The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl

Super-acceleration on the Brane by Energy Flow from the Bulk

We consider a brane cosmological model with energy exchange between brane and bulk. Parameterizing the energy exchange term by the scale factor and Hubble parameter, we are able to exactly solve the modified Friedmann equation on the brane. In this model, the equation of state for the effective dark energy has a transition behavior changing from $w_{de}^{eff}>-1$ to $w_{de}^{eff}<-1$, while the equation of state for the dark energy on the brane has $w>-1$. Fitting data from type Ia supernova, Sloan Digital Sky Survey and Wilkinson Microwave Anisotropy Probe, our universe is predicted now in the state of super-acceleration with $w_{de0}^{eff}=-1.21$.Comment: Revtex, 11 pages including 2 figures,v2: tpos fixed, references added, to appear in JCA

Bond and charge density waves in the isotropic interacting two-dimensional quarter-filled band and the insulating state proximate to organic superconductivity

We report two surprising results regarding the nature of the spatial broken symmetries in the two-dimensional (2D), quarter-filled band with strong electron-electron interactions. First, in direct contradiction to the predictions of one-electron theory, we find a coexisting ``bond-order and charge density wave'' (BCDW) insulating ground state in the 2D rectangular lattice for all anisotropies, including the isotropic limit. Second, we find that the BCDW further coexists with a spin-density wave (SDW) in the range of large anisotropy. Further, in contrast to the interacting half-filled band, in the interacting quarter-filled band there are two transitions: first, a similar singlet-to-AFM/SDW transition for large anisotropy and second, an AFM/SDW-to-singlet transition at smaller anisotropy. We discuss how these theoretical results apply to the insulating states that are proximate to the superconducting states of 2:1 cationic charge-transfer solids (CTS). An important consequence of this work is the suggestion that organic superconductivity is related to the proximate Coulomb-induced BCDW, with the SDW that coexists for large anisotropies being also a consequence of the BCDW, rather than the driver of superconductivity.Comment: 29 pages, 18 eps figures. Revised with new appendices; to appear in Phys. Rev. B 62, Nov 15, 200

Tunnelling Methods and Hawking's radiation: achievements and prospects

The aim of this work is to review the tunnelling method as an alternative description of the quantum radiation from black holes and cosmological horizons. The method is first formulated and discussed for the case of stationary black holes, then a foundation is provided in terms of analytic continuation throughout complex space-time. The two principal implementations of the tunnelling approach, which are the null geodesic method and the Hamilton-Jacobi method, are shown to be equivalent in the stationary case. The Hamilton-Jacobi method is then extended to cover spherically symmetric dynamical black holes, cosmological horizons and naked singularities. Prospects and achievements are discussed in the conclusions.Comment: Topical Review commissioned and accepted for publication by "Classical and Quantum Gravity". 101 pages; 6 figure

Improved Measurement of the Electroweak Penguin Process B->Xsll

We present an improved measurement of the branching fraction for the electroweak penguin process B->Xsll, where l is an electron or a muon and Xs is a hadronic system containing an s-quark. The measurement is based on a sample of 152*10^6 Upsilon(4S) -> BB events collected with the Belle detector at the KEKB energy asymmetric e+e- collider. The Xs hadronic system is reconstructed from one K^{+-} or K^{0}_{S} and up to four pions, where at most one pion can be neutral. Averaging over both lepton flavors, the inclusive branching fraction is measured to be Br(B->Xsll)=(4.11+-0.83(stat)+0.85-0.81(syst))*10^{-6} for M_ll > 0.2GeV/c2.Comment: 16 pages 5 figures Latex, Submitted to Physical Review

Observation of B0→D+D−B^0 \to D^+ D^-, B−→D0D−B^- \to D^0 D^- and B−→D0D∗−B^- \to D^0 D^{*-} decays

We report the first observation of the decay modes $B^0 \to D^+ D^-$, $B^- \to D^0 D^-$ and $B^- \to D^0 D^{*-}$ based on 152 $\times$ 10$^6$ $B\bar{B}$ events collected at KEKB. The branching fractions of $B^0 \to D^+ D^-$, $B^- \to D^0 D^-$ and $B^- \to D^0 D^{*-}$ are found to be $(3.21 \pm 0.57 \pm 0.48) \times 10^{-4}$, $(5.62 \pm 0.82 \pm 0.65) \times 10^{-4}$ and $(4.59 \pm 0.72 \pm 0.56) \times 10^{-4}$, respectively. Charge asymmetries in the $B^- \to D^0 D^-$ and $B^- \to D^0 D^{*-}$ channels are consistent with zero.Comment: 9 pages, 2 figures, KEK Preprint 2004-99, Belle Prerpint 2005-3, submitted to PR

Measurement of Azimuthal Asymmetries in Inclusive Production of Hadron Pairs in e+e- Annihilation at Belle

The Collins effect connects transverse quark spin with a measurable azimuthal dependence in the yield of hadronic fragments around the quark's momentum vector. Using two different reconstruction methods we observe statistically significant azimuthal asymmetries for charged pion pairs in e+e- annihilation at a center-of-mass energy of 10.52 GeV, which can be attributed to a transverse polarization of the primordial quarks. The measurement was performed using a sample of 79 million hadronic events collected with the Belle detector.Comment: 6 pages, 4 figure

Observation of B0->pi0pi0

We report the first observation of the decay B0->pi0pi0, using a 253/fb data sample collected at the Upsilon(4S) resonance with the Belle detector at the KEKB e+e- collider. The measured branching fraction is BF(B0->pi0pi0) = {2.32 +0.4-0.5(stat) +0.2-0.3(syst)} x 10^-6, with a significance of 5.8 standard deviations including systematic uncertainties. We also make the first measurement of the direct CP violating asymmetry in this mode.Comment: 6 pages, 2 figures, submitted to ICHEP04, Beijing and Physical Review Letters. v2: a possible pile-up background is checked and a systematic error for it is include