Asymptotic behaviors of zero modes of the massless Dirac operator H = α ·D+Q(x) are discussed, where α = (α1, α2, α3) is the triple of 4×4 Dirac matrices, D = 1i ∇x, and Q(x) = ( qjk(x) ) is a 4×4 Hermitian matrix-valued function with |qjk(x)| ≤ C〈x〉 −ρ, ρ > 1. We shall show that for every zero mode f , the asymptotic limit of |x|f(x) as |x| → +∞ exists. The limit is expressed in terms of an in...

We consider the problem of testing multiple quantum hypotheses {ρ 1 , . . . , ρ r }, where an arbitrary prior distribution is given and each of the r hypotheses is n copies of a quantum state. It is known that the minimal average error probability Pe decays exponentially to zero, that is, Pe = exp{−ξn+ o(n)}. However, this error exponent ξ is generally unknown, except for the case that r = 2. I...

We analyze radial velocities for a sample of 31 Class I and flat spectrum protostars in TaurusAuriga, ρ Ophiuchi and Serpens for evidence of the global dynamical state of extremely young stellar populations buried within parental molecular clouds. Comparing the radial velocity of each protostar to that of the local CO gas, we are able to constrain the one dimensional radial velocity dispersion ...

We calculate the density dependence of the ρ-meson mass and coupling constant(gρNN ) for ρ-nucleon-nucleon vertex at one loop using the lagrangian where the ρ-meson is included as a dynamical gauge boson of a hidden local symmetry. From the condition that thermodynamic potential should not depend on the arbitrary energy scale, renormalization scale, one can construct a renormalization group equ...

General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams. Talk given at the workshop “Advances in non-perturbative and perturbative techniques”, Ringberg Castle, November 13–19, 1994. Permanent address: Nuclear Physics Institute of Moscow State University, Moscow 119899, Russia; E-mai...

Normal mode structure coefficients provide important constraints on the long-wavelength component of 3-D mantle density (ρ) structure, but inversions for independent models of vs, vp, and ρ using normal mode data alone are ill-posed even at long wavelengths. Ill-posed inversions typically are regularized by imposing a priori assumptions on the set of estimated models, but such regularization ca...

We present Submillimeter Wave Astronomy Satellite (SWAS) observations of the 110 → 101 transition of orthoH2O at 557 GHz toward 12 molecular cloud cores. The water emission was detected in NGC 7538, ρ Oph A, NGC 2024, CRL 2591, W3, W3(OH), Mon R2, and W33, and was not detected in TMC-1, L134N, and B335. We also present a small map of the H2O emission in S140. Observations of the H18 2 O line we...