ukraine: Laws of Ukraine, Decrees of the Cabinet of Ministers of Ukraine, Orders of the Ministry of Healthcare of Ukraine. The research methods were legal, documentary and comparative analyzes. Results and discussion. However, production of extemporaneous preparations in the pharmacy requires a production base and the appropriate staff. Therefore, the authors based on pharmaceutical law proposed organizational and legal procedure regarding the regulation of extemporaneous preparations by developing the algorithm for determining the legal act which should follow in the event of conflicts concerning the law. Conclusions. Based on pharmaceutical law held organizational and legal procedure for the regulation of circulation of extemporal medicines. Proposed the algorithm for determining of the legal act used in the practice of pharmacy professionals. Considered the professional status of an authorized person on the stage of quality control of extemporal medicines in their treatment in healthcare institutions of private property

The Shapovalov determinant for the Poisson superalgebras

Among simple Z-graded Lie superalgebras of polynomial growth, there are several which have no Cartan matrix but, nevertheless, have a quadratic even Casimir element C_{2}: these are the Lie superalgebra k^L(1|6) of vector fields on the (1|6)-dimensional supercircle preserving the contact form, and the series: the finite dimensional Lie superalgebra sh(0|2k) of special Hamiltonian fields in 2k odd indeterminates, and the Kac--Moody version of sh(0|2k). Using C_{2} we compute N. Shapovalov determinant for k^L(1|6) and sh(0|2k), and for the Poisson superalgebras po(0|2k) associated with sh(0|2k). A. Shapovalov described irreducible finite dimensional representations of po(0|n) and sh(0|n); we generalize his result for Verma modules: give criteria for irreducibility of the Verma modules over po(0|2k) and sh(0|2k)

Some aspects of nonlinearity and self-organization in biosystems on examples of localized excitations in the DNA molecule and generalized Fisher-KPP model

This review deals with ideas and approaches to nonlinear phenomena, based on different branches of physics and related to biological systems, that focus on how small impacts can significantly change the state of the system at large spatial scales. This problem is very extensive, and it cannot be fully resolved in this paper. Instead, some selected physical effects are briefly reviewed. We consider sine-Gordon solitons and nonlinear Schrodinger solitons in some models of DNA as examples of self-organization at the molecular level, as well as examine features of their formation and dynamics under the influence of external influences. In addition, the formation of patterns in the generalized Fisher–KPP model is viewed as a simple example of self-organization in a system with nonlocal interaction at the cellular level. Symmetries of model equations are employed to analyze the considered nonlinear phenomena. In this context the possible relations between phenomena considered and released activity effect, which is assessed differently in the literature, are discussed