Classical Conformal Blocks and Painleve VI

We study the classical c\to \infty limit of the Virasoro conformal blocks. We point out that the classical limit of the simplest nontrivial null-vector decoupling equation on a sphere leads to the Painleve VI equation. This gives the explicit representation of generic four-point classical conformal block in terms of the regularized action evaluated on certain solution of the Painleve VI equation. As a simple consequence, the monodromy problem of the Heun equation is related to the connection problem for the Painleve VI.Comment: 19 pages, 5 figures; references adde

Max-plus definite matrix closures and their eigenspaces

In this paper we introduce the definite closure operation for max-plus matrices with finite permanent, reveal inner structures of definite eigenspaces, and establish some facts about Hilbert distances between these inner structures and the boundary of the definite eigenspaceComment: 20 pages,6 figures, v2: minor changes in figures and in the main tex

An interval version of separation by semispaces in max-min convexity

We study separation of a closed box from a max-min convex set by max-min semispace. This can be regarded as an interval extension of known separation results. We give a constructive proof of the separation in the case when the box and the max-min convex set satisfy certain condition, and we show that separation is never possible if this condition does not hold. We also study separation of max-min convex sets by boxes and by box and semispace

Generators, extremals and bases of max cones

Max cones are max-algebraic analogs of convex cones. In the present paper we develop a theory of generating sets and extremals of max cones in ${{\mathbb R}}_+^n$. This theory is based on the observation that extremals are minimal elements of max cones under suitable scalings of vectors. We give new proofs of existing results suitably generalizing, restating and refining them. Of these, it is important that any set of generators may be partitioned into the set of extremals and the set of redundant elements. We include results on properties of open and closed cones, on properties of totally dependent sets and on computational bounds for the problem of finding the (essentially unique) basis of a finitely generated cone.Comment: 15 pages, 1 figure; v2: new layout, several new references, renumbering of result

Epidemiology and Control of Leishmaniasis in the Former USSR: A Review Article

BACKGROUND. All types of the Old World’s leishmaniasis were endemic on the territoru of the ex-Soviet Republics in the Central Asia and Transcaucasia. Epidemiological situation was well under control during the USSR era, due to implementation of complex anti-leismaniasis measures. These interventions were dramatically stopped as a result of the collapse of the USSR in 1991. Within next years the incidence of leishmaniasis returned to the level of the 1950s threatening to reach epidemic proportions unless urgent measures are undertaking. METHODS. Most relevant publications on epidemiology and control of leishmaniases in the Republics of Central Asia  and Transcaucasia  of the ex-USSR were screened. Data from foreign publications, especially from countries with similar or close to that epidemiological situation in respect of leishmaniases were also included. RESULTS. Epidemiological analysis of spatial distribution of leishmaniases in the ex-USSR revealed that the northern borderline of these diseases is determined by the distribution of the vectors (42-460 North latitude). Within the endemic area, the foci of different kinds of leishmaniasis are often overlapped thus calling for deployment of integrated measures. The anthroponotic cutaneous leishmaniasis (ACL) was reported in settlements and towns of Central Asia and Transcaucasia of the ex-USSR. The natural foci of cutaneous leishmaniasis were widespread in the desert of Turkmenistan, Uzbekistan, southern Kazakhstan, and southern Tajikistan. The northern boundary of the zoonotic cutaneous leishmaniasis (ZCL) area coincided with the northern boundary of the distribution of great gerbils – the main reservoir of this infection in the ex-USSR. Visceral leishmaniasis (VL) occurred in the Central Asian Republics and in the republics of the Transcaucasia. The strategies of control and prevention of leishmaniases in the ex-USSR were based on good knowledge of epidemiology of infections. Holistic approach was adopted by the programs targeting the source of infection, vector(s) and man. CONCLUSION. The presence rise in the number of cases of different types of leishmaniasis in the ex-USSR strongly necessitates that health authorities should consider these diseases as an important public health problem. The immediate task would be re-building a comprehensive surveillance system consisting of active and passive case detection mechanism along with immediate treatment of the patients

Application of microwave photonics in fiber optical sensors

Microwave photonics is a new scientific and technical area of research, which was formed as a result of intensive development of such fields as fiber, integrated and nonlinear optics, laser physics, optoelectronics and microelectronics. A positive trend in the field of microwave photonic devices development has appeared in recent decades. The trend is related to the fact that these devices can operate in ultra-high and super-high frequencies and microwave ranges, and have parameters, which are unattainable by conventional electronic devices. Technical characteristics of microwave photonic measuring systems are comparable with those of traditional fiber-optic sensors. This technology can be used both for creation of new measuring devices and improvement of existing other types of measuring systems. This paper presents an analytical review of microwave photonics application technologies in fiber-optic measuring instruments. The general design concept for microwave photonic fiber-optic measuring devices is considered in the first part of the review paper. Microwave photonic filters are presented, which are the key elements of microwave photonic fiber-optic measuring devices. Their design technologies are described with indication of the features, advantages and disadvantages. Methods for creation of microwave photonic finite impulse response filters with positive and negative coefficients are considered. The following sections are devoted directly to the analysis of microwave photonic fiber-optic measuring devices and contain classification of such devices according to their principle of operation. The classification of spectral and interferometric microwave photonic fiber-optic measuring devices with indication of their distinctive features is proposed. Experimental data of the most common sensors is presented and analyzed; the main characteristics and areas of their practical application are presented for each of them. New approaches and methods are considered for creation of microwave photonic measuring systems and improvement of tactical and technical characteristics of existing devices. Comparison between microwave photonic fiber-optic measuring devices and traditional fiber-optic measuring systems is performed. According to comparison results, conclusions can be drawn about applicability of microwave photonic fiber-optic measuring devices and advantages of their use compared to other fiber-optic sensors.Радиофотоника является новым научно-техническим направлением, которое образовалось в результате интен-сивного развития таких областей, как волоконная, интегральная и нелинейная оптика, лазерная физика, опто- и микроэлектроника. В последние десятилетия наблюдается положительная динамика по созданию радиофотонных устройств, эта тенденция связана с возможностью создавать устройства ультравысоких и сверхвысоких частот с параметрами, недостижимыми обычными электронными устройствами. Характеристики радиофотонных измери-тельных систем сопоставимы с характеристиками традиционных волоконно-оптических датчиков, данная техно-логия может быть использована как для создания новых измерительных приборов, так и для усовершенствования уже существующих измерительных систем других типов. В работе представлен аналитический обзор способов применения радиофотонных технологий в волоконно-оптических измерительных приборах. В первой части обзорной статьи рассмотрен общий принцип построения радиофотонных волоконно-оптических измерительных приборов. Представлены ключевые элементы подобного рода систем — радиофотонные фильтры. Описаны тех-нологии их построения с указанием особенностей, преимуществ и недостатков. Рассмотрены способы создания радиофотонных фильтров с конечной импульсной характеристикой с положительными и отрицательными коэф-фициентами. Последующие разделы посвящены непосредственно анализу радиофотонных волоконно-оптиче-ских измерительных приборов и содержат классификацию таких устройств по их принципу работы. Предложена классификация спектральных и интерферометрических радиофотонных волоконно-оптических измерительных приборов с указанием их отличительных признаков. Представлены и проанализированы экспериментальные данные, основные характеристики и области практического применения наиболее распространенных датчи-ков. Рассмотрены новые подходы и методы по созданию радиофотонных измерительных систем и улучшению тактико-технических характеристик существующих приборов. Приведено сопоставление характеристик радио- фотонных волоконно-оптических измерительных приборов и традиционных волоконно-оптических датчиков, по результатам которого можно сделать вывод о применимости современного типа измерительных приборов, а также о преимуществах их использования по сравнению с другими волоконно-оптическими датчиками