Diameter and density of Neptune

Diameter, density, and atmospheric data calculated for Neptune from 7 Apr. 1968 occultatio

Quadratic algebras related to elliptic curves

We construct quadratic finite-dimensional Poisson algebras and their quantum versions related to rank N and degree one vector bundles over elliptic curves with n marked points. The algebras are parameterized by the moduli of curves. For N=2 and n=1 they coincide with the Sklyanin algebras. We prove that the Poisson structure is compatible with the Lie-Poisson structure on the direct sum of n copies of sl(N). The derivation is based on the Poisson reduction from the canonical brackets on the affine space over the cotangent bundle to the groups of automorphisms of vector bundles.Comment: 21 page

Elliptic Schlesinger system and Painlev{\'e} VI

We construct an elliptic generalization of the Schlesinger system (ESS) with positions of marked points on an elliptic curve and its modular parameter as independent variables (the parameters in the moduli space of the complex structure). ESS is a non-autonomous Hamiltonian system with pair-wise commuting Hamiltonians. The system is bihamiltonian with respect to the linear and the quadratic Poisson brackets. The latter are the multi-color generalization of the Sklyanin-Feigin-Odeskii classical algebras. We give the Lax form of the ESS. The Lax matrix defines a connection of a flat bundle of degree one over the elliptic curve with first order poles at the marked points. The ESS is the monodromy independence condition on the complex structure for the linear systems related to the flat bundle. The case of four points for a special initial data is reduced to the Painlev{\'e} VI equation in the form of the Zhukovsky-Volterra gyrostat, proposed in our previous paper.Comment: 16 pages; Dedicated to the centenary of the publication of the Painleve VI equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard Fuchs in 190

Uniform Boundedness of S-Units in Arithmetic Dynamics

Let K be a number field and let S be a finite set of places of K which contains all the Archimedean places. For any f(z) in K(z) of degree d at least 2 which is not a d-th power in \bar{K}(z), Siegel's theorem implies that the image set f(K) contains only finitely many S-units. We conjecture that the number of such S-units is bounded by a function of |S| and d (independently of K and f). We prove this conjecture for several classes of rational functions, and show that the full conjecture follows from the Bombieri--Lang conjecture

Magnetar Giant Flares --- Flux Rope Eruptions in Multipolar Magnetospheric Magnetic Fields

We address a primary question regarding the physical mechanism that triggers the energy release and initiates the onset of eruptions in the magnetar magnetosphere. A self-consistent stationary, axisymmetric model of the magnetar magnetosphere is constructed based on a force-free magnetic field configuration which contains a helically twisted force-free flux rope. Given the complex multipolar magnetic fields at the magnetar surface, we also develop a convenient numerical scheme to solve the GS equation. Depending on the surface magnetic field polarity, there exist two kinds of magnetic field configurations, inverse and normal. For these two kinds of configurations, variations of the flux rope equilibrium height in response to gradual surface physical processes, such as flux injections and crust motions, are carefully examined. We find that equilibrium curves contain two branches, one represents a stable equilibrium branch, the other an unstable equilibrium branch. As a result, the evolution of the system shows a catastrophic behavior: when the magnetar surface magnetic field evolves slowly, the height of flux rope would gradually reach a critical value beyond which stable equilibriums can no longer be maintained. Subsequently the flux rope would lose equilibrium and the gradual quasi-static evolution of the magnetar magnetosphere will be replaced by a fast dynamical evolution. In addition to flux injections, the relative motion of active regions would give rise to the catastrophic behavior and lead to magnetic eruptions as well. We propose that a gradual process could lead to a sudden release of magnetosphere energy on a very short dynamical timescale, without being initiated by a sudden fracture in the crust of the magnetar. Some implications of our model are also discussed.Comment: 26 pages, 5 figures, Accepted for publication in Ap

Управление поездообразованием. Часть 2

The publication in this issue is the second, final part of the article that shares the vision of the approaches to creation of optimal conditions of train operation, control the load of marshalling stations, their interaction with freight stations, redistribution of cargo operations, and suggests final conclusions.  As it was noted in the abstract of the first part, changes in management of train formation, which are put forward based on generalisation of a number of results of earlier author’s studies and publications (the vast of majority of them have not been published in English) and newly formulated proposals for discussion, will make it possible to manage the transportation process in a fundamentally new way.В номере публикуется вторая, заключительная часть статьи, в которой представлено видение подходов к созданию оптимальных условий поездной работы, регулированию загрузки сортировочных станций, их взаимодействию с грузовыми, перераспределению грузовой работы и предлагаются итоговые выводы.Как отмечалось в аннотации к первой части статьи, выносимые на основе обобщения целого ряда результатов более ранних авторских исследований и публикаций и вновь сформулированных предложений на обсуждение изменения в управлении поездообразованием позволят принципиально по-новому оперативно руководить перевозочным процессом

Оптимизация скорости движения поездов

The importance of the train speed is considered relative to activity of railways, presenting a wide panorama of influence, on the one hand of speed on the process of transportation of goods and passengers, and, on the other hand, of rolling stock, infrastructure, and organisation of transportation on speed.The objective of the article is to extend the ideas about the speed on railways with the help of analysis of Russian and international history of development and results of the study of the train speed.Despite, it would seem, all the certainty of speed of movement, the history of its development testifies to a wide range of opinions and non-obviousness of estimates. The historical review contains opinion on the development of the problem and interaction between the speed and other parameters.The interaction of train speed with all components of the transportation process is described by various dependencies. Therefore, the economic efficiency from increasing speed of trains can be obtained only with a system approach.Analysis of modern research shows the potential capacity to increase the speed. The results of the author’s research reveal the in-depth possibilities and expediency of increasing train speed.Рассматривается значение скорости движения поездов в деятельности железнодорожного транспорта, представлена широкая панорама влияния, с одной стороны, скорости на перевозочный процесс грузов и пассажиров, с другой стороны, – подвижного состава, инфраструктуры и организации перевозок на скорость.Целью статьи является расширение представления о скорости на железнодорожном транспорте с помощью анализа отечественной и зарубежной истории развития и полученных результатов исследования скорости движения поездов.Несмотря на, казалось бы, всю определённость скорости движения, история её развития свидетельствует о большом диапазоне мнений и неочевидности оценок. Исторический обзор содержит мнения о развитии проблемы и взаимодействии скорости с другими показателями.Взаимодействие скорости движения поездов со всеми составляющими перевозочного процесса описывается различными зависимостями. Поэтому экономическая эффективность от повышения скорости движения поездов может быть получена только при системном подходе.Анализ современных исследований показывает возможности повышения скорости. Результаты исследований автора раскрывают глубинные возможности и целесообразность повышения скорости движения поездов