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## Three-dimensional simulation of 2011 East Japan-off Pacific coast earthquake tsunami induced vortex flows in the Oarai port

Three-dimensional simulation of 2011 East Japan-off Pacific coast earthquake tsunami induced vortex flows in the Oarai port.

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.

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.

Data from a field survey of the 2011 Tohoku-oki tsunami in the Sanriku area of Japan is used to plot the distribution function of runup heights along the coast. It is shown that the distribution function can be approximated by a theoretical log-normal curve. The characteristics of the distribution functions of the 2011 event are compared with data from two previous catastrophic tsunamis (1896 and 1933) that occurred in almost the same region. The number of observations during the last tsunami is very large, which provides an opportunity to revise the conception of the distribution of tsunami wave heights and the relationship between statistical characteristics and the number of observed runup heights suggested by Kajiura (1983) based on a small amount of data on previous tsunamis. The distribution function of the 2011 event demonstrates the sensitivity to the number of measurements (many of them cannot be considered independent measurements) and can be used to determine the characteristic scale of the coast, which corresponds to the statistical independence of observed wave heights.

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.

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.