Gravitational waves in general relativity: XIV. Bondi expansions and the ``polyhomogeneity'' of \Scri

The structure of polyhomogeneous space-times (i.e., space-times with metrics which admit an expansion in terms of $r^{-j}\log^i r$) constructed by a Bondi--Sachs type method is analysed. The occurrence of some log terms in an asymptotic expansion of the metric is related to the non--vanishing of the Weyl tensor at Scri. Various quantities of interest, including the Bondi mass loss formula, the peeling--off of the Riemann tensor and the Newman--Penrose constants of motion are re-examined in this context.Comment: LaTeX, 28pp, CMA-MR14-9

Eigenfunctions decay for magnetic pseudodifferential operators

We prove rapid decay (even exponential decay under some stronger assumptions) of the eigenfunctions associated to discrete eigenvalues, for a class of self-adjoint operators in $L^2(\mathbb{R}^d)$ defined by ``magnetic'' pseudodifferential operators (studied in \cite{IMP1}). This class contains the relativistic Schr\"{o}dinger operator with magnetic field

On thin plate spline interpolation

We present a simple, PDE-based proof of the result [M. Johnson, 2001] that the error estimates of [J. Duchon, 1978] for thin plate spline interpolation can be improved by $h^{1/2}$. We illustrate that ${\mathcal H}$-matrix techniques can successfully be employed to solve very large thin plate spline interpolation problem

Relation between macroscopic and microscopic dielectric relaxation times in water dynamics

A simplified derivation for the ratio of macroscopic to microscopic relaxation times of polar liquids is based on the Mori-Zwanzig projection-operator technique, with added statistical assumptions. We obtain several useful forms for the lifetime ratio, which we apply to the dynamics of liquid water. Our theoretical single-molecule relaxation times agree with the second Debye relaxation times as measured by frequency-domain dielectric spectroscopy of water and alcohols. From the theory, fast relaxation modes couple to the Debye relaxation time, τD, through very large water clusters, and their temperature dependence is similar to that of τD. Slower modes are localized to smaller water clusters and exhibit weaker temperature dependence. This is exemplified by the lifetime ratios measured by time-domain dielectric spectroscopy and optical Kerr effect spectroscopy, respectively

Superconductivity in domains with corners

We study the two-dimensional Ginzburg-Landau functional in a domain with corners for exterior magnetic field strengths near the critical field where the transition from the superconducting to the normal state occurs. We discuss and clarify the definition of this field and obtain a complete asymptotic expansion for it in the large $\kappa$ regime. Furthermore, we discuss nucleation of superconductivity at the boundary

Conforming finite element methods for the clamped plate problem

Finite element methods for solving biharmonic boundary value problems are considered. The particular problem discussed is that of a clamped thin plate. This problem is reformulated in a weak, form in the Sobolev space Techniques for setting up conforming trial Functions are utilized in a Galerkin technique to produce finite element solutions. The shortcomings of various trial function formulations are discussed, and a macro—element approach to local mesh refinement using rectangular elements is given

Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n

Prevalence and correlates of diphtheria toxoid antibodies in children and adults in Israel

ABSTRACTA seroepidemiological study was performed to evaluate immunity to diphtheria and to determine the correlates of diphtheria toxoid antibody levels among children and adults in Israel. In total, 3185 sera from an age-stratified sample of children and adults, obtained in 2000–2001, were tested for diphtheria toxoid antibodies by an in-house double-antigen ELISA. A level of ≤0.01 IU /mL (no immune protection or seronegativity) was found in 168 (5.3%) of the 3185 subjects, 639 (20.1%) had antibody levels of 0.011–0.099 IU /mL (basic immunity or low seropositivity), and 2378 (74.7%) had antibody levels ≥0.1 IU /mL (full protection or seropositivity). Seronegativity increased significantly in subjects aged >50 years, reaching levels of 9.7%, 12.6% and 18.9% in the groups aged 50–54, 55–59 and >60 years, respectively (p 0.001), with rates of basic immunity following a similar pattern. Subjects born abroad had higher seronegativity rates than those born in Israel (7.7%vs. 4.9%; p 0.019). No difference in diphtheria toxoid antibody levels was found according to other demographical variables, such as gender, Jewish or Arab ethnicity, urban or rural settlements, and the subjects’ place of residence. The level of immunity to diphtheria among children and adults in Israel was satisfactory, with the exception of individuals aged >50 years. The risk of diphtheria outbreaks is low, but sporadic cases may occur among individuals lacking basic immunity against the disease

Second order perturbation theory for embedded eigenvalues

We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonians for arbitrary coupling.Comment: 30 pages, 2 figure

Magnetic calculus and semiclassical trace formulas

The aim of these notes is to show how the magnetic calculus developed in \cite{MP, IMP1, IMP2, MPR, LMR} permits to give a new information on the nature of the coefficients of the expansion of the trace of a function of the magnetic Schr\"odinger operator whose existence was established in \cite{HR2}