On Thermodynamics of Rational Maps. II: Non-Recurrent Maps

The pressure function p(t) of a non-recurrent map is real analytic on some interval (0,t_*) with t_* strictly greater than the dimension of the Julia set. The proof is an adaptation of the well known tower techniques to the complex dynamics situation. In general, p(t) need not be analytic on the whole positive axis

On one-point functions for sinh-Gordon model at finite temperature

Using fermionic basis we conjecture the exact formulae for the expectation values of local fields in sinh-Gordon model. The conjecture is checked against previously known results.Comment: 21 pages, some explanation on relation to the lattice model is adde

Random conformal snowflakes

In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the multifractal analysis of harmonic measure. We argue that, searching for extremals in such problems, one should work with random fractals rather than deterministic ones. We introduce a new class of fractals random conformal snowflakes and investigate its properties developing tools to estimate spectra and showing that extremals can be found in this class. As an application we significantly improve known estimates from below on the extremal behaviour of harmonic measure, showing how to constuct a rather simple snowflake, which has a spectrum quite close to the conjectured extremal value

Reflection relations and fermionic basis

There are two approaches to computing the one-point functions for sine-Gordon model in infinite volume. One is a bootstrap type procedure based on the reflection relations. Another uses the fermionic basis which was originally found for the lattice six-vertex model. In this paper we show that the two approaches are deeply interrelated.Comment: 17 pages; several typos are correcte

The history of constructivism in the Urals: 21st-century studies

The article was submitted on 28.07.2016.Статья посвящена научному обзору и анализу трудов современных исследователей по истории архитектуры конструктивизма на Урале. Наличие в крупных и малых городах Урала различных экспериментальных градостроительных решений и приемов квартальной застройки, типологического разнообразия общественных, жилых, производственных зданий и сооружений, реализованных в стилистических формах конструктивизма, существенно выделяет Уральский регион от других районов страны. По решению ЦИК СССР в 1923 г. была создана Уральская область с целью увеличения промышленно-хозяйственного потенциала страны, и попутно с целью решения основных проблем реконструкции «культуры и быта». Внедрение современных строительных материалов и конструкций, новаторские поиски в архитектуре объемно-пространственных решений, различных по типологии объектов в рациональной стилистике широко использовалось в застройке таких городов как Пермь, Челябинск, Магнитогорск, Курган, Нижний Тагил, Свердловск, Златоуст, Надеждинск и др. Социальная и художественная направленность современного по тем годам творческого течения повлияла на формирование новой структуры уральских городов, преобразовала архитектурный язык и облик построек, позволила создать новые, ранее не встречающиеся в архитектурной практике типы зданий, изменила представление людей об удобстве, стиле и качестве жизни. С середины 1930-х до начала 1990-х гг. многие уральские города решением правительства страны были закрыты для зарубежных исследователей советской авангардной архитектуры, а на публикации книг и статей об объектах конструктивизма в стране было наложено табу. Поэтому одни из первых серьезных публикаций конструктивистских объектов, сооруженных в уральских городах, появились только на рубеже ХХ–ХХΙ вв. С начала нового века стала складываться научная школа истории уральской авангардной архитектуры, известными представителями которой являются А. А. Барабанов, Е. В. Конышева, Л. Н. Смирнов, А. А. Стариков, Л. И. Токменинова, Л. П. Холодова и другие ученые.The article features a comprehensive review of recent research on the history of Constructivism in the Urals. Various experimental urban solutions in Ural cities and towns, innovative models of quarter planning, and the typological diversity of public, residential, and industrial buildings built in Constructivist style makes Ural region distinct from other parts of the country. The introduction of contemporary building materials and designs and novel research into the usage of space can be seen in diverse buildings in Perm, Chelyabinsk, Magnitogorsk, Kurgan, Nizhny Tagil, Sverdlovsk, Zlatoust, Nadezhdinsk, and others. The social and artistic direction of Constructivism as an ultra-modern creative movement greatly influenced the new architectural look of cities in the Urals. It also transformed the language of architecture and the visual imagery of buildings: it allowed for the creation of new, unprecedented architectural types and changed people’s ideas about convenience, style, and quality of life. From the mid-1930s until the early 1990s, many towns in the Urals were closed off to foreign researchers: the publication of books and articles about Constructivism was also prohibited. This is why the first serious publications about the Constructivist heritage of the Urals appeared only at the beginning of the 21st century. Thus began a rise in scholarship on this subject

An Algorithm to Construct Groebner Bases for Solving Integration by Parts Relations

This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. The algorithm is used for calculating Feynman integrals and has proven itself efficient in several complicated cases.Comment: LaTeX, 9 page