Semiclassical Limits of Extended Racah Coefficients

We explore the geometry and asymptotics of extended Racah coeffecients. The extension is shown to have a simple relationship to the Racah coefficients for the positive discrete unitary representation series of SU(1,1) which is explicitly defined. Moreover, it is found that this extension may be geometrically identified with two types of Lorentzian tetrahedra for which all the faces are timelike. The asymptotic formulae derived for the extension are found to have a similar form to the standard Ponzano-Regge asymptotic formulae for the SU(2) 6j symbol and so should be viable for use in a state sum for three dimensional Lorentzian quantum gravity.Comment: Latex2e - 26 pages, 6 figures. Uses AMS-fonts, AMS-LaTeX, epsf.tex and texdraw. Revised version with improved clarity and additional result

Global continuous solutions to diagonalizable hyperbolic systems with large and monotone data

In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show in particular cases some uniqueness results. We also remark that these results cover the case of systems which are hyperbolic but not strictly hyperbolic. Physically, this kind of diagonalizable hyperbolic systems appears naturally in the modelling of the dynamics of dislocation densities

On the Satisfiability Threshold and Clustering of Solutions of Random 3-SAT Formulas

We study the structure of satisfying assignments of a random 3-SAT formula. In particular, we show that a random formula of density 4.453 or higher almost surely has no non-trivial "core" assignments. Core assignments are certain partial assignments that can be extended to satisfying assignments, and have been studied recently in connection with the Survey Propagation heuristic for random SAT. Their existence implies the presence of clusters of solutions, and they have been shown to exist with high probability below the satisfiability threshold for k-SAT with k>8, by Achlioptas and Ricci-Tersenghi, STOC 2006. Our result implies that either this does not hold for 3-SAT or the threshold density for satisfiability in 3-SAT lies below 4.453. The main technical tool that we use is a novel simple application of the first moment method

Measurement of Neutrino-Electron Scattering Cross-Section with a CsI(Tl) Scintillating Crystal Array at the Kuo-Sheng Nuclear Power Reactor

The $\bar{\nu}_{e}-e^{-}$ elastic scattering cross-section was measured with a CsI(Tl) scintillating crystal array having a total mass of 187kg. The detector was exposed to an average reactor $\bar{\nu}_{e}$ flux of $\rm{6.4\times 10^{12} ~ cm^{-2}s^{-1}}$ at the Kuo-Sheng Nuclear Power Station. The experimental design, conceptual merits, detector hardware, data analysis and background understanding of the experiment are presented. Using 29882/7369 kg-days of Reactor ON/OFF data, the Standard Model(SM) electroweak interaction was probed at the squared 4-momentum transfer range of $\rm{Q^2 \sim 3 \times 10^{-6} ~ GeV^2}$. The ratio of experimental to SM cross-sections of $\xi =[ 1.08 \pm 0.21(stat)\pm 0.16(sys)]$ was measured. Constraints on the electroweak parameters $(g_V , g_A)$ were placed, corresponding to a weak mixing angle measurement of \s2tw = 0.251 \pm 0.031({\it stat}) \pm 0.024({\it sys}) . Destructive interference in the SM \nuebar -e process was verified. Bounds on anomalous neutrino electromagnetic properties were placed: neutrino magnetic moment at \mu_{\nuebar}< 2.2 \times 10^{-10} \mu_{\rm B} and the neutrino charge radius at -2.1 \times 10^{-32} ~{\rm cm^{2}} < \nuchrad < 3.3 \times 10^{-32} ~{\rm cm^{2}}, both at 90% confidence level.Comment: 18 Figures, 7 Tables; published version as V2 with minor revision from V