Monodromy dependence and connection formulae for isomonodromic tau functions

We discuss an extension of the Jimbo-Miwa-Ueno differential 1-form to a form closed on the full space of extended monodromy data of systems of linear ordinary differential equations with rational coefficients. This extension is based on the results of M. Bertola generalizing a previous construction by B. Malgrange. We show how this 1-form can be used to solve a long-standing problem of evaluation of the connection formulae for the isomonodromic tau functions which would include an explicit computation of the relevant constant factors. We explain how this scheme works for Fuchsian systems and, in particular, calculate the connection constant for generic Painlev\'e VI tau function. The result proves the conjectural formula for this constant proposed in \cite{ILT13}. We also apply the method to non-Fuchsian systems and evaluate constant factors in the asymptotics of Painlev\'e II tau function.Comment: 54 pages, 6 figures; v4: rewritten Introduction and Subsection 3.3, added few refs to match published articl

Theoretical Approach for Developing the Thermographic Method in Ultrasonic Fatigue

AbstractIn the last years, several approaches were developed in literature for predicting the fatigue strength of different kinds of materials. One approach is the Thermographic Method, based on the thermographic technique. This study is devoted to the development of a theoretical approach for modeling of surface and undersurface fatigue crack initiation and temperature evolution during ultrasonic fatigue test. The proposed model is based on the statistical description of mesodefect ensemble and describes an energy balance in materials (including power of energy dissipation) under cyclic loading. The model allows us to simulate the damage to fracture transition and corresponding temperature evolution in critical cross section of a sample tested in very high cyclic fatigue regime

International cooperation in combating illicit trafficking in cultural property

The paper discusses the basics of international cooperation in the field of combating illicit trafficking in cultural property. The directions of international cooperation in the field of combating illicit trafficking in cultural property and works of art are considered: interaction between international organizations, representatives of governments of UN member states, non-governmental organizations and the private secto

The Keele STarT Back Screening Tool Questionnaire: linguistic adaptation of the Russian language version

Introduction. The original English-language questionnaire for identifying the risks of developing chronic back pain The Keele STarT Back Screening Tool was developed in 2007 and adapted for use in many languages. The article describes the linguistic adaptation of the Russian version of the questionnaire The Keele STarT Back Screening Tool conducted in accordance with generally accepted rules.Aim. Linguistic adaptation of the Russian-language version of The Keele STarT Back Screening Tool.Materials and methods. Linguistic adaptation was carried out in five stages: 1) direct translation by three translators; 2) development of one version of direct translation; 3) reverse translation by two native English speakers; 4) development of one reverse version and its discussion by a committee of experts; 5) preliminary testing of the Russian version in a group of 30 patients (10 men and 20 women) aged from 28 to 84 years (average age 61.3 ± 8.7 years) with acute back pain, who in the period of April-June 2022 were on outpatient or inpatient treatment at the Clinic of Nervous Diseases of Sechenov University for nonspecific back pain (n = 21) and radiculopathy (n = 9).Results and discussion. All patients reported that the wording of the questionnaire items was clear and did not raise additional questions. The response time to the questions ranged from 30 seconds to 2 minutes 20 seconds (on average – 1 minute 18 seconds).Conclusion. The adapted Russian version of The Keele STarT Back Screening Tool questionnaire to identify the risks of developing chronic back pain did not cause comments from patients and experts. This version can be used to confirm its psychometric properties