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## Optimization and applications (OPTIMA-2014)

Proceedings include abstracts of reports presented at the V International Cjnference on Optimization Methods and Applications "Optimization and applications" (OPTIMA-2014) held in Petrovac, Montenegro, September 28 - October 4, 2014.

We consider a particular case of railway problems, namely, the optimal scheduling of the train operation by a double-track railroad when one of the segments is under repair works.Application of the dynamic programming is effective to solve this problem. In this paper we suggest an exact algorithm.

We consider the problem of trainings planning on ISS. Shown that the problem is a combination of a k Partition Problem and an Assignment Problem. NP-compleeteness is proofed. A heuristic and an exact algorithms are proposed.

We consider the problem of planning the cousmonaut's time in ISS with given set of tasks, time planning horizon and load constraints. Shown that the problem is NP-hard in a strong sense. The heuristic algorithm was proposed. Proved that proposed algorithm is exact for problem with requirement of performing all tasks. Program C++ was written and algorithm's work was qualitatively analyzed.

This article examines the actual problems of the implementation of institute of outsourcing in Russian legal system. The authors focus on such issues as the legal nature of the contract of outsourcing, correlation of outsourcing with related legal categories such as outstaffing, borrowed labor, paid service contract and employment contract. The authors try to avoid extreme positions considering both advantages and disadvantages of outsourcing from the point of view of the organization – customer and possible risks for employees of company – customer and company – outsourcer indicated that the most of problems related with breach of rights and legal interests of employees by transfer to the outsourcing caused by not only legal nature of the outsourcing but rather gaps in the civil and employment law. Based on the analysis of legislation, court practice and legal doctrine authors offer original solutions to existing problems.

Methods of the steganography are characterized by such efficiency rates as invisibility, robustness and capacity. There is considered the maximum capacity support of the information embedding into the DCT-domain. It is investigated the known algorithm that realizes the adaptive information embedding into the digital images frequency domain. The adaptivity is reached due to the image partition into the unequal blocks using a quad-tree. There is received the improved modification of the algorithm based on the reference point variation in case of the image partition into the blocks. The received modification allows to provide the better invisibility at the same capacity.

This paper presents a brief description of a method of automated parametric and structural optimization of temperature control systems of electronic equipment using criteria of solution effectiveness evaluation. Methods and models, that allow automating the process of choosing both thermal regulation (temperature control) tools for electronic equipment and their parameters, are proposed. The problems of formalization of temperature control means selection criteria for electronic components through the cost coefficients, specified by the expert, are considered. The criteria for optimal design allow estimating the effectiveness of heat balance diagram and temperature control means, as well as their parameters. The optimization algorithm, proposed in the article, considers a variety of different continuous states of variable heat balance diagram that depends on the thermal model temperature control means and their parameters. At the same time, temperature control means, that have the greatest impact on the thermal model at the next step with taking into account the cost function, are selected. As an example, the optimal synthesis of temperature control means of a typical electronic equipment block with taking into account the necessity to assess the feasibility of using aluminum heat sinks with electronic components as compared to heat pipes was made.

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 paper presents a description of the method of automated parametric and structural optimization of systems for ensuring thermal regime of microelectronic devices using modern information technologies.

Distant learning has weaknesses related to missing tutor and kind of autodidacticism of the process, which may cause learner’s frustration in uncertain situations and force him or her to drop the learning course. Inasmuch as it is very important to help learner to select a set of needed courses, the article deals with the task of forming the optimal individual educational trajectory of a learner when studying massive open online courses on the basis of knowledge and skills of the learner, knowledge and skills he or she wants to acquire and prerequisite and postrequisite skills and knowledge of available courses. The mathematical model is proposed, and problems of integer programming are formulated, which allow to find the optimal individual educational trajectory for different preferences of the learner

This book addresses the optimization of taxation systems, a topic currently being explored by scholars all over the world. It puts forward a critical opinion on the problem and offers an original approach to solving it – through informatization. The target audience of the book includes not only scholars and experts who professionally deal with taxation optimization issues, but also representatives of public authorities, and the general public. The book offers sound and practical solutions for the informatization-based optimization of taxation systems, and its conclusions and recommendations could be used in the management of tax systems for modern economic systems and in taxation optimization for specific economic subjects – individuals and organizations alike – , ensuring a broad range of practical applications.

The task is to sharply reduce the complexity of analysis, multivariate analysis and parametric optimization of linear and linearized equivalent electrical circuits. The source of such schemes are not only linear electronic circuits, but also circuits formed on the basis of artificial electrical analogies. They can be formed on the basis of finite element methods and finite difference methods used in solving partial differential equations. The reduction in the complexity of computations is carried out by formal methods of transforming the model into a macromodel, which reflects only the input - output type relations of the original model. The e ssence of the work lies in the formal transformation of the model of a linear or linearized equivalent electrical circuit, formed using artificial electrical analogies methods, into a macromodel, according to which the same output characteristics can be calculated with the same accuracy but with increased speed by several orders of magnitude. Algorithms for such transformations are given. Using a macromodel, one can calculate static characteristics, frequency characteristics, zeros and poles of system functions, dynamic characteristics, eigenvalues, and vectors of a macromodel matrix, which make it possible to determine the stability and stability margin of the original circuit using the first А.М. Lyapunov method, its resonant eigenfrequencies and the duration of the transition process, as well as partial derivatives of the above characteristics for a small number of variable circuit parameters to replace the optimization of the circuit with the methods of the 1st order with its optimization by the macro model. In addition, macromodels can be used to create a new element, constructional, and technological base for design. Macromodel can serve as an element of a model of a higher hierarchical level. Block hierarchical process of macromodelling is possible.

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.