Twisted Hecke L-values and period polynomials

Let $f_1,...,f_d$ be an orthogonal basis for the space of cusp forms of even weight $2k$ on $\Gamma_0(N)$. Let $L(f_i,s)$ and $L(f_i,\chi,s)$ denote the $L$-function of $f_i$ and its twist by a Dirichlet character $\chi$, respectively. In this note, we obtain a ``trace formula'' for the values $L(f_i,\chi,m)\overline{L(f_i,n)}$ at integers $m$ and $n$ with $0<m,n<2k$ and proper parity. In the case N=1 or N=2, the formula gives us a convenient way to evaluate precisly the value of the ratio $L(f,\chi,m)/L(f,n)$ for a Hecke eigenform $f$.Comment: 20 page

The Effect of Hydrogen Content on Ballistic Transport Behaviors in the Ni-Nb-Zr-H Glassy Alloys

The electronic transport behaviors of (Ni0.39Nb0.25Zr0.35)100−xHx (0 ≤ x < 23.5) glassy alloys with subnanostructural icosahedral Zr5Nb5Ni3 clusters have been studied as a function of hydrogen content. These alloys show semiconducting, electric current-induced voltage (Coulomb) oscillation and ballistic transport behaviors. Coulomb oscillation and ballistic transport occur at hydrogen contents between 6.7 and 13.5 at% and between 13.5 and 21.2 at%, respectively. These results suggest that the localization effect of hydrogen in the clusters plays an important role in various electron transport phenomena

Estimating a preference-based index from the Japanese SF-36

Objective: The main objective of the study was to estimate a preference-bascd Short Form (SF)-6D index from the SF-36 for Japan and compare it with the UK results. Study Design and Setting: The SF-6D was translated into Japanese. Two hundred and forty-nine health states defined by this version of the SF-6D were then valued by a representative sample of 600 members of the Japanese general population using standard gamble (SG). These health-state values were modeled using classical parametric random-effect methods with individual-level data and ordinary least squares (OLS) on mean health-state values, together with a new nonparametric approach using Bayesian methods of estimation. Results: All parametric models estimated on Japanese data were found to perform less well than their UK counterparts in terms of poorer goodness of fit, more inconsistencies, larger prediction errors and bias, and evidence of systematic bias in the predictions. Nonparametric models produce a substantial improvement in out-of-sample predictions. The physical, role, and social dimensions have relatively larger decrements than pain and mental health compared with those in the United Kingdom. Conclusion: The differences between Japanese and UK valuations of the SF-6D make it important to use the Japanese valuation data set estimated using the nonparametric Bayesian technique presented in this article. (C) 2009 Elsevier Inc. All rights reserved

All-Optical Formation of Quantum Degenerate Mixtures

We report the realization of quantum degenerate mixed gases of ytterbium (Yb) isotopes using all-optical methods. We have succeeded in cooling attractively interacting 176Yb atoms via sympathetic cooling down to below the Bose-Einstein transition temperature, coexisting with a stable condensate of 174Yb atoms with a repulsive interaction. We have observed a rapid atom loss in 176Yb atoms after cooling down below the transition temperature, which indicates the collapse of a 176Yb condensate. The sympathetic cooling technique has been applied to cool a 173Yb-174Yb Fermi-Bose mixture to the quantum degenerate regime.Comment: 4 pages, 3 figure

Degenerate Fermi Gases of Ytterbium

An evaporative cooling was performed to cool the fermionic 173Yb atoms in a crossed optical dipole trap. The elastic collision rate, which is important for the evaporation, turns out to be large enough from our study. This large collision rate leads to efficient evaporation and we have successfully cooled the atoms below 0.6 of the Fermi temperature, that is to say, to a quantum degenerate regime. In this regime, a plunge of evaporation efficiency is observed as the result of the Fermi degeneracy.Comment: 4 pages, 3figure

Bose-Einstein Condensation of an Ytterbium Isotope

We report the observation of a Bose Einstein condensate in a bosonic isotope of ytterbium (170Yb). More than 10^6 atoms are trapped in a crossed optical dipole trap and cooled by evaporation. Condensates of approximately 10^4 atoms have been obtained. From an expansion of the condensate, we have extracted the scattering length a=3.6(9) nm.Comment: 4 pages, 3 figure