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## Об условиях $L^2$-диссипативности линеаризованных явных КГД-разностных схем для уравнений одномерной газовой динамики

Proceedings of the III International Conference in memory of V.I. Zubov "Stability and Control Processes (SCP 2015)".

For the quasi-gasdynamic system of equations, there holds the law of nondecreasing entropy. Difference methods based on this system have been successfully used in numerous applications and test gasdynamic computations. In theoretical terms, however, for standard spatial discretizations of this system, the nondecreasing entropy law does not hold exactly even in the one-dimensional case because of the mesh imbalance terms. For the quasi-gasdynamic equations, a new conservative spatial discretization is proposed for which the entropy balance equation has an appropriate form and the entropy production is guaranteed to be nonnegative (which also holds in the presence of body forces and heat sources). An important element of this discretization is that it makes use of nonstandard space-averaging techniques, including a nonlinear "logarithmic" averaging of the density and internal energy. The results hold on arbitrary nonuniform meshes

Data mining aims at finding interesting patterns from datasets, where “interesting” means reflecting intrinsic dependencies in the domain of interest rather than just in the dataset. Concept stability is a popular relevancy measure in FCA but its behaviour have never been studied on various datasets. In this paper we propose an approach to study this behaviour. Our approach is based on a comparison of stability computation on datasets produced by the same general population. Experimental results of this paper show that high stability of a concept in one dataset suggests that concepts with the same intent in other dataset drawn from the population have also high stability. Moreover, experiments shows some asymptotic behaviour of stability in such kind of experiments when dataset size increases.

There is a lot of usefulness measures of patterns in data mining. This paper is focused on the measures used in Formal Concept Analysis (FCA). In particular, concept stability is a popular relevancy measure in FCA. Experimental results of this paper show that high stability of a pattern in a given dataset derived from the general population suggests that the stability of that pattern is high in another dataset derived from the same population. At the second part of the paper, a new estimate of stability is introduced and studied. It es performance is evaluated experimentally. And it is shown that it is more efficient.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

This volume is dedicated to the 80th anniversary of academician V. M. Matrosov. The book contains reviews and original articles, which address the issues of development of the method of vector Lyapunov functions, questions of stability and stabilization control in mechanical systems, stability in differential games, the study of systems with multirate time and other. Articles prepared specially for this edition.

Using the Kepler problem as an example, one describes the Routh method for determination of steady motions and investigation of their stability.

Subsystem ASONIKA-T can operate in standalone mode or as part of ASONIKA in combination with other subsystems. Subsystem ASONIKA-T is designed to automate the modeling of thermal processes such as micro assemblies, radiators, heat-removing bases, hybrid-integrated modules, power cordwood structure, cabinets, racks, and atypical (arbitrary) structures electronics.

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.

A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.