Universality of the limit shape of convex lattice polygonal lines

Let ${\varPi}_n$ be the set of convex polygonal lines $\varGamma$ with vertices on $\mathbb {Z}_+^2$ and fixed endpoints $0=(0,0)$ and $n=(n_1,n_2)$. We are concerned with the limit shape, as $n\to\infty$, of "typical" $\varGamma\in {\varPi}_n$ with respect to a parametric family of probability measures $\{P_n^r,0<r<\infty\}$ on ${\varPi}_n$, including the uniform distribution ($r=1$) for which the limit shape was found in the early 1990s independently by A. M. Vershik, I. B\'ar\'any and Ya. G. Sinai. We show that, in fact, the limit shape is universal in the class $\{P^r_n\}$, even though $P^r_n$ ($r\ne1$) and $P^1_n$ are asymptotically singular. Measures $P^r_n$ are constructed, following Sinai's approach, as conditional distributions $Q_z^r(\cdot |{\varPi}_n)$, where $Q_z^r$ are suitable product measures on the space ${\varPi}=\bigcup_n{\varPi}_n$, depending on an auxiliary "free" parameter $z=(z_1,z_2)$. The transition from $({\varPi},Q_z^r)$ to $({\varPi}_n,P_n^r)$ is based on the asymptotics of the probability $Q_z^r({\varPi}_n)$, furnished by a certain two-dimensional local limit theorem. The proofs involve subtle analytical tools including the M\"obius inversion formula and properties of zeroes of the Riemann zeta function.Comment: Published in at http://dx.doi.org/10.1214/10-AOP607 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Effects of alloying on aging and hardening processes of steel with 20% nickel

Measurements of hardness, thermal emf, and electrical resistance were used to study the effects of Co, Mo, Ti and Al contents on aging and hardening processes in Fe 20%Ni steel. It is shown that the effects of these alloying elements differ substantially. Anomalies which arise in the temperature dependence of physical properties due to the presence of cobalt and molybdenum are reduced by the inclusion of titanium and aluminum (and vice versa)

Identifying the factors that contribute to sustainable development of the national economy

The structural imbalance is the main problem hindering the development of the Russian national economy. It leads to significant difference in economic efficiency of various industrial sectors. Moreover, the structural imbalance adversely affects the interaction between industries and hampers to foster an enabling environment that would accelerate economic growth consistent with the principles of sustainable development. The right balance between economic sectors provides favorable conditions for a successful interaction between industries. The article suggests the methodology intended to identify the factors contributing to sustainable development of the national economy, to assess the status of the economy as well as to estimate the dynamics of economic growth. The methodology is a promising approach building a network of interactions between different industries to deepen the diversification of economic sectors. The authors propose a set of indicators - indicators of economic imbalances - that allow, based on primary statistical data, to quantitatively determine the degree of difference and the changing dynamics in economic, financial, technological and social characteristics of several economic sectors. The paper details the developed system of monitoring and multi-criteria evaluation of growth in several economic sectors. The system makes it possible to estimate key factors affecting sustainable development of the economy as well as to get the right diagnosis of economic processes that shape the sectoral structure of the Russian economy.peer-reviewe

Анализ конкурентоспособности малых портов Азово-Черноморского бассейна в мультимодальных перевозках: технологические аспекты, оптимизационная задача транспортного типа

A new approach is proposed to the study of functioning of the connecting and transforming link of the multimodal transport and logistics chain, implemented by railway cargo transportation. The methodological basis of the research is classical principles of egalitarianism in the theory of welfare, which allow, based on assessment of the transport and technological infrastructure of the network segment and tariff rates, to build mathematical models that are economically justified, customer-oriented and in demand in management of cargo transportation processes. An algorithm for solving a multi-criteria and multi-extremal problem of integer linear programming with a set of cost objective functions has been developed in the medium of the analytical computing system. The computational experiment is used as a guiding heuristic tool in finding the optimal level of organization and economic efficiency of the cargo transportation process.Optimal combinations of distributions of the number of departure routes per loading stations and related plans of transportation to the reloading stations were found with the help of the Pareto criterion. The obtained values of cost indicators provide the participants of the transportation process with the opportunity to choose competitive options in transportation schemes using small port transshipment stations of the Azov-Black Sea basin.Предложен оригинальный подход к исследованию функционирования связующего и преобразующего звена мультимодальной транспортно-логистической системы, реализуемого железнодорожными грузоперевозками. Методологическую основу исследований составляют классические принципы эгалитаризма в теории благосостояния, позволяющие на основе оценки транспортно-технологической инфраструктуры полигона и тарифных ставок строить математические модели, являющиеся экономически обоснованными, клиентоориентированными и востребованными в управлении процессами грузоперевозок.В среде системы аналитических вычислений разработан алгоритм решения многокритериальной и многоэкстремальной задачи целочисленного линейного программирования с набором стоимостных целевых функций. Вычислительный эксперимент используется в качестве направляющего эвристического инструмента при нахождении оптимального уровня организации и экономической эффективности процесса грузоперевозок. С помощь критерия Парето найдены оптимальные сочетания распределений числа отправительских маршрутов по станциям погрузки и относящихся к ним планов перевозок в адрес станций перегрузки. Найденные значения стоимостных показателей предоставляют участникам перевозочного процесса возможность выбора конкурентоспособных вариантов в схемах перевозок, использующих малые припортовые станции перегрузки Азово-Черноморского бассейна

Systemic Diagnostics of the Arctic Industry Development Strategy

The article analyzes organizational and economic problems of the industry in the Arctic and discloses methods and tools for researching these problems. An attempt to use the method of system diagnostics is made, which has established itself as a basis for determining the development strategy of industry in the Arctic zone of the Russian Federation (AZRF). This method allows to explore the mechanism of natural resources development in the Arctic, such as hydrocarbons and marine biological resources; as well as the organization of logistics and transport corridors for trade of goods produced in the North and in the central regions of Russia. The role, significance and content of the strategy as an essential element of the system for managing natural wealth development in the Arctic in the context of its growing importance in development of global transport corridor are revealed. Importance of a systematic approach to the development of industry in the Arctic is substantiated, it will ensure development of all investors interested in this region; will allow the state, large corporations, small and medium-sized businesses to work together for the long term. The proposed method for system diagnostics of strategizing the development of industrial potential in the AZRF can be used in the implementation of «Development Strategy for the Arctic Region» as part of roadmap realization for the Arctic region

Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States

Random banded matrices with linearly increasing diagonal elements are recently considered as an attractive model for complex nuclei and atoms. Apart from early papers by Wigner \cite{Wig} there were no analytical studies on the subject. In this letter we present analytical and numerical results for local spectral density of states (LDOS) for more general case of matrices with a sparsity inside the band. The crossover from the semicircle form of LDOS to that given by the Breit-Wigner formula is studied in detail.Comment: Misprints are corrected and stylistic changes are made. To be published in PR

PROBLEMS OF DIGITALIZATION OF THE RUSSIAN INDUSTRY

The article is devoted to the substantiation of the model of the formation of an industrial development ecosystem based on modern digital technologies in industry.The article deals with the problems of technological sovereignty of the Russian economy. It is shown that the solution of this problem is possible only on the basis of an industrial development ecosystem – a system of production chains of the most important types of industrial products, a technological development platform, interaction of subjects of industrial production with consumers of its products in the domestic and foreign markets. The necessity of concentration of industrial potential, resources of technological development, qualified personnel potential and direction to create conditions for providing the Russian economy with products corresponding to the world technological level is shown. The article analyzes the main existing and promising models of the functioning of an industrial enterprise. A detailed description of the barriers and difficulties on the way of digitalization of industrial enterprises in the Russian Federation is given.In order to form the ecosystem of industrial development of the Russian Federation, the directions of identifying and assessing the state of production and technological personnel potential, its compliance with the needs of the domestic market are formulated. Recommendations are given on the creation of an ecosystem structure, mechanisms for the interaction of its various elements, a management and coordination system based on digital technologies for creating a system of individual elements that form information and analytical centers in various functional areas of the ecosystem.A model of the ecosystem of industrial and technological development of the Russian economy based on digital technologies is proposed.A set of mechanisms that contribute to reducing the level of uncertainty is proposed, and a design method of interaction within the framework of the digital industrial enterprise technology platform model is described.The article formulates recommendations for the digitalization of an industrial enterprise in the new technological conditions of economic and social development, in the so-called new technological paradigm “Industry 4.0”, the characteristic features of which are minimal use of manual and mechanized labor, as well as a low level of transaction costs.A new approach is proposed, on the basis of which industrial enterprises will interact on the basis of shared access to information and digital resources and the ability to combine the development of innovative projects and value chains necessary to create competitive products in order to increase the operational efficiency of enterprises

Correlator Bank Detection of GW chirps. False-Alarm Probability, Template Density and Thresholds: Behind and Beyond the Minimal-Match Issue

The general problem of computing the false-alarm rate vs. detection-threshold relationship for a bank of correlators is addressed, in the context of maximum-likelihood detection of gravitational waves, with specific reference to chirps from coalescing binary systems. Accurate (lower-bound) approximants for the cumulative distribution of the whole-bank supremum are deduced from a class of Bonferroni-type inequalities. The asymptotic properties of the cumulative distribution are obtained, in the limit where the number of correlators goes to infinity. The validity of numerical simulations made on small-size banks is extended to banks of any size, via a gaussian-correlation inequality. The result is used to estimate the optimum template density, yielding the best tradeoff between computational cost and detection efficiency, in terms of undetected potentially observable sources at a prescribed false-alarm level, for the simplest case of Newtonian chirps.Comment: submitted to Phys. Rev.