Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods

A model second-order elliptic equation on a general convex polyhedral domain in three dimensions is considered. The aim of this paper is twofold: First sharp Hölder estimates for the corresponding Green’s function are obtained. As an applications of these estimates to finite element methods, we show the best approximation property of the error in \({W^1_{\infty}}\) . In contrast to previously known results, \({W_p^{2}}\) regularity for p > 3, which does not hold for general convex polyhedral domains, is not required. Furthermore, the new Green’s function estimates allow us to obtain localized error estimates at a point.     

An effective molecular orbital basis selection scheme to calculate resonant frequency-dependent polarizabilities and polarizability derivatives by time-dependent Hartee—Fock theory

A non-iterative method for calculating frequency-dependent polarizabilities is developed using time-dependent Hartrec—Fock theory. A simple procedure for selecting molecular orbitals and two-electron integrals in this method is proposed and shown to be effective in reducing computational effort.     

On nonrepetitive sequences

We prove the following results: (1) There exists an infinite binary sequence having no identical adjacent blocks of length 3 or greater. (2) Every binary sequence of length greater than 18 has identical adjacent blocks of length 2 or greater. (3) Every infinite binary sequence has arbitrarily long adjacent blocks that are permutations of each other.     

Magnetic circular dichroism of the U center in KCl

The magnetic circular dichroism (MCD) and absorption spectrum of the U center in KCl have been measured at liquid helium temperature. The results are consistent with the usual ¹S(l s²) → ¹P(ls2p) assignment with the temperature independent MCD yielding an excited state magnetic moment only about 40 per cent that calculated for a hydride ion in an octahedral crystal field.     

Relativmessung der Elektronenpolarisation beim β-Zerfall: Re186 und P32

The ratio of longitudinal polarization values of Re¹⁸⁶ and P³² β-particles was measured by the method of double scattering. The result obtained isP(Re¹⁸⁶)/P(P³²)=1,002 _?0,016 ⁺ at 540 keV. The contributions of the ground state transition and the first excited state transition of Re¹⁸⁶ are 78% and 22% respectively at this energy for the apparatus used.     

Analysis of polar organic micropollutants in water with ion chromatography-electrospray mass spectrometry

The coupling of ion chromatography (IC) with electrospray mass spectrometry (ES-MS) opens new ways for the determination of polar organic micropollutants in water samples. The technique of conductivity suppression has been found to reduce the background signal in the range of about two orders of magnitude leading to a significant increase in sensitivity. In addition, the formation of salt adducts has been avoided. The usefulness of this method was proven on several polar and environmentally relevant micropollutants such as the herbicide glyphosate and its metabolite aminomethylphosphonic acid (AMPA), the chelating agent ethylenediamine tetraacetate (EDTA) and diacetonketogulonic acid (DAG). This present study has shown that IC-ES-MS is a simple, sensitive and quick method for the determination of these polar organic traces in water samples after separation on an anion-exchange column without any derivatization. In this work, several possibilities of applications of IC-ES-MS (with varying conditions) are presented. Analysis of glyphosate, AMPA, DAG and EDTA in ground and surface water has been achieved by IC-ES-MS without additional sample preparation at a concentration level of 1 microgram/l.     

The level scheme of 137Pr; evidence for prolate nuclear shape

The level scheme of ¹³⁷Pr was investigated by means of the γ-rays following the β-decay of ¹³⁷Nd as well as by prompt γ-rays accompanying (α, xn) reactions. We measured γ-ray single spectra, γγ coincidences (both in-beam and off-beam), angular distributions of prompt γ-rays and conversion electrons. About 100 γ-rays were assigned to the 38 min decay of ¹³⁷Nd most of which fit into a scheme of 26 deduced levels. From in-beam experiments we tentatively assigned an $\text{11}\text{2}$^? level which is the basis of a strong cascade of stretched E2 transitions with a probable level sequence of $\text{23}\text{2}$^? ?$\text{19}\text{2}$^? ?$\text{15}\text{2}$^? ?$\text{11}\text{2}$^?. The interpretation of this cascade in the framework of a strong coupling model indicates a prolate deformation of ¹³⁷Pr. Another indication for such a deformation was obtained from the very low energy (75 keV) of the first $\text{3}\text{2}$⁺ level which could not be interpreted in an intermediate coupling model, but is suggested by a Nilsson scheme.     

Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part II: The piecewise linear case

We extend results from Part I about estimating gradient errors elementwise a posteriori, given there for quadratic and higher elements, to the piecewise linear case. The key to our new result is to consider certain technical estimates for differences in the error, , rather than for itself. We also give a posteriori estimators for second derivatives on each element.