Correct statement of a scattering problem for quantum charged scalar particles on the Reissner-Nordstr\"{o}m black holes

We study a correct statement of the scattering problem arising for quantum charged scalar particles on the Reissner-Nordstr\"{o}m black holes when taking into account the own electric field of black hole. The elements of the corresponding S-matrix are explored in the form convenient to physical applications and for applying numerical methods. Some further possible issues are outlined.Comment: 12 pages, LaTeX with using the ijmpd1.sty file from the package of World Scientific Publishing Co., to appear in Int. J. Mod. Phys. D7 (1998

Radiative decay effects influence the local electromagnetic response of the monolayer graphene with surface corrugations in terahertz range

We continue the study of surface corrugations influence on the monolayer graphene local electromagnetic response in terahertz range we started earlier. The effects of radiative decay, double-valley structure of charge carriers spectrum in graphene and the breathing surface curvature form induced synthetic electric fields are taken into account. To fulfill this program the generalized nonlinear self-consistent equation is obtained. In case of weak external alternating electric field for the obtained equation in linear approximation on the external electric field the exact solution is found. It shows that in this case we get local dephasing in induced current paths depending on the surface form . This theoretical result qualitatively explains the corresponding experiments with local current patterns in graphene without using fully quantum approach which is necessary for theoretical description of such phenomenon in graphene nanoribbons. Besides the formulae obtained in the present paper could become the basis of the new method of the imaging of surface corrugations form for given picture of local current paths. The obtained results allow to study mechanical behavior of materials at nanoscale deviates from macroscoping established concepts and this is of particular importance for graphene

Periodic Jacobi operator with finitely supported perturbation on the half-lattice

We consider the periodic Jacobi operator $J$ with finitely supported perturbations on the half-lattice. We describe all eigenvalues and resonances of $J$ and give their properties. We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the Jost functions is one-to-one and onto, we show how the Jost functions can be reconstructed from the eigenvalues, resonances and the set of zeros of S(\l)-1, where S(\l) is the scattering matrix.Comment: 29 page

On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations

We solve the Cauchy problem for the Korteweg-de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finite-gap potentials under the assumption that the respective spectral bands either coincide or are disjoint.Comment: 29 page

Traditions and future directions in research and education at the Pedagogical Institute of Saratov State University

The relevance of the research is due to the need to analyze, conceptualize, and integrate both traditions and innovations in the research and education at the Teacher Training College of Saratov State University (SSU). Key focus areas include transformation of scientifi c schools, changes in classroom and extracurricular work, quantitative and qualitative transformation of practical training, formation of a common educational environment, and fostering interdepartmental interaction. The study aims to identify directions and strategies for developing research and education at the Teacher Training College of SSU. Methods (tools) include retrospective and comparative analyses of relevant scientifi c literature and bibliographic sources. Results highlight the strategies for research and education at the Teacher Training College of SSU, drawing on the analysis of methodological research of the founders of pedagogical, psychological, defectological, and methodical schools, as well as their substantive and technological content in response to modern challenges of higher pedagogical education. A scientifi c and educational cluster of the college has been established, identifying infrastructure and relevant scientifi c and methodological interests among the faculty. Conclusion: This research summarizes the transformation experiences of teacher training at Saratov State University, revealing strategies and future directions aligned with public demand and the current socio-cultural context. It presents common educational, personal development and research agendas of the Teacher Training College of SSU, focusing on integrating deep subject knowledge and innovative teaching methods, practice-oriented classes and extracurricular events. The study emphasizes close collaboration and interaction with educational organizations to cultivate traditional values, professional and personal qualities, and proactive behavior essential for future educators’ professional training. Practical significance: This study offers a model for replicating successful practices from the Saratov School of Higher Pedagogical Education

ANTITOXIC ANTIDIPHTHERIAL ANTIBODIES IN BLOOD SERUM OF HEALTHY ADULTS UNDER DIFFERENT VACCINATION SCHEMES

Intensity of immunity to the diphtheria is analyzed, in the article according to the levels of antitoxic antibodies in blood serum, of healthy adults from 20 to 51 years and older who live in England, Italy, Latvia, Lithuania, Russia and. Finland. In Russia displacement of morbidity during the epidemic of 1993—1996 to the older age groups caused, inclusion of compulsory revaccination of adults every 10 years after the latest vaccination, of teenagers in 14 years in National calendar of o prophylactic vaccination, in 1998. Chosen tactics of vaccinal prevention, wasn't included, in National calendars of o prophylactic vaccination, of other countries including European except for Finland. On the basis of the analysis for the optimization, of vaccinal prevention, of diphtheria the authors propose: to transfer revaccination of children from the age of 18 months to the age of 3—6 years (like in Italy, England, and. Finland), to realize vaccination, of adults individually taking into account the content of antitoxic antibodies in blood serum.. Key words: diphtheria, vaccinal prevention, antitoxic antibodie