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## Multistability in dynamics of an encapsulated bubble contrast agent: coexistence of three attractors

In this work we discuss complex dynamics arising in a model describing behaviorof an encapsulated bubble contrast agent oscillating close to an elastic wall. We demonstratepresence of three coexisting attractors in the system. We propose an efficient numericalprocedure based on the continuation method that can be used to locate the area of coexistenceof these attractors in the parameters space. We provide area of coexistence of three attractorsobtained by means of the proposed procedure.

In this paper, the authors apply a continuous-time stochastic process model developed by Shiryaev and Zhutlukhin for optimally stopping random price processes that appear to be bubbles, defined as price increases that are largely based on the expectation of higher and higher future prices. Futures traders, such as George Soros, attempt to trade such markets, trying to exit near the peak from a starting long position. The model applies equally well to the question of when to enter and exit a short position. In this article, the authors test the model in two technology markets. These include the price of Apple computer stock from various times in 2009–2012 after the local low of March 6, 2009, plus a market in which the generally very successful bubble trader George Soros lost money by shorting the NASDAQ-100 stock index too soon in 2000. The model provides good exit points in both situations; these would have been profitable to speculators who employed the model.

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.

Game-theoretic model of Minsky’s tension is proposed. This model illustrates logic of actions for potential sellers in the context of «animal spirit» of confidence realization and herding behavior for situation when sufficient mass of players has doubts about further market price rise in a period from the end of euphoria until the beginning of panic. The logic of behavior for potential sellers and features of the way «animal spirit» of confidence influences them are revealed.

We study the land and stock markets in Japan circa 1990 and in 2013. While the Nikkei stock average in the late 1980s and its (Formula presented.) % crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the land market. The crash in the Nikkei which started on the first trading day of 1990 was predictable in April 1989 using the bond-stock earnings yield model which signalled a crash but not its exact moment. We show that it was possible to use the changepoint detection model based solely on price movements for profitable exits of long positions both circa 1990 and in 2013. © 2015 Taylor & Francis.

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.