On Cores and Stable Sets for Fuzzy Games

AMS classifications: 90D12; 03E72;cooperative games;decision making;fuzzy games

Compromising in Partition Function Form Games and Cooperation in Perfect Extensive Form

In this paper reasonable payoff intervals for players in a game in partition function form (p.f.f.game) are introduced and used to define the notion of compromisable p.f.f. game.For a compromisable p.f.f. game a compromise value is defined for which an axiomatic characterization is provided.Also a generic subclass of games in extensive form of perfect information without chance moves is introduced.For this class of perfect extensive form games there is a natural credible way to define a p.f.f. game if the players consider cooperation.It turns out that the p.f.f. games obtained in this way are compromisable.game theory

A deformed QRPA formalism for single and two-neutrino double beta decay

We use a deformed QRPA formalism to describe simultaneously the energy distributions of the single beta Gamow-Teller strength and the two-neutrino double beta decay matrix elements. Calculations are performed in a series of double beta decay partners with A = 48, 76, 82, 96, 100, 116, 128, 130, 136 and 150, using deformed Woods-Saxon potentials and deformed Skyrme Hartree-Fock mean fields. The formalism includes a quasiparticle deformed basis and residual spin-isospin forces in the particle-hole and particle-particle channels. We discuss the sensitivity of the parent and daughter Gamow-Teller strength distributions in single beta decay, as well as the sensitivity of the double beta decay matrix elements to the deformed mean field and to the residual interactions. Nuclear deformation is found to be a mechanism of suppression of the two-neutrino double beta decay. The double beta decay matrix elements are found to have maximum values for about equal deformations of parent and daughter nuclei. They decrease rapidly when differences in deformations increase. We remark the importance of a proper simultaneous description of both double beta decay and single Gamow-Teller strength distributions. Finally, we conclude that for further progress in the field it would be useful to improve and complete the experimental information on the studied Gamow-Teller strengths and nuclear deformations.Comment: 33 pages, 19 figures. To be published in Phys. Rev.

Precise measurements of electron and hole g-factors of single quantum dots by using nuclear field

We demonstrated the cancellation of the external magnetic field by the nuclear field at one edge of the nuclear polarization bistability in single InAlAs quantum dots. The cancellation for the electron Zeeman splitting gives the precise value of the hole g-factor. By combining with the exciton g-factor that is obtained from the Zeeman splitting for linearly polarized excitation, the magnitude and sign of the electron and hole g-factors in the growth direction are evaluated.Comment: 3 pages, 2 figure

The Effect of Poloidal Magnetic Field on Type I Planetary Migration: Significance of Magnetic Resonance

We study the effect of poloidal magnetic field on type I planetary migration by linear perturbation analysis in the shearing-sheet approximation and the analytic results are compared with numerical calculations. In contrast to the unmagnetized case, the basic equations that describe the wake due to the planet in the disk allow magnetic resonances at which density perturbation diverges. In order to simplify the problem, we consider the case without magneto-rotational instability. We perform two sets of analyses: two-dimensional and three-dimensional. In two-dimensional analysis, we find the generalization of the torque formula previously known in unmagnetized case. In three-dimensional calculations, we focus on the disk with very strong magnetic field and derive a new analytic formula for the torque exerted on the planet. We find that when Alfven velocity is much larger than sound speed, two-dimensional torque is suppressed and three-dimensional modes dominate, in contrast to the unmagnetized case.Comment: 33 pages, 10 figures, typos corrected, discussion added, reference added, Accepted for publication in Ap

Fuzzy Clan Games and Bi-monotonic Allocation Rules

Clan game;Big boss game;Core;Decision making;Fuzzy coalition;Fuzzy game;Monotonic allocation rule

Phase transitions in systems with two species of molecular motors

Systems with two species of active molecular motors moving on (cytoskeletal) filaments into opposite directions are studied theoretically using driven lattice gas models. The motors can unbind from and rebind to the filaments. Two motors are more likely to bind on adjacent filament sites if they belong to the same species. These systems exhibit (i) Continuous phase transitions towards states with spontaneously broken symmetry, where one motor species is largely excluded from the filament, (ii) Hysteresis of the total current upon varying the relative concentrations of the two motor species, and (iii) Coexistence of traffic lanes with opposite directionality in multi-filament systems. These theoretical predictions should be experimentally accessible.Comment: 7 pages, 4 figures, epl style (.cls-file included), to appear in Europhys. Lett. (http://www.edpsciences.org/epl

Multi-antikaonic nuclei in the relativistic mean-field theory

Properties of multi-antikaonic nuclei (MKN), where several numbers of $K^-$ mesons are bound, are studied in the relativistic mean-field model, combined with chiral dynamics for kaonic part of the thermodynamic potential. The density profiles for nucleons and $K^-$ mesons, the single particle energy of the $K^-$ mesons, and binding energy of the MKN are obtained. The effects of the $\bar K-\bar K$ interactions on these quantities are discussed in comparison with other meson ($\sigma$, $\omega$, and $\rho$)-exchange models. It is shown that the $\bar K-\bar K$ interactions originate from two contributions: One is the contact interaction between antikaons inherent in chiral symmetry, and the other is the one generated through coupling between the $K^-$ and meson mean fields. Both effects of the $\bar K-\bar K$ repulsive interactions become large on the ground state properties of the MKN as the number of the embedded $K^-$ mesons increases. A relation between the multi-antikaonic nuclei and kaon condensation in infinite and uniform matter is mentioned.Comment: 27 pages, 13 figure

Trapping Low-mass Planets at the Inner Edge of the Protostellar Disk

The formation of multiple close-in low-mass exoplanets is still a mystery. The challenge is to build a system wherein the outermost planet is beyond 0.2 au from the star. Here, we investigate how the prescription for type I planet migration affects the ability to trap multiple planets in a resonant chain near the inner edge of the protostellar disk. A sharp edge modeled as a hyperbolic tangent function coupled with supersonic corrections to the classical type I migration torques results in the innermost planets being pushed inside the cavity through resonant interaction with farther planets because migration is starward at slightly supersonic eccentricities. Planets below a few Earth masses are generally trapped in a resonant chain with the outermost planet near the disk edge, but long-Term stability is not guaranteed. For more massive planets the migration is so fast that the eccentricity of the innermost resonant pair is excited to highly supersonic levels due to decreased damping on the innermost planet as it is pushed inside the cavity; collisions frequently occur, and the system consists of one or two intermediate-mass planets residing closer to the star than the disk's inner edge. We found a neat pileup of resonant planets outside the disk edge only if the corotation torque does not rapidly diminish at high eccentricity. We call for detailed studies on planet migration near the disk's inner edge, which is still uncertain, and for an improved understanding of eccentricity damping and disk torques in the supersonic regime.</p