On a Certain Algebraic Property of Block Ciphers

This is a study on a certain group theoretic property of the set of encryption functions of a block cipher. We have shown how to construct a subset which has this property in a given symmetric group by a computer algebra software GAP4.2 (Groups, Algorithms, and Programming, Version 4.2). These observations on group structures of block ciphers suggest us that we may be able to set a trapdoor based on meet-in-the-middle attack on block ciphers.

Two-dimensional photonic lattices in polymer-dispersed liquid crystal composites

The relationship between liquid crystal orientational ordering and optical diffraction properties is investigated for a two-dimensional square photonic lattice fabricated in a polymer-dispersed liquid crystal (PDLC) composite. Modifications of the nematic director field in the liquid crystal domains were induced by an external applied voltage and by heating over the nematic-isotropic (N-I) phase transition. They were studied by optical polarization microscopy and by analysing far-field optical diffraction patterns. The intensities of various diffraction orders (from the zeroth up to the eighth diffraction order) were monitored with a CCD camera, and their variations were correlated with the modifications of the director field.

Asymmetric heat conduction in nonlinear lattices

In this Letter, we conduct an extensive study of the two-segment Frenkel-Kontorova model. We show that the rectification effect of the heat flux reported in recent literature is possible only in the weak interfacial coupling limit. The rectification effect will be reversed when the properties of the interface and the system size change. These two types of asymmetric heat conduction are governed by different mechanisms though both are induced by nonlinearity. An intuitive physical picture is proposed to interpret the reversal of the rectification effect. Since asymmetric heat conduction depends critically on the properties of the interface and the system size, it is probably not an easy task to fabricate a thermal rectifier or thermal diode in practice.

White light emission from Eu3+ in CaIn2O4 host lattices

CaIn2O4:xEu(3+) (x=0.5%,1.0%,1.5%) phosphors were prepared by the Pechini sol-gel process [U.S. Patent No. 3,330,697 (1967)] and characterized by x-ray diffraction and photoluminescence and cathodoluminescence spectra as well as lifetimes. Under the excitation of 397 nm ultraviolet light and low voltage electron beams, these phosphors show the emission lines of Eu3+ corresponding to D-5(0,1,2,3)-F-7(J) (J=0,1,2,3,4) transitions from 400 to 700 nm (whole visible spectral region) with comparable intensity, resulting in a white light emission with a quantum efficiency near 10%. The luminescence mechanism for Eu3+ in CaIn2O4 has been elucidated.

The relationship between chemical bond properties and Stokes shift of Eu2+ in some silicate host lattices

The covalency of each bond in divalent europium doped hosts CaSiO3, SrSiO3, BaSiO3, Sr2LiSiO4F, Ba5SiO4Cl6 and Ba5SiO4Br6 were calculated by using the complicate crystal chemical bond theory. The relationship between the Stokes shift and the bond properties of Eu2+ in these crystals was discussed. The result demonstrates that, in the isostructural crystals that being doped with Eu2+, there is a more precise connection between the magnitude of Stokes shift and the mean covalency of the dopant site.

AN ALGEBRAIC METHOD TO ESTIMATE GENERAL TYPE OF PHASES OF STRUCTURE FACTORS

The algebraic formulas of 1.5 and 2.5 rank are given for four space groups P2(1), Pn, Pna2(1), P2(1)2(1)2(1). It is better that the results of applying them to estimating general type of phases for four correspondent crystal structures. And a method of transforming algebraic formulas from 1.5(2.5) rank is proposed.

THE ALGEBRAIC-METHOD ESTIMATING +/-PI/2 TYPE OF PHASES OF STRUCTURE FACTORS

The algebraic formulas of 1.5 and 2.5 rank which can be applied to estimating +/- pi/2 type of phases for P2(1)2(1)2(1) space group were derived using the method of structure factor algebra. Both types of the formulas are satisfactory for two known crystal structures in estimating their +/- pi/2 type of phases.