A comment on SCF energy partitioning schemes

Starting from the symmetry groupG × SU(2) for the special case of negligible spin-orbit coupling, a general character formula is derived for them-tuplet representation, which is realized in the space of state functions ofn-electron systems in fields with symmetryG. Apart from the characters of the initial representation for the single electron space function, the formula only contains the number of particlesn and the multiplicitym.

Herrn Professor Dr. Hermann Hartmann zu seinem 60. Geburtstag gewidmet.     

Algebraic Cayley graphs over finite fields

A new algebraic Cayley graph is constructed using finite fields. It provides a more flexible source of expander graphs. Its connectedness, the number of connected components, and diameter bound are studied via Weil's estimate for character sums. Furthermore, we study the algorithmic problem of computing the number of connected components and establish a link to the integer factorization problem.     

Spencer <Emphasis Type="Italic">δ</Emphasis>-cohomology,Restrictions, Characteristics and Involutive Symbolic PDEs

We generalize the notion of involutivity to systems of differential equations of different orders and show that the classical results relating involutivity, restrictions, characteristics and characteristicity, known for first order systems, extend to the general context. This involves, in particular, a new definition of strong characteristicity. The proof exploits a spectral sequence relating Spencer δ-cohomology of a symbolic system and its restriction to a non-characteristic subspace.      

Quantitative analysis of DNA methylation in the promoter region of the methylguanine‐O6‐DNA‐methyltransferase gene by COBRA and subsequent native capillary gel electrophoresis

Along with histone modifications, RNA interference and delayed replication timing, DNA methylation belongs to the key processes in epigenetic regulation of gene expression. Therefore, reliable information about the methylation level of particular DNA fragments is of major interest. Herein the methylation level at two positions of the promoter region of the gene methylguanine‐O⁶‐DNA‐Methyltransferase (MGMT) was investigated. Previously, it was demonstrated that the epigenetic status of this DNA region correlates with response to alkylating anticancer agents. An automated CGE method with LIF detection was established to separate the six DNA fragments resulting from combined bisulfite restriction analysis of the methylated and non‐methylated MGMT promoter. In COBRA, the DNA was treated with bisulfite converting cytosine into uracil. During PCR uracil pairs with adenine, which changes the original recognition site of the restriction enzyme Taql. Artificial probes generated by mixing appropriate amounts of DNA after bisulfite treatment and PCR amplification were used for validation of the method. The methylation levels of these samples could be determined with high accuracy and precision. DNA samples prepared by mixing the corresponding clones first and then performing PCR amplification led to non‐linear correlation between the corrected peak areas and the methylation levels. This effect is explained by slightly different PCR amplification of DNA with different sequences present in the mixture. The superiority of CGE over PAGE was clearly demonstrated. Finally, the established method was used to analyze the methylation levels of human brain tumor tissue samples.     

High order moments of character sums

We establish the upper bound

with a prime and any positive integer, the sum being over all nonprincipal multiplicative characters .

     

Phase separation in colloidal dispersions with nonadsorbing polymer

The influence of the volume restriction effect on phase separation in colloidal dispersions consisting of a nonadsorbing polymer has been studied using statistical mechanical cell models and perturbation theories in combination with Monte Carlo experiments. The attractive interparticle potential proposed by Asakura and Oosawa is used to represent the effect of polymer depletion between the particles. The equilibrium properties are determined using the cell model for the solid-like phase (with Monte Carlo simulations for the structure of the solid phase) and a perturbation theory for the liquid-like phase. Both aqueous and nonaqueous dispersions are considered, and the phase separation behavior predicted is compared with available experimental and theoretical results.     

Genetic evidence of an Asian background in heteroplasmic Iberian cattle (Bos taurus): effect on food authentication studies based on polymerase chain reaction-restriction fragment length polymorphism analysis

This work was aimed at identifying nucleotide polymorphic sites in a 359 bp region of the cytochrome b (cytb) mitochondrial gene of Iberian cattle (Bos taurus). This region is widely used as target in polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) species identification studies in foodstuffs destined for human and animal consumption. Two different coexisting restriction patterns were observed in four of the six animals studied when the 359 bp DNA fragment was cleaved with PalI, HinfI, MvaI, RsaI, or MboI. The amplification of both genotypes with the mitochondrial-specific primers L14735 and H15149 revealed the absence of nuclear pseudo-cytb genes, confirming the existence of mitochondrial heteroplasmy. The two coexisting mtDNA fragments were selectively sequenced in PCR extracts in which one genotype predominated over the other, both exhibiting a sequence variation of 10.4%. From the 37 nucleotide mismatches observed between genotypes, 32 were transitions and five were transversions. While 31 of the nucleotide mismatches between genotypes resulted to be conservative at the amino acid level, six changes implied amino acid substitutions, five of them being located in the variable transmembrane region. Genetic analysis suggests the presence of an Asian background in the mitochondria of Iberian cattle: while one of the genotypes matched the published sequence for Bos taurus, the other genotype clustered with a B. primigenius indicus animal and close to an Asian Bos taurus animal. These results also suggest that a number of current PCR-RFLP species identification methods based on cytb sequences may not be reliable for the accurate detection and identification of bovine material: an alternative battery of enzymes consisting of MmeI, NlaIV, and AluI is proposed.     

广义迹函数

本文引进两类新的广义迹函数,用矩阵理论和有限群的表示论研究它们的性质,给出它们在分块厄米特矩阵上的应用.     

On some constants in the supercuspidal characters of

The article gives explicit values of some constants which appear in the character formula for the irreducible supercuspidal representation of for a local field of the residual characteristic .

     

Primitive normal polynomials with a prescribed coefficient

In this paper, we established the existence of a primitive normal polynomial over any finite field with any specified coefficient arbitrarily prescribed. Let n15 be a positive integer and q a prime power. We prove that for any aF_q and any 1m<n, there exists a primitive normal polynomial f(x)=xⁿ−σ₁xⁿ⁻¹++(−1)ⁿ⁻¹σ_n−1x+(−1)ⁿσ_n such that σ_m=a, with the only exceptions σ₁≠0. The theory can be extended to polynomials of smaller degree too.