Composition-Diamond lemma for λ\lambda-differential associative algebras with multiple operators

In this paper, we establish the Composition-Diamond lemma for $\lambda$-differential associative algebras over a field $K$ with multiple operators. As applications, we obtain Gr\"{o}bner-Shirshov bases of free $\lambda$-differential Rota-Baxter algebras. In particular, linear bases of free $\lambda$-differential Rota-Baxter algebras are obtained and consequently, the free $\lambda$-differential Rota-Baxter algebras are constructed by words

The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

Splitting fields and general differential Galois theory

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions..Comment: 33 pages, this version coincides with the published on

Random Networks Tossing Biased Coins

In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to generate an ensemble of random directed graphs with, asymptotically, scale-free outdegree and compact indegree. Entries in each row of the adjacency matrix are set to be zero or one according to the toss of a biased coin, with a chosen probability distribution for the biases. This defines a quick and simple algorithm, which yields good results already for graphs of size n ~ 100. Perhaps more importantly, many of the relevant observables are accessible analytically, improving upon previous estimates for similar graphs

The place and role of leisure in the Moscow students’ everyday life in the context of the information society development

The proposed article discusses issues related to the daily life of Moscow students and their leisure, the relevance of which in the context of the development of the information society is associated with increased attention of the state to the educational component of modern educational systems. Moreover, in the conditions of modern realities of the development of the information society, and, consequently, information culture, the format of leisure becomes a significant factor in the socialisation of the individual.   As a goal, the authors of the article identified the analysis of various forms of leisure activities of Moscow students through their questionnaires, which was designed to outline vectors for further research of the place and role of study, family relations and forms of spending free time in a student’s life.   Special attention is paid to modern forms of leisure for students, such as: spending time on the Internet, visiting experimental theaters and cinemas, watching talk shows and entertainment programs, visiting immersive shows, participating in modern youth organisations, etc. Summarising the results of the study, it was concluded that at the moment no more than 20 % of the surveyed Moscow students choose “modern” forms of leisure activities. The conducted research revealed the students’ clear preferences in spending their free time, as well as their value orientations

A Bose-Einstein Approach to the Random Partitioning of an Integer

Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of connected components. Questions such as the evaluation of the probability of random covering and parking configurations, number and length of the gaps are addressed. They are the discrete versions of similar problems raised in the continuum. For each value of k, asymptotic results are presented when n,N both go to infinity according to two different regimes. This model may equivalently be viewed as a random partitioning problem of N items into n recipients. A grand-canonical balls in boxes approach is also supplied, giving some insight into the multiplicities of the box filling amounts or spacings. The latter model is a k-nearest neighbor random graph with N vertices and kn edges. We shall also briefly consider the covering problem in the context of a random graph model with N vertices and n (out-degree 1) edges whose endpoints are no more bound to be neighbors

The conditional maximum of Poisson random variables

© 2017 Taylor & Francis Group, LLC The conditional maxima of independent Poisson random variables are studied. A triangular array of row-wise independent Poisson random variables is considered. If condition is given for the row-wise sums, then the limiting distribution of the row-wise maxima is concentrated onto two points. The result is in accordance with the classical result of Anderson. The case of general power series distributions is also covered. The model studied in Theorems 2.1 and 2.2 is an analogue of the generalized allocation scheme. It can be considered as a non homogeneous generalized scheme of allocations of at most n balls into N boxes. Then the maximal value of the contents of the boxes is studied

Gravitational detection of a low-mass dark satellite at cosmological distance

The mass-function of dwarf satellite galaxies that are observed around Local Group galaxies substantially differs from simulations based on cold dark matter: the simulations predict many more dwarf galaxies than are seen. The Local Group, however, may be anomalous in this regard. A massive dark satellite in an early-type lens galaxy at z = 0.222 was recently found using a new method based on gravitational lensing, suggesting that the mass fraction contained in substructure could be higher than is predicted from simulations. The lack of very low mass detections, however, prohibited any constraint on their mass function. Here we report the presence of a 1.9 +/- 0.1 x 10^8 M_sun dark satellite in the Einstein-ring system JVAS B1938+666 at z = 0.881, where M_sun denotes solar mass. This satellite galaxy has a mass similar to the Sagittarius galaxy, which is a satellite of the Milky Way. We determine the logarithmic slope of the mass function for substructure beyond the local Universe to be alpha = 1.1^+0.6_-0.4, with an average mass-fraction of f = 3.3^+3.6_-1.8 %, by combining data on both of these recently discovered galaxies. Our results are consistent with the predictions from cold dark matter simulations at the 95 per cent confidence level, and therefore agree with the view that galaxies formed hierarchically in a Universe composed of cold dark matter.Comment: 25 pages, 7 figures, accepted for publication in Nature (19 January 2012

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.Comment: 11 page

A 700 year-old Pulsar in the Supernova Remnant Kes 75

Since their discovery 30 years ago, pulsars have been understood to be neutron stars (NSs) born rotating rapidly (~ 10-100 ms). These neutron stars are thought to be created in supernova explosions involving massive stars, which give rise to expanding supernova remnants (SNRs). With over 220 Galactic SNRs known (Green 1998) and over 1200 radio pulsars detected (Camilo et al. 2000), it is quite surprising that few associations between the two populations have been identified with any certainty. Here we report the discovery of a remarkable 0.3 sec X-ray pulsar, PSR J1846-0258, associated with the supernova remnant Kes 75. With a characteristic age of only 723 yr, consistent with the age of Kes 75, PSR J1846-0258 is the youngest pulsar yet discovered and is being rapidly spun down by torques from a large magnetic dipole of strength ~ 5E13 G, just above the so-called quantum critical field. PSR J1846-0258 resides in this transitional regime where the magnetic field is hypothesized to separate the regular pulsars from the so-called magnetars. PSR J1846-0258 is evidently a Crab-like pulsar, however, its period, spin-down rate, spin-down conversion efficiency, are each an order-of-magnitude greater, likely the result of its extreme magnetic field.Comment: 4 pages, 3 figures, LaTex, emulateapj.sty. Submitted to The Astrophysical Journa