Darboux Transformation of the Green Function for the Dirac Equation with the Generalized Potential

We consider the Darboux transformation of the Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We obtained the Green functions of the transformed Dirac equation with the initial regular boundary conditions. We also construct the formula for the unabridged trace of the difference of the transformed and the initial Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We illustrate our findings by the consideration of the Darboux transformation for the Green function of the free particle Dirac equation on an interval.Comment: 14 pages,zip. file: Latex, 1 figure. Typos corrected, the figure replace

Interdependence between integrable cosmological models with minimal and non-minimal coupling

We consider the relation between exact solutions of cosmological models having minimally and non-minimally coupled scalar fields. This is done for a particular class of solvable models which, in the Einstein frame, have potentials depending on hyperbolic functions and in the Jordan frame, where the non-minimal coupling is conformal, possess a relatively simple dynamics. We show that a particular model in this class can be generalized to the cases of closed and open Friedmann universes and still exhibits a simple dynamics. Further we illustrate the conditions for the existences of bounces in some sub-classes of the set of integrable models we have considered.Comment: 15 pages, v2: figures and references added, accepted for publication in CQ

Integrable cosmological models with non-minimally coupled scalar fields

We obtain general solutions for some flat Friedmann universes filled with a scalar field in induced gravity models and models including the Hilbert-Einstein curvature term plus a scalar field conformally coupled to gravity. As is well known, these models are connected to minimally coupled models through the combination of a conformal transformation and a transformation of the scalar field. The explicit forms of the self-interaction potentials for six exactly solvable models are presented here. We obtain the general solution for one of the integrable models, namely, the induced gravity model with a power-law potential for the self-interaction of the scalar field. We argue that although being mathematically in a one-to-one correspondence with the solutions in the minimally coupled models, the solutions in the corresponding non-minimally coupled models are physically different. This is because the cosmological evolutions seen by an internal observer connected with the cosmic time can be quite different. The study of a few induced gravity models with particular potentials gives us an explicit example of such a difference.Comment: 20 pages, v3: references added, accepted for publication in CQ

Induced gravity, and minimally and conformally coupled scalar fields in Bianchi-I cosmological models

We study the cosmological evolution and singularity crossing in the Bianchi-I universe filled with a conformally coupled scalar field and compare them with those of the Bianchi-I universe filled with a minimally coupled scalar field. We also write down the solution for the Bianchi-I Universe in the induced gravity cosmology.Comment: 11 pages, 3 figures, final version, to appear in Physical Review

Connection between the Green functions of the supersymmetric pair of Dirac Hamiltonians

The Sukumar theorem about the connection between the Green functions of the supersymmetric pair of the Schr\"odinger Hamiltonians is generalized to the case of the supersymmetric pair of the Dirac Hamiltonians.Comment: 12 pages,Latex, no figure

Complex treatment of accommodation disturbances in students

Purpose: Assessment of the effectiveness of different methods of treatment accommodation disturbances in patients 18‑23 years old.Methods: Determination of refraction and the size of the absolute accommodation and reserves of the relative accommodationbefore and after the treatment with Midrimax and Irifrin 2.5 % in combination with the course of electrostimulation.Results: The clinical effect was obtained in all patients. The maximum improvement of visual functions with a lower degree of myopia (1.0‑3.0 D), increase of absolute accommodation (by 2.5‑3,.D) and reserves of the relative accommodation (up to age norms) were observed in the younger age group of patients, wich had received the treatment with Midrimax, especially when combined with electrostimulation.Conclusion: Instillation of Midrimax in the treatment of violations of accommodation contribute to the effective reduction in the degree of myopia and improve of accomodation in patients 18‑23 years old. The combination of this therapy with functional methods of treatment increase its effectiveness.</p

Coherent Schwinger Interaction from Darboux Transformation

The exactly solvable scalar-tensor potential of the four-component Dirac equation has been obtained by the Darboux transformation method. The constructed potential has been interpreted in terms of nucleon-nucleon and Schwinger interactions of neutral particles with lattice sites during their channeling Hamiltonians of a Schwinger type is obtained by means of the Darboux transformation chain. The analitic structure of the Lyapunov function of periodic continuation for each of the Hamiltonians of the family is considered.Comment: 12 pages, Latex, six figures; six sections, one figure adde

Клинические случаи вирусного гепатита Е у детей

The article presents an analysis of the literature data on the prevalence of viral hepatitis E, the peculiarities of the course of the disease, including in children, and describes own cases of viral hepatitis E in children.Viral hepatitis E is a common infection worldwide. Sporadic and group cases of the disease are also registered on the territory of the Russian Federation. Epidemio-logical and clinical features of the course of the disease depending on the genotype were revealed. Children rarely get sick with manifest forms all over the world.Infection of the fetus and newborns with the development of fulminant hepatitis is typical for developing countries. The development of chronic infection is described in children who have undergone liver transplantation. In the Udmurt Republic, during the period of rising incidence of viral hepatitis A, 4 cases of viral hepatitis E were registered in 2017 in different age groups and different clinical manifestations. Registered cases of viral hepatitis E in children in the Russian Federation determine the need for mandatory examination of patients with cytolysis syndrome for this infection.В статье представлен анализ литературных данных по распространенности вирусного гепатита Е, особенностям течения заболевания, в том числе у детей, описаны собственные случаи наблюдения вирусного гепатита Е у детей.Вирусный гепатит Е является распространенной инфекцией во всем мире. Спорадические и групповые случаи заболевания регистрируются в том числе и на территории Российской Федерации. Выявлены эпидемиологические и клинические особенности течения заболевания в зависимости от генотипа. Во всем мире манифестными формами дети болеют редко. Инфицирование плода и новорожденных с развитием фульминантной формы гепатита характерно для развивающихся стран. Развитие хронической инфекции описано у детей, перенесших трансплантацию печени. В Удмуртской Республике в период подъема заболеваемости вирусным гепатитом А зарегистрировано 4 случая вирусного гепатита Е в 2017 году в различных возрастных группах и разными клиническими проявлениями. Регистрируемые случаи вирусного гепатита Е на территории Российской Федерации у детей определяют необходимость обязательного обследования пациентов с синдромом цитолиза на данную инфекцию