Strict solutions to stochastic parabolic evolution equations in M-type 2 Banach spaces

We study a stochastic linear evolution equation $dX+A(t)Xdt=F(t)dt+ G(t)dw_t$ in a Banach space of M-type 2. We construct unique strict solutions to the equation on the basis of the theory of deterministic linear evolution equations. The abstract results are applied to stochastic diffusion equations.Comment: 27 pages, to appear in Funkcialaj Ekvacio

Searching for the squark flavor mixing in CP violations of Bs -> K+ K- and K0bar K0 decays

We study CP violations in the B_s-> K+K- and Bs->K0K0 decays in order to find the contribution of the supersymmetry, which comes from the gluino-squark mediated flavor changing current. We obtain the allowed region of the squark flavor mixing parameters by putting the experimental data, the mass difference Delta M_Bs, the CP violating phase phi_s in Bs to J/psi phi decay and the b to s gamma branching ratio. In addition to these data, we take into account the constraint from the asymmetry of B0->K+pi because the Bs->K+K- decay is related with the B0->K+pi- decay by replacing the spectator s with d. Under these constraints, we predict the magnitudes of the CP violation in the Bs->K+K- and Bs->K0K0 decays. The predicted region of the CP violation C_{K+K-} is strongly cut from the direct CP violation of barB0 to K-pi+, therefore, the deviation from the SM prediction of C_{K+K-} is not found. On the other hand, the CP violation S_{K+K-} is possibly deviated from the SM prediction considerably, in the region of 0.1- 0.5. Since the standard model predictions of C_{K0bar K0} and S_{K0bar K0} are very small, the squark contribution can be detectable in C_{K0bar K0} and S_{K0bar K0}. These magnitudes are expected in the region C_{K0bar K0}=-0.06-0.06 and S_{K0bar K0}=-0.5-0.3. More precise data of these CP violations provide us a crucial test for the gluino-squark mediated flavor changing current.Comment: 20 pages, 10 figures, discussions added, references added. arXiv admin note: substantial text overlap with arXiv:1307.037

Repeated Multimarket Contact with Private Monitoring: A Belief-Free Approach

This paper studies repeated games where two players play multiple duopolistic games simultaneously (multimarket contact). A key assumption is that each player receives a noisy and private signal about the other's actions (private monitoring or observation errors). There has been no game-theoretic support that multimarket contact facilitates collusion or not, in the sense that more collusive equilibria in terms of per-market profits exist than those under a benchmark case of one market. An equilibrium candidate under the benchmark case is belief-free strategies. We are the first to construct a non-trivial class of strategies that exhibits the effect of multimarket contact from the perspectives of simplicity and mild punishment. Strategies must be simple because firms in a cartel must coordinate each other with no communication. Punishment must be mild to an extent that it does not hurt even the minimum required profits in the cartel. We thus focus on two-state automaton strategies such that the players are cooperative in at least one market even when he or she punishes a traitor. Furthermore, we identify an additional condition (partial indifference), under which the collusive equilibrium yields the optimal payoff.Comment: Accepted for the 9th Intl. Symp. on Algorithmic Game Theory; An extended version was accepted at the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20

Simultaneous constraints on the growth of structure and cosmic expansion from the multipole power spectra of the SDSS DR7 LRG sample

The anisotropic galaxy clustering on large scales provides us with a unique opportunity to probe into the gravity theory through the redshift-space distortions (RSDs) and the Alcock-Paczynski effect. Using the multipole power spectra up to hexadecapole (ell=4), of the Luminous Red Galaxy (LRG) sample in the data release 7 (DR7) of the Sloan Digital Sky Survey II (SDSS-II), we obtain simultaneous constraints on the linear growth rate f, angular diameter distance D_A, and Hubble parameter H at redshift z = 0.3. For this purpose, we first extensively examine the validity of a theoretical model for the non-linear RSDs using mock subhalo catalogues from N-body simulations, which are constructed to match with the observed multipole power spectra. We show that the input cosmological parameters of the simulations can be recovered well within the error bars by comparing the multipole power spectra of our theoretical model and those of the mock subhalo catalogues. We also carefully examine systematic uncertainties in our analysis by testing the dependence on prior assumption of the theoretical model and the range of wavenumbers to be used in the fitting. These investigations validate that the theoretical model can be safely applied to the real data. Thus, our results from the SDSS DR7 LRG sample are robust including systematics of theoretical modeling; f(z = 0.3) sigma_8(z = 0.3) =0.49+-0.08(stat.)+-0.04(sys.), D_A (z = 0.3) =968+-42(stat.)+-17(sys.)[Mpc], H (z = 0.3) =81.7+-5.0(stat.)+-3.7(sys.)[km/s/Mpc]. We believe that our method to constrain the cosmological parameters using subhaloes catalogues will be useful for more refined samples like CMASS and LOWZ catalogues in the Baryon Oscillation Spectroscopic Survey in SDSS-III.Comment: accepted for publication in MNRA

EXPONENTIAL ATTRACTORS FOR NON-AUTONOMOUS DISSIPATIVE SYSTEM

In this paper we will introduce a version of exponential attractor for non-autonomous equations as a time dependent set with uniformly bounded finite fractal dimension which is positively invariant and attracts every bounded set at an exponential rate. This is a natural generalization of the existent notion for autonomous equations. A generation theorem will be proved under the assumption that the evolution operator is a compact perturbation of a contraction. In the second half of the paper, these results will be applied to some non-autonomous chemotaxis system

質量分析における光イオン化、精密質量測定などの新技術の保健衛生・環境分野への展開

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