There exists no self-dual [24,12,10] code over $${{\mathbb F}_5}$$

Self-dual codes over exist for all even lengths. The smallest length for which the largest minimum weight among self-dual codes has not been determined is 24, and the largest minimum weight is either 9 or 10. In this note, we show that there exists no self-dual [24, 12, 10] code over , using the classification of 24-dimensional odd unimodular lattices due to Borcherds.      

基于综合权重的理想模糊物元多属性决策法及应用

研究了属性指标具有不相容性和模糊性及其指标的权重完全未知的模糊多属性决策问题.分析了目前广泛采用的模糊物元分析法以及仅有主观赋权法或客观赋权法确定其指标权重的缺点.根据物元可拓理论和理想解法的思想,定义了理想模糊物元和负理想模糊物元的概念.利用兼顾主观偏好和客观信息的综合权重赋值法,提出了基于综合权重的理想模糊物元多属性决策方法.该法既能充分利用指标本身所包含的客观信息,又能充分发挥决策者的主观能动性.实例研究结果表明该法能反映出决策方案间的细微差别,能对决策方案的优劣做出更准确有效的评价.     

一个含多参量的反向Hilbert型积分不等式

引入权函数,建立一个含多参量与最佳常数因子的新的反向Hilbert型积分不等式.作为应用,给出了其两个等价式及几个特殊结果.     

Gaining efficiency via weighted estimators for multivariate failure time data

Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper, three weighted estimators are proposed based on three different optimal criteria in terms of the asymptotic covariance of weighted estimators. Simplified close-form solutions are found, which always outperform the working independence estimator. We also prove that the working independence estimator has high statistical efficiency, when asymptotic covariance of derivatives of partial log-likelihood functions is nearly exchangeable or diagonal. Simulations are conducted to compare the performance of the weighted estimator and working independence estimator. A data set from Busselton population health surveys is analyzed using the proposed estimators. This work was supported by National Natural Science Foundation of China (Grant No. 10628104), Fan was also supported by National Institutes of Health (Grant No. R01-GM072611) and Natural Science Foundation (Grant No. DMS-0714554), Zhou was supported by National Natural Science Funds for Distinguisheel Young Scholar (Grant No. 70825004), National Natural Science Foundation of China (Grant Nos. 10731010, 10628104), the National Basic Research Program (Grant No. 2007CB814902), Creative Research Groups of China (Grant No. 10721101) and Leading Academic Disipline Program, the 10 ^th five year plan of 211 Project for Shanghai University of Finance and Economics (the 3 ^rd phase), Cai was supported by National Institutes of Health (Grant No. R01-HL57444)     

基于主客观权重集成的电子商务网站评价方法

研究了不确定决策环境下企业电子商务网站评价问题。利用专家给出的区间互补判断矩阵,获得属性的主观权重;定义了区间数的平均差,提出了一种属性客观权重确定方法——平均差极大化方法;通过加权系数把主观权重与客观权重线性集成,使得到的综合权重同时反映主观和客观程度,并给出了一种基于投影模型的决策方案排序方法。最后通过算例说明该方法的可行性和有效性。     

Weighted boundedness of parametric Marcinkiewicz integral and higher order commutator

In this paper, the weighted boundedness of parametric Marcinkiewicz integral and its commutator with rough kernels are considered. In addition, the weak type norm inequalities for parametric Marcinkiewicz integral and its commutator with different weight functions and Dini kernel are also discussed.     

Living Anionic Polymerization of 4-(α-Alkylvinyl)styrene Derivatives

Summary. The anionic polymerization of four bis-functionalized styrene derivatives with α-alkylvinyl groups have been carried out in THF at −78°C with the initiator prepared from oligo(α-methylstyryl)lithium and potassium tert-butoxide. The four monomers herein used are 4-isopropenylstyrene (4), 3-isopropenylstyrene (5), 2-isopropenylstyrene (6), and 4-(α-isopropylvinyl)styrene (7). It was found that under such polymerization conditions, the vinyl groups of both 4 and 7 are selectively polymerized and the isopropenyl and α-isopropylvinyl groups remain completely intact to afford stable living anionic polymers. As expected, the resulting polymers possessed precisely controlled chain lengths and narrow molecular weight distributions. More importantly, they also possessed the pendant isopropenyl and α-isopropylvinyl group in each monomer unit possible for further modification. On the other hand, the anionic polymerization of either 5 or 6 proceeded more or less along with the unwanted side reactions leading to chain-branching, followed by cross-linking. The positional effect of isopropenyl group on the polymerization and the cause of possible side reactions were discussed.     

Effects of molecular weight and small amounts of d-lactide units on hydrolytic degradation of poly(l-lactic acid)s

Films of poly(l-lactic acid) (PLLA) with different number-average molecular weights (M_n) and d-lactide unit contents (X_d) were made amorphous and the effects of molecular weight and small amounts of d-lactide units on the hydrolytic degradation behavior in phosphate-buffered solution at 37 °C of PLLA were investigated. The degraded films were investigated using gravimetry, gel permeation chromatography, polarimetry, differential scanning calorimetry, X-ray diffractometry, and tensile testing. To exclude the effects of crystallinity on the hydrolytic degradation, the films were made amorphous by melt-quenching. The incorporation of small amounts of d-lactide units drastically enhanced the hydrolytic degradation of PLLA. In the period of 0-32 weeks, the hydrolytic degradation rate constant (k) of PLLA films increased with increasing X_d, while the k values did not depend on M_n. This means that the effects of X_d on the hydrolytic degradation rate of the films are higher than those of M_n. In contrast, in the period of 32-60 weeks neither X_d nor M_n was a crucial parameter to determine k values, probably because in addition to these parameters the differences in the amount of catalytic oligomers accumulated in films and crystallinity affect the hydrolytic degradation behavior of the films. The initially amorphous PLLA films remained amorphous even after the hydrolytic degradation for 60 weeks.     

Molecular weight characterization of poly[(R)-3-hydroxybutyrate] synthesized by genetically engineered strains of Escherichia coli

This study investigated the relationship of growth conditions, host strains and molecular weights of poly[(R)-3-hydroxybutyrate] [P(3HB)] synthesized by genetically engineered Escherichia coli. Various PHA synthases belonging to types I-IV enzymes were expressed in E. coli JM109 under the same experimental conditions, and the molecular weights of the polymers were characterized by gel permeation chromatography. The results demonstrate that P(3HB) polymers have varied molecular weights and polydispersities dependent on the characteristics of the individual PHA synthase employed. P(3HB) with high number-average molecular weights (M_n) [(1.5-4.0) × 10⁶] and narrow polydispersities (1.6-1.8) were synthesized by PHA synthases from Ralstonia eutropha (type I), Delftia acidovorans (type I) and Allochromatium vinosum (type III). Contrary to these, P(3HB) with relatively low M_n [(0.17-0.79) × 10⁶] and broad polydispersities (2.2-9.0) were synthesized by PHA synthases from Aeromonas caviae (type I), Pseudomonas sp. 61-3 (type II) and Bacillus sp. INT005 (type IV). Furthermore, the molecular weights of P(3HB) synthesized under various culture conditions, in various hosts of E. coli and by mutants of PHA synthase were characterized. It was found that, in addition to culture pH [Kusaka et al. Appl Microbiol Biotechnol 1997;47:140], other variances such as culture temperature, host strain and use of mutants are effective in changing polymer molecular weight.     

Calculation of CLD Using Population Balance Equations of Generating Functions: Linear and Non‐Linear Ideal Controlled Radical Polymerization

Population balance equations in terms of generating functions (GF) are used to predict chain length distributions (CLD) of linear and non‐linear ideal controlled radical polymerization (CRP) systems. It is here shown that under simplified conditions analytical solutions for the CLD can be found and moreover the fundamental CLD derived by H. Tobita in 2006 is a limiting case of the more general solutions here presented. In order to deal with more complex CRP systems, solutions based upon the numerical inversion of GF are presented. These studies are also extended to the non‐linear CRP of vinyl/divinyl monomers where multimodal CLDs are predicted to occur.