System of cryostating wide-aperture nonlinear crystals for generating the fifth harmonic of neodymium-laser radiation

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 51, No. 5, pp. 867–870, November, 1989.     

Strukturelle Aspekte bei Korngrenzensegregationsuntersuchungen

Ohne Zusammenfassung

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Structural aspects for grain boundary segregation studies

     

Second order Runge–Kutta methods for Stratonovich stochastic differential equations

The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly. AMS subject classification (2000)  65C30, 65L06, 60H35, 60H10     

Practical stopping criteria for validating safety-critical software by estimating impartial reliability

In this research, we investigate stopping rules for software testing and propose two stopping rules from the aspect of software reliability testing based on the impartial reliability model. The impartial reliability difference (IRD-MP) rule considers the difference between the impartial transition-probability reliabilities estimated for both software developer and consumers at their predetermined prior information levels. The empirical–impartial reliability difference (EIRD-MP) rule suggests stopping a software test when the computed empirical transition reliability is tending to its estimated impartial transition reliability. To insure the high-standard requirement for safety-critical software, both rules take the maximum probability (MP) of untested paths into account.     

The coexistence of γ(γ′) and θ alumina observed by STM and LEED on top of oxide layer grown on CoAl(1 0 0)

We report the coexistence of γ(γ′) and θ alumina grown on the CoAl(1 0 0) surface. Both phases were observed after annealing of alumina at 1150 K by means of scanning tunnelling microscopy (STM). The crystal structures of γ(γ′) and θ alumina were indexed based on low energy electron diffraction (LEED) and STM experimental data.     

A method for estimating the local lattice distortions near a magnetic ion from ligand hyperfine parameters: Yb3+trigonal centers in SrF2 and BaF2

An empirical relationship describing the radial dependence of the nondipole part of the anisotropic constant for the ligand hyperfine interaction in alkaline-earth fluorides is proposed. This relationship is used for calculating the distances between the magnetic ion and the fluorine ions involved in its nearest environment. The results of the calculations are in good agreement with the values obtained by other methods for both cubic and tetragonal fluorine centers in these crystals. The distances from the magnetic ion to different groups of nonequivalent fluorine ions of the nearest environment in Yb³⁺ trigonal centers of SrF₂ and BaF₂ are determined. It is found that the Yb³⁺ ion is slightly displaced along the trigonal axis away from the compensating fluorine ion.