On Two Theorems of Finite Solvable Groups

For a finite group G, let T（G） denote a set of primes such that a prime p belongs to T（G） if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions： （1） G has a p-complement for each p∈T（G）; （2）│T（G）│= 2： （3） the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T（G）; then G either is solvable or G/Sol（G）≌PSL（2, 7） where Sol（G） is the largest solvable normal subgroup of G.     

Some New uniform frames with block size four and index one or three

In this paper, some new uniform frames with block size four and index one or three are obtained. The known existence results for (4,1)‐frames and (4,3)‐frames are both improved to the extent that only a finite number of possible exceptions remain. © 2003 Wiley Periodicals, Inc.     

Preparation of a cyclodextrin dimer linked with a bis(picolinyl)cystine moiety and its intra- and intermolecular inclusion behavior

A novel cyclodextrin (CD) dimer linked with a bis(picolinyl)cystine (Cys) moiety was prepared by the coupling of Boc-protected Cys with amino-modified CDs, followed by deprotection of the Boc groups and bispicolinylation. The dimer showed less affinity to an organic guest molecule compared to that of a native CD monomer. It was attributed to an intramolecular inclusion of the pyridine moiety into CD cavity. The dimer caused significant increase of its organic guest affinity by an addition of a copper ion. The included pyridine group may come out of a CD cavity to bind the copper ion and the two CDs included cooperatively and intermolecularly a guest molecule with high affinity.     

Thermolyzable polymer networks and star polymers containing a novel,compact, degradable acylal‐based dimethacrylate cross‐linker: Synthesis,characterization, and thermolysis

A compact, cleavable acylal dimethacrylate cross‐linker, 1,1‐ethylenediol dimethacrylate (EDDMA), was synthesized from the anhydrous iron(III) chloride‐catalyzed reaction between methacrylic anhydride and acetaldehyde. The ability of EDDMA to act as cross‐linker was demonstrated by using it for the preparation of one neat cross‐linker network, four star polymers of methyl methacrylate (MMA), and four randomly cross‐linked MMA polymer networks using group transfer polymerization (GTP). For comparison, the corresponding polymer structures based on the commercially available ethylene glycol dimethacrylate (EGDMA) cross‐linker (isomer of EDDMA) were also prepared via GTP. The number of arms of the EDDMA‐based star polymers was lower than that of the corresponding EGDMA polymers, whereas the degrees of swelling in tetrahydrofuran of the EDDMA‐based MMA networks were higher than those of their EGDMA‐based counterparts. Although none of the EDDMA‐containing polymers could be cleanly hydrolyzed under basic or acidic conditions, they could be thermolyzed at 200 °C within 1 day giving lower molecular weight products. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5811–5823, 2007     

Brauer第24问题的推广

本文对Ｂｒａｕｅｒ第２４问题［１］作了推广．利用Ｄａｄｅ关于循环块的理论得到如下结果：设Ｇ是有限群，Ｐ是Ｇ的循环Ｓｙｌｏｗｐ子群．设｜Ｐ｜＝ｐａ，ａ为正整数．令Ｐｉ为Ｐ中唯一的ｐｉ阶子群，１ｉａ．则｜Ｃｌ（Ｇ）｜＝｜Ｃｌ（ＮＧ（Ｐｉ））｜的充分必要条件为ＰｉＧ．     

群体决策的偏好协调性检验

对于一类群体决策问题，本文引进群体的偏好协调性指标，并且给出了偏好协调性指标的统计检验．在此基础上，还提出一个求该类群体决策问题的方法，以及讨论了群体的偏好快调性指标和群体决策结果间的关系．     

Strongly Modular Subgroup in Finite Group

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Cyclic BSEC of block size 3

Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao and Stufken in 1988. In this note, we discuss constructions of these designs having cyclic automorphisms. We use Langford sequences to construct all possible cyclic BSEC (or CBSEC) with block size 3 and λ = 1,2, which establishes the necessary and sufficient conditions for such designs. Some constructions of the balanced sampling plan avoiding adjacent units, a generalization of BSEC, are also given for fixed λ.     

In situ Synthesis of Oligonucleotides on Plasma Treated Polypropylene Microporous Membrane

Polypropylene microporous membranes were treated with plasma in a mixture of N2 and H2 (1:2 in volume). Attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR), X-ray photoelectron spectroscopy (XPS) and ultra-violet (UV) spectra demonstrated the success of grafting amino groups. The density of the polar amino groups on the membrane surface is about 0.59 μmol/cm^2. The as-treated membranes were successively applied to the in situ synthesis of oligonucleotides and an average coupling yield was more than 98%. The surface feature of the treated membrane is suggested to be responsible for its advantage over a glass slide.