Giant components in Kronecker graphs

Let \begin{align*}n\in\mathbb{N}\end{align*}, 0 <α,β,γ< 1. Define the random Kronecker graph K(n,α,γ,β) to be the graph with vertex set \begin{align*}\mathbb{Z}_2^n\end{align*}, where the probability that u is adjacent to v is given by p_u,v =α ^{u ? v} γ^{( 1‐u )?( 1‐v )}β^{n‐ u ? v ‐( 1‐u )?( 1‐v )}. This model has been shown to obey several useful properties of real‐world networks. We establish the asymptotic size of the giant component in the random Kronecker graph.© 2011 Wiley Periodicals, Inc. Random Struct. Alg.,2011     

Investigation of the Crystalline State of Identical Sample Domains by Means of Divergent X-ray Beam Technique in the Direction of Transmission and Reflection in the Scanning Electron Microscope (SEM)

A supplementary device to a scanning electron microscope allows the simultaneous taking of wide-angle interferences in the directions of transmission and back reflection of identical specimen areas. A developed computer program simulates the complete reflex system so that the identity with the pattern is obtained. This results, on the one hand, in qualitative and quantitative statements concerning the real structure of the specimen and, on the other hand, shadings of reflexes caused by the target holder tube can be distinguished from interruptions of reflexes caused by the grain size effects. The efficiency of the supplementary device for the characterizing of mono- and polycrystalline specimens is demonstrated by several examples.     

Magnetically induced rhombohedral distortion in the UxTh1−xSe and UxY1−xSe solid solutions

Solid solutions of U_xTh_1−xSe for x = 1.00 ÷ 0.80 and the solid solutions of U_xY_1−xSe for x = 1.00 ÷ 0.60 were studied by the X-ray diffraction over the temperature range 100 ÷ 200 K. In both systems rhombohedral distortions of the cubic rock-salt crystal structure was observed below the Curie temperatures. The temperature and composition dependences of the rhombohedral angle ω of the rhomboedral cell and the \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{c' - a'}}{{a'}} $\end{document} ratio were determined.