Divergence-free vector-field and reduction

By the Lie symmetry group, the reduction for divergence-free vector-fields (DFVs) is studied, and the following results are found. A n-dimensional DFV can be locally reduced to a (n - 1)-dimensional DFV if it admits a one-parameter symmetry group that is spatial and divergenceless. More generally, a n-dimensional DFV admitting a r-parameter, spatial, divergenceless Abelian (commutable) symmetry group can be locally reduced to a (n - r)-dimensional DFV.

Local exponential divergence plot and optimal embedding of a chaotic time-series

we propose here a local exponential divergence plot which is capable of providing a new means of characterizing chaotic time series. The suggested plot defines a time dependent exponent LAMBDA and a ''plus'' exponent LAMBDA+ which serves as a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time and the largest Lyapunov exponent.

A novel method to measure coma aberration of projection system

A novel method to measure coma aberration by pattern displacements at different defocus positions is proposed in this paper. The effect of defocus on coma-induced pattern displacement is analyzed. The measuring principle of the method is described in detail. Using the simulation program PROLITH, the proportionality factors between pattern displacement and coma aberration at different defocus positions are calculated. It is proved that the method is simple to perform and the measurement accuracy of coma can increase approximately by 25% by this novel method. (c) 2006 Elsevier GmbH. All rights reserved.

Protein polymorphism and genetic divergence in slow loris (Genus nycticebus)

In this study, protein electrophoresis was assayed to detect genetic variation in Genus Nycticebus. A total of 29 samples (2 N. coucang and 27 N. pygmaeus) were analyzed for 42 genetic loci. In the 27 samples of N. pygmaeus, 4 loci were observed to be polymorphic. Therefore, the estimated P value (proportion of polymorphic loci) is 0.095, the A value (average number of alleles each locus) is 1.045, and the H value (mean individual heterozygosity) is 0.040. After comparing the H of N. pygmaeus with those of other primates reported, we found that the protein variation in N. pygmaeus is slightly lower than the average level. Additionally, we also observed obvious allele difference between N. pygmaeus and N. coucang. There are no shared alleles between these two species in eight loci. The NEI's genetic distance between them was calculated as 0.2541, which falls in the spectrum of genetic difference between species in primates.

Genetic diversity and divergence in Chinese yak (Bos grunniens) populations inferred from blood protein electrophoresis

In 6 Chinese yak (Bos. grunniens) populations including 177 yaks, 34 blood protein loci were studied by horizontal starch gel electrophoresis, four of these loci (AKP: ALB, LDH-1, TF) were found to be polymorphic. The percentage of polymorphic loci(P) is 0.118, the mean individual heterozygosity(H) is 0.015, which means a low level of genetic diversity in the whole Chinese yak population. The coefficient of gene differentiation (G(ST)) is 0.0625, which indicated an almost-indistinguishable divergence among different populations at the level of blood protein electrophoresis.

Genetic divergence of orangutan subspecies (Pongo pygmaeus)

Microsatellites and mitochondrial DNA sequences were studied for the two subspecies of orangutans (Pongo pygmaeus), which are located in Borneo (P. p, pygmaeus) and Sumatra (P. p. abelii), respectively. Both subspecies possess marked genetic diversity. Ge