Approximation in the finite element method

Summary The rate of convergence of the finite element method depends on the order to which the solutionu can be approximated by the trial space of piecewise polynomials. We attempt to unify the many published estimates, by proving that if the trial space is complete through polynomials of degreek–1, then it contains a functionv ^h such that |u–v ^h | _s ch ^k–s|u| _k . The derivatives of orders andk are measured either in the maximum norm or in the mean-square norm, and the estimate can be made local: the error in a given element depends on the diameterh _i of that element. The proof applies to domains in any number of dimensions, and employs a uniformity assumption which avoids degenerate element shapes.This research was supported by the National Science Foundation (GP-13778).     

Neutron activation determination of impurities in germanium

A neutron activation (NA) method for the determination of 24 microimpurities in germanium has been developed. The method is based on the separation of the matrix and isotopes genetically connected by extraction chromatography.     

Calcul de la fonction correlation de phonon pour la diffraction d'une particule par un solide

A method of calculating expressions of the type $\text{<T exp[?i}\text{k}{}_1\text{u}{}_{\ln }\text{(t}{}_1\text{)] ... exp [?i}\text{k}{}_{\mathrm{n}}\text{u}{}_{\ln }\text{(t}{}_{\mathrm{n}}\text{>}$ which is simpler than that based on Wick's theorem is proposed. Expressions of the above type are widely used in studying the effects of temperature in electron and neutron diffraction.     

Diazothenes: evidence for their production by way of a Wittig reaction.

Base-promoted reaction of dimethyl diazomethylphosphonate ($\text{1}$) with dialkyl and cyclic ketones affords species having the chemical properties associated with vinylidenes ($\text{3}$) or their equivalents. Data are presented showing that diazoethenes ($\text{2}$) are unexpectedly unstable, losing nitrogen even at ?78°C to give the corresponding carbenes or carbenoids.     

13C NMR studies of some hydroxycoumarins and related compounds

The ¹³C chemical shifts and one-bond carbon-hydrogen coupling constants have been obtained for some hydroxycoumarins and their corresponding acetoxy and methoxy derivatives. The changes in the one-bond carbon-hydrogen coupling constants resulting from the conversion of a hydroxy group to an acetoxy group represent a simple method of assignment of the ¹³C NMR signals in coumarins which contain one or more hydroxy groups in the benzenoid ring.     

Inversion von schwingungselastischen Streudaten

Ohne Zusammenfassung