Counting the number of indecomposable representations and a q-analogue of the Weyl-Kac denominator identity of type _n

By using Frobenius maps and F-stable representations,we count the number of isomor- phism classes of indecomposable representations with the fixed dimension vector of a species of type _n over a finite field,first,and then,as an application,give a q-analogue of the Weyl-Kac denominator identity of type _n.     

Two new eudesmane derivatives from Verbesina virginica

<正>Two new eudesmane derivatives were isolated from the leaves and flowers of Verbesina virginica,along with the known 6-O-β-E -p-coumaroyl-4α-hydroxyeudesmane(1).Their structures were determined as 6-O-β-Z-p-coumaroyl-4α-hydroxyeudesmane(2) and 6-O-α-E-p-coumaroyl-1β-4α-dihydroxyeudesmane(3) by spectroscopic methods.     

Interaction of bis-aryl functionalized molecules with nucleosides and nucleic acids

A series of novel molecules with a cyclen(1,4,7,10-tetraazacyclododecane) moiety appended on and bearing different aromatic fragments in the structures were synthesized and characterized.The binding activities of these compounds towards DNA were systematically studied by spectroscopic,viscometric and gel electrophoresis methods.The results suggest that the stacking interaction plays an important role in improving the DNA binding ability of the compounds.The binding modes of the compounds towards DNA are als...     

利用天然手性源合成复杂手性化合物的方法

利用天然手性源来合成一些复杂的手性化合物,其合成策略往往具有很高的艺术性.本文主要对糖类和甘露糖以及一些氨基酸类天然产物作为合成子来合成手性分子的一些新方法作了报道.     

Different self-assembly behaviors of mono-modified β-cyclodextrin substituted by benzoic acid derivatives

The mono-modified β-cyclodextrin derivative,6-O-(4-aminobenzoyl)-β-cyclodextrin(1) ,was synthesized and characterized. We compared its self-assembling behavior with structurally related β-cyclodextrin derivative,6-O-(4-hydroxybenzoyl)-βcyclodextrin(2) ,in aqueous solution and in the solid state using NMR spectroscopy and single crystal X-ray structure analysis. The two complexes displayed different self-assembling behaviors.Complex 1 formed a head-to-tail helical columnar superstructure in which the substit...     

Construction and evaluation of a novel end-column amperometric detection system for electrophoresis microchips

A set of integrated end-column amperometric detection system has been developed,onto which an electrophoresis microchip can be conveniently integrated.Finely machined by a piece of transparent organic glass,the system consists of an electrophoresis microchip platform and an amperometric detection reservoir,in which the microchip can be fixed onto the platform by microchip grooves and with stainless steel fixture.Each detection electrode can be directly fixed in the amperometric detection reservoir by screws...     

The toxicity of Cu~(2+) to Microcystis aeruginosa using dielectric spectroscopy

Dielectric spectroscopy(DS) was utilized to investigate the toxicity of the Cu2+ solution to Microcystis aeruginosa.It was found that 0.04 mM Cu2+ had no effect on dielectric increment,whereas the Cu2+ concentrations above 0.1 mM decreased the value of Δε/Δε intact.The toxic effect of Cu2+ on M.aeruginosa cells was time-dependent and concentration-dependent.There was a threshold concentration between 0.04 mM and 0.1 mM,which affected the cell membrane,suggesting that Cu2+ at the concentrations higher than 0...     

Constructions of optimal difference systems of sets

Difference systems of sets (DSSs) are combinatorial configurations which were introduced in 1971 by Levenstein for the construction of codes for synchronization. In this paper, we present two kinds of constructions of difference systems of sets by using disjoint difference families and a special type of difference sets, respectively. As a consequence, new infinite classes of optimal DSSs are obtained.     

Approximation for counts of head runs

In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein’s method and coupling.     

On anti-pluricanonical systems of Q-Fano 3-folds

We investigate birationality of the anti-pluricanonical map Φ-m,the rational map defined by the anti-pluricanonical system |-mKX|,on weak Q-Fano 3-folds.