Naphthyl azomesogens with lateral chloro groups

A homologous series of azomesogens, 2″-[4-(4′-n-alkoxybenzoyloxy)-2-chlorophenylazo] naphthalenes, with lateral chloro groups was synthesised. All the homologues synthesized exhibit enantiotropic nematic mesophase. The mesomorphic properties of the present series are compared with other structurally related series to evaluate the effect of lateral chloro group and its position on mesomorphism This paper was presented at the 10th National Conference on Liquid Crystals held at Bangalore, India during 9–11 October 2003.     

Coset extensions of <Emphasis Type=”Italic”>S</Emphasis>-sets

Summary Three weak variants of compactness which lie strictly between compactness and quasicompactness, are introduced. Their basic properties are studied. The interplay with mapping and their direct and inverse preservation under mappings are investigated. In the process three decompositions of compactness are observed.     

Free probability and the von Neumann algebrasof free groups

This short note summarizes the circumstances of the birth of free probability theory andsome of the recent achievements.     

Virtual logarithms

The modification of the number field sieve which Joux and Lercier recently used to compute logarithms in a prime field of a record 120 decimal digits makes use of the notion of a virtual logarithm of a prime ideal in a number ring. We provide necessary and sufficient conditions for their method to succeed and give an explicit formula for the virtual logarithm of an ideal.     

The mesa problem for Neumann boundary value problem

In this paper, we study the singular limit of the Porous Medium equation u_t=Δu^m+g(x,u), as m→∞, in a bounded domain with Neumann boundary condition.     

CAP-子群与p-幂零性

设G是有限群。H是G的一个正规子群。P是|H|的一个素因子。P是H的一个Sylow p-子群。若下列条件之一满足。则H是p-幂零：1)P的极大子群都是G的CAP-子群且(|H|，P-1)=1；2)P的二次极大子群都是G的CAP-子群且(|H|，P^2-1)=1。特别地，若进一步假设G／H为P-幂零且(|G|，P-1)=1或(|G|，P^2-1)=1。则G自身亦为P-幂零。     

Generating Quadratic Pseudo-Anosov Homeomorphisms of Closed Surfaces

In this note, we show that given a closed, orientable genus-g surface S _g , any hyperbolic toral automorphism has a positive power which induces a quadratic, orientable pseudo-Anosov homeomorphism on S _g . To show this, we lift Anosov toral automorphisms through a ramified topological covering and present the lifted homeomorphism via a standard set of Lickorish twists. This construction provides a general method of producing pseudo-Anosov maps of closed surfaces with predetermined orientable foliations and quadratic dilatation. Since these lifted automorphisms have orientable foliations, this construction is a sort of converse to that of Franks and Rykken [Trans. Amer. Math. Soc. 1999], who established that one can associate to a quadratic pseudo-Anosov homeomorphism with oriented unstable foliation a hyperbolic toral automorphism.     

On the counting function of the lattice profile of periodic sequences

The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period.