### Book

## Сборник докладов шестой всероссийской научно-практической конференции «Имитационное моделирование. Теория и практика» (ИММОД-2013)

The monograph presents results by professor Dr. A. Shalumov’s Research School of Modeling, Information Technology and Automated Systems (Russia). The program, ASONIKA, developed by the school is reviewed here regarding reliability and quality of devices for simulation of electronics and chips during harmonic and random vibration, single and multiple impacts, linear acceleration and acoustic noise, and steady-state and transient thermal effects. Calculations are done for thermal stress during changes in temperature and power in time. Calculations are done for number of cycles to fatigue failure under mechanical loads as well as under cyclic thermal effects. Simulation results for reliability analysis are taken into account. Models, software interface, and simulation examples are presented.

For engineers and scientists involved in design automation of electronics.

It is difficult to imagine an enterprise, company, firm, an education organizations or organizations of health which does not deal with information systems. The openness and flexibility of the information systems provide a flexible and effective management. So it is necessary to adapt information system to new conditions being changed and to team up with other systems, with simulation system, for example. So it is possible change business processes, to execute their reengineering and to anticipate the conse-quences of any event and to take into account the different risks.

Nested Petri nets (NP-nets) are Petri nets with net tokens - an extension of high-level Petri nets for modeling active objects, mobility and dynamics in distributed systems. In this paper we present an algorithm for translating two-level NP-nets into behaviorally equivalent Colored Petri nets with the view of applying CPN methods and tools for nested Petri nets analysis. We prove, that the proposed translation preserves dynamic semantics in terms of bisimulation equivalence.

Financial markets have always been attractive as a means of increasing one's wealth, and those who make accurate predictions take the prize. Forecasting models such as linear ones are simple to compute, however, they give rough approximations of the underlying relationships in the data, thus, producing poor forecasts. The solution to this issue could be the nonlinear models which try to fit the data and display the relationships with higher accuracy. Previous research seems to prove this statement from the statistician's point of view which might be of little use for an investor. Therefore, the focus of this paper is on the comparison of three types of models (nonlinear: ANN, STAR, and linear: AR) in terms of financial performance. Our research is based on the initial code for GAUSS and papers by Dick van Dijk. The data used is the monthly S&P 500 Index values from 1970 to 2012 provided by the Robert Shiller's website. Forecasting index changes begins at 1995 and ends in 2012 providing up-to-date results for 14 model specifications. The best model proves to be the flexible ANN, beating the linear AR in the majority of cases, leaving the underperforming heavy-parameterized STAR model behind. Thus, it is evident that the more flexible nonlinear models outperform the heavily parameterized ones as well as linear models for the S&P 500 Index. The introduced type of performance evaluation has a more comprehensible application to the financial market analysis.

In the paper integrated information systems for corporate planning and budgeting are considered. Four groups of practical tasks exceeding the bounds of typical functionality of special-purpose planning and budgeting information systems are allocated. Several classes of information systems (simulation, statistical analysis, financial analysis and modeling, group decision making, business intelligence), which may provide the completeness of corporate planning and budgeting are denoted as solutions complementary to special-purpose planning and budgeting systems.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.

The problem of minimizing the root mean square deviation of a uniform string with clamped ends from an equilibrium position is investigated. It is assumed that the initial conditions are specified and the ends of the string are clamped. The Fourier method is used, which enables the control problem with a partial differential equation to be reduced to a control problem with a denumerable system of ordinary differential equations. For the optimal control problem in the l2 space obtained, it is proved that the optimal synthesis contains singular trajectories and chattering trajectories. For the initial problem of the optimal control of the vibrations of a string it is also proved that there is a unique solution for which the optimal control has a denumerable number of switchings in a finite time interval.

For a class of optimal control problems and Hamiltonian systems generated by these problems in the space *l *2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space *l *2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.

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.

In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.