Моделирование эпидемической ситуации с учетом внешних рисков
In this paper we propose a method of mathematical modeling of the epidemiological situation, taking into account external factors. An algorithm for finding the parameters of the model based on the results of observations, based on the method of least squares. Investigated the dependence of the epidemiological situation of the various parameters and external factors, as well as the ability to manage the development of epidemics by influencing these factors. Proposed the concept of the system of monitoring the epidemic situation, taking into account the external risks.
The article discusses the prospects of qualitative sociological research online, with the main focus on the survey, observation and analysis of documents. Online conditions require not only the use of innovative technological developments for contact in the field, but has earned the recognition and adaptation of offline methods in the interaction between researchers and respondents.The author believes that there is no single solution for or against online qualitative methods. Rather, it is a methodologically diversified access, which combines Internet-based approaches, depending on the current task with the help of proven methods in online research.
We develop a consensus clustering framework developed three decades ago in Russia and experimentally demonstrate that our least squares consensus clustering algorithm consistently outperforms several recent consensus clustering methods.
The new economic-mathematical model based on complex variables theory and the new approach to complex variables usage in economics are suggested in the article. The comparison of modeling results of actual production processes using Cobb-Douglass production function and complex variables production function is conducted. It is shown that the instrumental base of economicmathematical methods can be widen with usage of complex variables theory.
The article examines an episode in the history of nineteenth-century agricultural improvement, the attempt to change the climate of Russia’s southern steppe provinces by planting forests. The afforestation efforts carried out in the Velikii Anadol’ forestry district in the eastern Ukraine were closely interwoven with debates about the potential climatic impact of deforestation – debates that were waged across Europe from the eighteenth century onwards and that are often considered by historians as crucial for the emergence of modern environmental consciousness. This chapter focuses on the changing character of experiments and observations carried out in Velikii Anadol’, and analyzes the ways in which they reflect a broader transformation of evidentiary standards in the nineteenth-century life sciences. It also explores the ways in which different scientific agendas were applied in the Russian frontier as part of attempts at agricultural colonization.
Education by observation: Students in research process The article argues for a new technology in teaching students of state and municipal management. The method is based on direct observation and description of management practices by students who lack any systematic research skills (the «naive observer» method). The authors ague that the use of this method allows to solve two types of problem at once: a pedagogical one and a scientific one. Students observe, and provide a description of, facts of the Russian provincial life without any interpretation whatsoever, which allows to obtain a picture of the social life that is closer to the reality than the one obtained by use of interpretational schemes of sociologists and journalists. It is only the latter picture that is currently used by the authorities as a basis for management decisions and for developing projects of social changes.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.
Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.