Hamiltonian circuits in Cayley graphs

The following result is proved: If either G is a finite abelian group or a semidirect product of a cyclic group of prime order by a finite abelian group of odd order, then every connected Cayley graph of G is hamiltonian.     

Repulsion of interfaces due to boundary water

The exponential repulsion of bilayers in lecithin-water dispersions is explained as arising from modification of water structure near the lecithin-water interface.     

Theory of moving striations in plasma of D-C discharge I. Basic equation and its general solution

As a base for the theory of moving striations a partial integro-differential equation (26) is derived from the equations of continuity (1), (2), the Laplace-Poisson equation (3) and relation (4) between the electric field and the temperature of the electrons. Apart from the processes necessary for the actual formation of striations according to [1] and for the amplification of the wave of stratification according to [2], the equation also includes the processes defining the Debye length of the electrons, the influence of the axial electric field and of its local deflections on the motion of current carriers and the direct influence of the deviations in concentration of the electrons on the rate of production of current carriers. In deriving the equation the main attention is paid to the physical sense of the mathematical operations applied. The general solution is found by the method of the two-sided Laplace transformation and is described by triple integral convolution (42).

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I.

(1), (2), - (3) (4) (26). , , [1], , [2], , , . . (42).

     

Investigation of the kinetics of exchange reactions by the method of constant velocity supply of the labelled component into the system

The method of constant velocity supply of the radioactive labelled component into the system was used to study the kinetics of the isotope exchange Tl(I)-hydroxyquinolate-Tl(III)-hydroxyquinolate in chloroform. The second order exchange reaction with a halftime less than 1 min was determined in the range of concentrations 0.2–2·10⁻³ M of both components.     

The use of substitution groups to derive thermodynamical relations between the material constants of piezoelectric materials

It is shown how substitution groups can be used to derive relations between the material constants of an anisotropic homogeneous piezoelectric medium. The structure of these relations is explained by means of a general record and independent systems are found, the existence of which has a clear physical interpretation. The concept of substitution group is generalized and some important thermodynamic substitution groups are derived; the method can be applied without substantial changes to an arbitrary type of anisotropic homogeneous medium.     

The nuclear magnetic resonance of Co59 and hyperfine fields in Fe-Co alloy

The nuclear magnetic resonance of Co⁵⁹ in an Fe-Co alloy was studied for a concentration of 4 to 17% Co. The resonance frequency was found to be independent of the concentration in this range. This observation is discussed together with the experimentally found dependence of the hyperfine field of iron in this alloy on the concentration of Co [8]. Use is made of a band model for 3d electrons of iron, in which the Co atoms behave as impurities on which certain wave functions of the band are localized and other delocalized. The values obtained for the line width show the presence of a mechanism of broadening, dependent on 3d wave functions.