A model of structure periodically modulated in three dimensions

A model of structure periodically modulated in three dimensions is calculated in the presented paper and applied to the alloy Cu₈₀Au₂₀. The existence and intensity of the side-bands of the Bragg lines appearing with hyperstructural lines on films of this alloy after heating to temperature on the border of the order-disorder transformation are explained by means of the given model and the value of the period of sinusoidal variation of the lattice parameter and scattering power is calculated.ikova 22, Brno, Czechoslovakia.The author thanks Mrs. V. Gregor and Mr. M. Jelínek who prepared the necessary pictures.     

Analysis of finite element methods for second order boundary value problems using mesh dependent norms

This paper presents a new approach to the analysis of finite element methods based onC ⁰-finite elements for the approximate solution of 2nd order boundary value problems in which error estimates are derived directly in terms of two mesh dependent norms that are closely ralated to theL ₂ norm and to the 2nd order Sobolev norm, respectively, and in which there is no assumption of quasi-uniformity on the mesh family. This is in contrast to the usual analysis in which error estimates are first derived in the 1st order Sobolev norm and subsequently are derived in theL ₂ norm and in the 2nd order Sobolev norm — the 2nd order Sobolev norm estimates being obtained under the assumption that the functions in the underlying approximating subspaces lie in the 2nd order Sobolev space and that the mesh family is quasi-uniform.     

Arc plasma in air with calcium and fluorine—I. Calculation of the plasma composition

The equilibrium composition of the gaseous system containing N, O, C, F and Ca was calculated in the temperature range between 298 and 7000 K. This gas mixture corresponds to the plasma of a d.c. low current arc freely burning in the air between graphite electrodes in the presence of fluorine and calcium.     

Basicity of nitropyrazoles and their simultaneous spectrophotometric determination

The protonation constants of some 1-, 3(5)-, 3-, 4- and 5-nitropyrazoles have been determined, and compared with those of nitroimidazoles. The effect of the position of the nitro group in the pyrazole and imidazole ring is discussed. The ortho effects of the nitro group in pyrazole and imidazole are compared and found to have identical values. The effect of the nitro group on protonation constants is greater when the nitro group is close to the pyridine nitrogen atom. This, together with the ability of N-unsubstituted nitropyrazoles to dissociate to give nitropyrazole anions, with an accompanying shift of the spectra to longer wavelengths, permits the simultaneous spectrophotometric determination of nitropyrazoles.     

External inversion,internal inversion,and reflection invariance

Having in mind that physical systems have different levels of structure we develop the concept of external, internal and total improper Lorentz transformation (space inversion and time reversal). A particle obtained from the ordinary one by the application of internal space inversion or time reversal is generally a different particle. From this point of view the intrinsic parity of a nuclear particle (elementary particle) is in fact the external intrinsic parity, if we take into account the internal structure of a particle. We show that non-conservation of the external parity does not necessarily imply noninvariance of nature under space inversion. The conventional theory of beta-decay can be corrected by including the internal degrees of freedom to become invariant under total space inversion, though not under the external one.