Hybrid bounds for twisted L-functions

The aim of this paper is to derive bounds on the critical line Rs 1/2 for L- functions attached to twists f circle times chi of a primitive cusp form f of level N and a primitive character modulo q that break convexity simultaneously in the s and q aspects. If f has trivial nebentypus, it is shown that L(f circle times chi, s) << (N vertical bar s vertical bar q)(epsilon) N-4/5(vertical bar s vertical bar q)(1/2-1/40), where the implied constant depends only on epsilon > 0 and the archimedean parameter of f. To this end, two independent methods are employed to show L(f circle times chi, s) << (N vertical bar s vertical bar q)(epsilon) N-1/2 vertical bar S vertical bar(1/2)q(3/8) and L(g,s) << D-2/3 vertical bar S vertical bar(5/12) for any primitive cusp form g of level D and arbitrary nebentypus (not necessarily a twist f circle times chi of level D vertical bar Nq(2))

Ray and wave chaos in asymmetric resonant optical cavities

Optical resonators are essential components of lasers and other wavelength-sensitive optical devices. A resonator is characterized by a set of modes, each with a resonant frequency omega and resonance width Delta omega=1/tau, where tau is the lifetime of a photon in the mode. In a cylindrical or spherical dielectric resonator, extremely long-lived resonances are due to `whispering gallery' modes in which light circulates around the perimeter trapped by total internal reflection. These resonators emit light isotropically. Recently, a new category of asymmetric resonant cavities (ARCs) has been proposed in which substantial shape deformation leads to partially chaotic ray dynamics. This has been predicted to give rise to a universal, frequency-independent broadening of the whispering-gallery resonances, and highly anisotropic emission. Here we present solutions of the wave equation for ARCs which confirm many aspects of the earlier ray-optics model, but also reveal interesting frequency-dependent effects characteristic of quantum chaos. For small deformations the lifetime is controlled by evanescent leakage, the optical analogue of quantum tunneling. We find that the lifetime is much shortened by a process known as `chaos-assisted tunneling'. In contrast, for large deformations (~10%) some resonances are found to have longer lifetimes than predicted by the ray chaos model due to `dynamical localization'.Comment: 4 pages RevTeX with 7 Postscript figure

Possible approach to improve sensitivity of a Michelson interferometer

We propose a possible approach to achieve an 1/N sensitivity of Michelson interferometer by using a properly designed random phase modulation. Different from other approaches, the sensitivity improvement does not depend on increasing optical powers or utilizing the quantum properties of light. Moreover the requirements for optical losses and the quantum efficiencies of photodetection systems might be lower than the quantum approaches and the sensitivity improvement is frequency independent in all detection band.Comment: 8 pages, 3 figures, new versio

Restricted infinitesimal deformations of restricted simple Lie algebras

We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic different from 2 and 3.Comment: 15 pages; final version, to appear in Journal of Algebra and Its Application

Broadband X-ray spectrum of XTE J1550-564 during 2003 outburst

Results of broadband INTEGRAL and RXTE observations of the Galactic microquasar XTE J1550-564 during outburst in spring 2003 are presented. During the outburst the source was found in a canonical low/hard spectral state.Comment: 5 pages, 3 figures. Accepted for publication in Astronomy Letter

Synthesis and characterization of photoaffinity labelling reagents towards the Hsp90 C-terminal domain

Glucosyl-novobiocin-based diazirine photoaffinity labelling reagents (PALs) were designed and synthesized to probe the Hsp90 C-terminal domain unknown binding pocket and the structure-activity relationship. Five PALs were successfully synthesized from novobiocin in six consecutive steps employing phase transfer catalytic glycosylation. Reactions were monitored and guided by analytical LC/MS which led to different strategies of adding either a PAL precursor or a sugar moiety first. The structures and bonding linkages of these compounds were characterised by various 2D-NMR spectroscopy and MS techniques. Synthetic techniques provide powerful probes for unknown protein binding pockets

Criminal Justice and Suicide Outcomes with Indiana's Risk-Based Gun Seizure Law

This article examines the application and effectiveness of a 2006 Indiana law designed to prevent gun violence by authorizing police officers to separate firearms from persons who present imminent or future risk of injury to self or others, or display a propensity for violent or emotionally unstable conduct. A court hearing is held to determine ongoing risk in these cases; a judge decides whether to return the seized firearms or retain them for up to five years. The study examines the frequency of criminal arrest as well as suicide outcomes for 395 gun-removal actions in Indiana. Fourteen individuals (3.5%) died from suicide, seven (1.8%) using a firearm. The study population's annualized suicide rate was about 31 times higher than that of the general adult population in Indiana, demonstrating that the law is being applied to a population genuinely at high risk. By extrapolating information on the case fatality rate for different methods of suicide, we calculated that one life was saved for every 10 gun-removal actions, similar to results of a previous study in Connecticut. Perspectives from key stakeholders are also presented along with implications for gun policy reform and implementation

Super Yangian Double DY(gl(1∣1))DY( gl(1|1)) and Its Gauss Decomposition

We extend Yangian double to super (or graded) case and give its Drinfel'd generators realization by Gauss decomposition.Comment: 6 pages, Latex, no figure