Decomposition of Games: Some Strategic Considerations

Orthogonal direct-sum decompositions of finite games into potential, harmonic and nonstrategic components exist in the literature. In this paper we study the issue of decomposing games that are strategically equivalent from a game-theoretical point of view, for instance games obtained via transformations such as duplications of strategies or positive affine mappings of the payoffs. We show the need to define classes of decompositions to achieve commutativity of game transformations and decompositions.

Study of Zero Temperature Ground State Properties of the Repulsive Bose-Einstein Condensate in an Anharmonic Trap

The zero-temperature ground state properties of experimental 87Rb condensate are studied in a harmonic plus quartic trap [ V(r) = ½mω2r2 + λr4 ]. The anharmonic parameter (λ) is slowly tuned from harmonic to anharmonic. For each choice of λ, the many-particle Schrödinger equation is solved using the potential harmonic expansion method and determines the lowest effective many-body potential. We utilize the correlated two-body basis function, which keeps all possible two-body correlations. The use of van der Waals interaction gives realistic pictures. We calculate kinetic energy, trapping potential energy, interaction energy, and total ground state energy of the condensate in this confining potential, modelled experimentally. The motivation of the present study is to investigate the crucial dependency of the properties of an interacting quantum many-body system on λ. The average size of the condensate has also been calculated to observe how the stability of repulsive condensate depends on anharmonicity. In particular, our calculation presents a clear physical picture of the repulsive condensate in an anharmonic trap.

Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker-Planck equation

Based on the idea of variable separation, the time-fractional Fokker-Planck equation with external force field is studied by using the property of Mittag-Leffler function and some special algorithm skills. In the cases of various external potential functions such as linear potential, harmonic potential, logarithmic potential, exponential potential, and quartic potential, exact solutions and dynamical properties of the above mentioned equation is investigated. The some interesting dynamical behaviors and phenomena are discovered. The profiles of some representative exact solutions are illustrated by 3D-graphs.

Harmonic Analysis and Simulation of Medium Frequency Furnace

Basic structure and operational principle of medium frequency furnace (MFF) are introduced in this paper. The characteristics of harmonic currents produced by MFF are analyzed theoretically. A harmonic analysis simulation model for MFF with 12-pulse reciter based on Matlab/Simulink is presented. The validity of it is proved for the simulation harmonic currents accord to the theoretical anticipation. This model could be used to predict the harmonic of MFF not in operation. Based on this model, potential harmonic pollution of a new steel plant is studied by simulation with Matlab/ Simulink.