Projective Differential Geometrical Structure of the Painlevé Equations

AbstractThe necessary and sufficient conditions that an equation of the form y″=f(x, y, y′) can be reduced to one of the Painlevé equations under a general point transformation are obtained. A procedure to check these conditions is found. The theory of invariants plays a leading role in this investigation. The reduction of all six Painlevé equations to the form y″=f(x, y) is obtained. The structure of equivalence classes is investigated for all the Painlevé equations. Following Cartan the space of the normal projective connection which is uniquely associated with any class of equivalent equations is considered. The specific structure of the spaces under investigation allows us to immerse them into RP3. Each immersion generates a triple of two-dimensional manifolds in RP3. The surfaces corresponding to all the Painlevé equations are presented

Exact Solution for the Critical State in Thin Superconductor Strips with Field Dependent or Anisotropic Pinning

An exact analytical solution is given for the critical state problem in long thin superconductor strips in a perpendicular magnetic field, when the critical current density j_c(B) depends on the local induction B according to a simple three-parameter model. This model describes both isotropic superconductors with this j_c(B) dependence, but also superconductors with anisotropic pinning described by a dependence j_c(theta) where theta is the tilt angle of the flux lines away from the normal to the specimen plane

The Kuiper Belt and Other Debris Disks

We discuss the current knowledge of the Solar system, focusing on bodies in the outer regions, on the information they provide concerning Solar system formation, and on the possible relationships that may exist between our system and the debris disks of other stars. Beyond the domains of the Terrestrial and giant planets, the comets in the Kuiper belt and the Oort cloud preserve some of our most pristine materials. The Kuiper belt, in particular, is a collisional dust source and a scientific bridge to the dusty "debris disks" observed around many nearby main-sequence stars. Study of the Solar system provides a level of detail that we cannot discern in the distant disks while observations of the disks may help to set the Solar system in proper context.Comment: 50 pages, 25 Figures. To appear in conference proceedings book "Astrophysics in the Next Decade

Мусульмане в Европе. Сосуществование, взаимодействие, межцивилизационный диалог

This collective monograph results from the researches of groups of experts in Islamic studies from different regions of Russia. Its articles are joint by the topic of dialogue of Islamic and European civilizations on the territory of the Old World. New times set new challenges: migration, demography, pandemic etc. And sometimes Europeans do not have adequate responses to the new challenges of modernity. This study is the first, but, hopefully, not the last, experience of scientific dialogue on this topic. Russia as the territory of peaceful coexistence of various religions, including Christianity and Islam, can share its experience with European countries, for many of which the dialogue of religions and coexistence of different cultures is a new and complex challenge.Данная коллективная монография представляет собой результат исследований групп учёных-исламоведов, культурологов, антропологов из различных регионов России. Материалы работы объединяет основная тема – диалог мусульманской и европейской цивилизаций на территории Старого Света. Новые времена рождают новые вызовы: миграционный, демографический, пандемийный и пр. Жизнь показывает, что порой у европейцев нет адекватных ответов на новые вызовы современности. Эта монография – первый и, будем надеяться, не последний опыт диалога учёных по данной проблематике. Россия как территория мирного существования различных религий, в том числе христианства и ислама, способна поделиться своим опытом с европейскими государствами, для многих из которых межрелигиозный диалог и взаимодействие различных культур – новый и сложный вызов

Multicomponent nutritional supplement Oncoxin and its influence on quality of life and therapy toxicity in patients receiving adjuvant chemotherapy

Treatment of cancer often requires the use of adjuvant chemotherapy (ACT). In real clinical practice, numerous patients suffer from severe toxicity and reduced quality of life (QoL). Hence, there is a need to maintain QoL and to reduce therapy toxicity to comply with recommended chemotherapy (CT) regimens. The present study focused on the effects of the multi-component nutritional supplement Oncoxin (ONCX) on QoL and CT-induced toxicity in patients undergoing ACT. A total of 133 patients aged 50-70 years with gastric cancer IIB-IIIC or non-small cell lung cancer IIB-IIIA were enrolled in the present study: 84 received ONCX, and 49 were included in the control arm and received CT only. It was identified that after 2 weeks of treatment the patients receiving ONCX exhibited clinically meaningful improvement of QoL (measured by Edmonton Symptom Assessment System Questionnaire) compared with those in the control group (odds ratio, 2.07; 95% CI, 1.00-4.29). By the end of a 3 week-period, the albumin level was higher in patients of the ONCX group compared with those in the control group (mean, 38.1; 95% CI, 37.1-39.1 g/l; vs. mean, 35.5; 95% CI, 33.9-37.0; P=0.03; respectively). Furthermore, the use of ONCX substantively reduced the hepatic toxicity of ACT. The present prospective real clinical setting study revealed positive effects of ONCX on QoL and ACT toxicity. The present study was retrospectively registered under the study registration number NCT03550482 at ClinicalTrials. gov (June 8, 2018). © 2019 Spandidos Publications. All rights reserved