On the instability of resonances in parallel-plane waveguides under local perturbations of the boundary

We study the large-time asymptotics for solutions u( x , t) of the wave equation with Dirichlet boundary data, generated by a time-harmonic force distribution of frequency ω, in a class of domains with non-compact boundaries and show that the results obtained in [11] for a special class of local perturbations of Ω₀ ? ?² × (0,1) can be extended to arbitrary smooth local perturbations Ω of Ω₀. In particular, we prove that u is bounded as t → ∞ if Ω does not allow admissible standing waves of frequency ω in the sense of [8]. This implies in connection with [8]. Theorem 3.1 that the logarithmic resonances of the unperturbed domain Ω₀ at the frequencies ω = πk (k = 1, 2,…) observed in [14] can be simultaneously removed by small perturbations of the boundary. As a main step of our analysis, the determination of admissible solutions of the boundary value problem ΔU + κ²U = ? f in Ω, U = 0 on ?Ω is reduced to a compact operator equation.     

Energy of the 5− isomer and (πg 9/2⊗vg 9/2) states in82Rb

Excited states in the doubly-odd nucleus⁸²Rb have been investigated via the reactions⁷⁹Br(,n) and⁷⁸Se(⁷Li,3n) using in-beam-ray spectroscopy. The level energy of the longlived 5^– isomer has been determined to 68.3 keV which is below the energy of the 2^– state found at 88.9 keV with a lifetime of=2.4(2) ns. A sequence of positive-parity states beginning with a 6⁺ level at 191.3 keV (=20(3) ns) and extending to a (10⁺) level has been interpreted to contain the two-particle configuration (g ₉/2 _9/2) and collective excitations.     

Measurement of the muon capture rate in hydrogen gas and determination of the proton's pseudoscalar coupling gP

The rate of nuclear muon capture by the proton has been measured using a new technique based on a time projection chamber operating in ultraclean, deuterium-depleted hydrogen gas, which is key to avoiding uncertainties from muonic molecule formation. The capture rate from the hyperfine singlet ground state of the microp atom was obtained from the difference between the micro(-) disappearance rate in hydrogen and the world average for the micro(+) decay rate, yielding Lambda(S)=725.0+/-17.4 s(-1), from which the induced pseudoscalar coupling of the nucleon, g(P)(q(2)=-0.88m(2)(micro))=7.3+/-1.1, is extracted.     

The steady shear viscosity of filled polymeric liquids described by a linear superposition of two relaxation mechanisms

Filled polymeric liquids often exhibit apparent yielding and shear thinning in steady shear flow. Yielding results from non-hydrodynamic particle—particle interactions, while shear thinning results from the non-Newtonian behavior of the polymer melt. A simple equation, based on the linear superposition of two relaxation mechanisms, is proposed to describe the viscosity of filled polymer melts over a wide range of shear rates and filler volume fraction.The viscosity is written as the sum of two generalized Newtonian liquid models. The resulting equation can describe a wide range of shear-thinning viscosity curves, and a hierarchy of equations is obtained by simplifying the general case. Some of the parameters in the equation can be related to the properties of the unfilled liquid and the solid volume fraction. One adjustable parameter, a yield stress, is necessary to describe the viscosity at low rates where non-hydrodynamic particle—particle interaction dominate. At high shear rates, where particle—particle interactions are dominated by interparticle hydrodynamics, no adjustable parameters are necessary. A single equation describes both the high and low shear rate regimes. Predictions of the equation closely fit published viscosity data of filled polymer melts. n power-law index - n ₁,n ₂ power-law index of first (second) term - shear rate - steady shear viscosity - ₀ zero-shear rate viscosity - _{0, 1}, _{0, 2} zero-shear rate viscosity of first (second) term - time constant - ₁, ₂ time constant of first (second) term - µ _r relative viscosity of filled Newtonian liquid - ₀ yield stress - ø solid volume fraction - ø _m maximum solid volume fraction     

Nonperturbative light cone quantum field theory beyond the tree level

We demonstrate the appearance of spontaneous symmetry breaking induced by nonperturbative quantum corrections for scalar light cone quantum field theory in 1+1 dimensions. We define a light cone effective potential and obtain a second order phase transition.     

An invariant trace formula for the universal covering group of SL(2,ℝ)

Automorphic forms of arbitrary real weight can be considered as functions on the universal covering group of SL(2, ). In this situation, we prove an invariant form of the Selberg trace formula for Hecke operators. For this purpose, the Fourier transforms of weightet orbital integrals, obtained by J. Arthur, R. Herb and P. Sally, jr., are explicitly calculated. Our formula does not follow from Arthur's invariant trace formula, since the group has infinite centre, and vector-valued automorphic forms with respect to non-congruence lattices are considered.