Geometric Approach to Lyapunov Analysis in Hamiltonian Dynamics

As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function. To separate out these two directions and to apply Lyapunov analysis effectively in directions for which Lyapunov exponents are not trivial, a geometric method is proposed for natural Hamiltonian systems, in particular. In this geometric method, Hamiltonian flows of a natural Hamiltonian system are regarded as geodesic flows on the cotangent bundle of a Riemannian manifold with a suitable metric. Stability/instability of the geodesic flows is then analyzed by linearized equations of motion which are related to the Jacobi equations on the Riemannian manifold. On some geometric setting on the cotangent bundle, it is shown that along a geodesic flow in question, there exist Lyapunov vectors such that two of them are in the two marginal directions and the others orthogonal to the marginal directions. It is also pointed out that Lyapunov vectors with such properties can not be obtained in general by the usual method which uses linearized Hamilton's equations of motion. Furthermore, it is observed from numerical calculation for a model system that Lyapunov exponents calculated in both methods, geometric and usual, coincide with each other, independently of the choice of the methods.Comment: 22 pages, 14 figures, REVTeX

Human PSF binds to RAD51 and modulates its homologous-pairing and strand-exchange activities

RAD51, a eukaryotic recombinase, catalyzes homologous-pairing and strand-exchange reactions, which are essential steps in homologous recombination and recombinational repair of double strand breaks. On the other hand, human PSF was originally identified as a component of spliceosomes, and its multiple functions in RNA processing, transcription and DNA recombination were subsequently revealed. In the present study, we found that PSF directly interacted with RAD51. PSF significantly enhanced RAD51-mediated homologous pairing and strand exchange at low RAD51 concentrations; however, in contrast, it inhibited these RAD51-mediated recombination reactions at the optimal RAD51 concentration. Deletion analyses revealed that the N-terminal region of PSF possessed the RAD51- and DNA-binding activities, but the central region containing the RNA-recognition motifs bound neither RAD51 nor DNA. These results suggest that PSF may have dual functions in homologous recombination and RNA processing through its N-terminal and central regions, respectively

Measurement of the CP Violation Parameter sin(2phi_1) in B^0_d Meson Decays

We present a measurement of the Standard Model CP violation parameter sin(2phi_1) based on a 10.5 fb^{-1} data sample collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric e+e- collider. One neutral B meson is reconstructed in the J/psi K_S, psi(2S) K_S, chi_{c1} K_S, eta_c K_S, J/psi K_L or J/psi pi^0 CP-eigenstate decay channel and the flavor of the accompanying B meson is identified from its charged particle decay products. From the asymmetry in the distribution of the time interval between the two B-meson decay points, we determine sin(2phi_1) = 0.58 +0.32-0.34 (stat) +0.09-0.10 (syst).Comment: LaTex, 13 pages, 3 figures, submitted to P.R.

Measurement of B0d - B0d-bar mixing rate from the time evolution of dilepton events at the Upsilon(4S)

We report a determination of the B0d - B0d-bar mixing parameter Delta-m_d based on the time evolution of dilepton yields in Upsilon(4S) decays. The measurement is based on a 5.9 /fb data sample collected by the Belle detector at KEKB. The proper-time difference distributions for same-sign and opposite-sign dilepton events are simultaneously fitted to an expression containing Delta-m_d as a free parameter. Using both muons and electrons, we obtain Delta-m_d = 0.463 +- 0.008(stat.) +- 0.016(sys.) ps^{-1} This is the first determination of Delta-m_d from time evolution measurements at the Upsilon(4S). We also place limits on possible CPT violations.Comment: 12 pages, 2 figure

A Measurement of the Branching Fraction for the Inclusive B --> X(s) gamma Decays with the Belle Detector

We have measured the branching fraction of the inclusive radiative B meson decay B --> X(s) gamma to be Br(B->X(s)gamma)=(3.36 +/- 0.53(stat) +/- 0.42(sys) +0.50-0.54(th)) x 10^{-4}. The result is based on a sample of 6.07 x 10^6 BBbar events collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric e^+e^- storage ring.Comment: 14 pages, 6 Postsript figures, uses elsart.cl

Measurement of the Branching Fraction for B->eta' K and Search for B->eta'pi+

We report measurements for two-body charmless B decays with an eta' meson in the final state. Using 11.1X10^6 BBbar pairs collected with the Belle detector, we find BF(B^+ ->eta'K^+)=(79^+12_-11 +-9)x10^-6 and BF(B^0 -> eta'K^0)=(55^+19_-16 +-8)x10^-6, where the first and second errors are statistical and systematic, respectively. No signal is observed in the mode B^+ -> eta' pi^+, and we set a 90% confidence level upper limit of BF(B^+-> eta'pi^+) eta'K^+- decays is investigated and a limit at 90% confidence level of -0.20<Acp<0.32 is obtained.Comment: Submitted to Physics Letters

Measurement of Inclusive Production of Neutral Pions from Upsilon(4S) Decays

Using the Belle detector operating at the KEKB e+e- storage ring, we have measured the mean multiplicity and the momentum spectrum of neutral pions from the decays of the Upsilon(4S) resonance. We measure a mean of 4.70 +/- 0.04 +/- 0.22 neutral pions per Upsilon(4S) decay.Comment: 15 pages, 4 figs. Submitted to Phys.Rev.

Search for Direct CP Violation in B -> K pi Decays

We search for direct CP violation in flavor specific B -> K pi decays by measuring the rate asymmetry between charge conjugate modes. The search is performed on a data sample of 11.1 million B B bar events recorded on the Upsilon(4S) resonance by the Belle experiment at KEKB. We measure 90% confidence intervals in the partial rate asymmetry A_CP of -0.25 < A_CP(K-/+ pi+/-) < 0.37, -0.40 < A_CP(K-/+ pi^0) < 0.36, and -0.53 < A_CP(K^0 pi-/+) < 0.82. By combining the K-/+ pi+/- and K-/+ pi^0 final states, we conclude that -0.22 < A_CP[K-/+(pi+/- + pi^0)] < 0.25 at the 90% confidence level.Comment: Submitted to PRD Rapid Communication