Spectral approach to linear programming bounds on codes

We give new proofs of asymptotic upper bounds of coding theory obtained within the frame of Delsarte's linear programming method. The proofs rely on the analysis of eigenvectors of some finite-dimensional operators related to orthogonal polynomials. The examples of the method considered in the paper include binary codes, binary constant-weight codes, spherical codes, and codes in the projective spaces.Comment: 11 pages, submitte

Exceptional Collections and del Pezzo Gauge Theories

Stacks of D3-branes placed at the tip of a cone over a del Pezzo surface provide a way of geometrically engineering a small but rich class of gauge/gravity dualities. We develop tools for understanding the resulting quiver gauge theories using exceptional collections. We prove two important results for a general quiver gauge theory: 1) we show the ordering of the nodes can be determined up to cyclic permutation and 2) we derive a simple formula for the ranks of the gauge groups (at the conformal point) in terms of the numbers of bifundamentals. We also provide a detailed analysis of four node quivers, examining when precisely mutations of the exceptional collection are related to Seiberg duality.Comment: 26 pages, 1 figure; v2 footnote 2 amended; v3 ref adde

Creation of the web-based database of maser sources

Для решения проблемы поиска и систематизации данных по астрономическим мазерным источникам был создан программный код, работающий в режиме онлайн, предназначенный для хранения, анализа и визуализации данных о мазерных источниках. Система предназначена для хранения больших объемов данных по мазерному излучению в различных линиях межзвездной среды, в том числе с учетом отрицательных регистраций. Имеется возможность отождествления мазерных источников с данными из популярных астрономических каталогов. В настоящий момент система успешно применена для проекта eDAMS extensive Database of Astrophysical Maser Sources, целью которого является сбор наиболее полных сведений об околозвездных мазерных источниках в линиях H2O, OH и SiO. Для этой цели уже собрано более 25 тыс. наблюдений из различных источников в 10 тыс. объектах. Адрес сайта для ознакомления с возможностями системы http://maserdb.ins.urfu.ru.To solve the problem of searching and collecting the data of astronomical maser sources, the Web-based code was developed in order to store, analyze and visualize the data of astronomical masers. The system is designed to store large amounts of data on maser emission in various lines of the interstellar medium, including negative results. Cross-checking of maser sources with popular astronomical catalogs is implemented. At the moment, the system has been successfully applied for the eDAMS project — the Extensive Database of Astrophysical Maser Sources, whose goal is to collect the complete information about circumstellar maser sources in the H2O, OH and SiO lines. For this purpose, more than 25 000 observations from various sources in 10 thousand objects have already been collected. Current internet-address of the system is http://maserdb.ins.urfu.ru

On some generalizations of the properties of the multidimensional generalized Erdélyi-Kober operators and their applications

In this paper we investigate the composition of a multidimensional generalized Erdélyi-Kober operator with differential operators of high order. In particular, with powers of the differential Bessel operator. Applications of proved properties to solving the Cauchy problem for a multidimensional polycaloric equation with a Bessel operator are show