Rehabilitation of the Gauss-Jordan algorithm

Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.     

K(o)the-Bochner空间的凸性

本文利用K(o)the函数空间的性质以及K(o)the函数空间与K(o)the-Bochner空间的关系,讨论了K(o)the-Bochner空间E(X)的凸性,主要结果如下:(a)给出E(X)的端点的充分条件,得到了E(X)严格凸的判据,相应地推广了Lp(μ,X)以及LΦ(X)的结果;(b)讨论了E(X)的弱局部一致凸和局部完全k-凸;(c)刻画了E(X)的强凸,给出了E(X)强凸的充要条件.     

Non-universal critical behaviour of heteronuclear dimers on a square lattice––A Monte Carlo study

Monte Carlo simulation within the grand canonical ensemble, the histogram reweighting technique, and finite size scaling analysis are used to explore the phase behaviour of heteronuclear dimers, composed of A and B type atoms, on a square lattice. We have found that for the models with attractive BB and AB nearest-neighbour energy, u_BB=u_AB=−1, and for non-repulsive energy between AA nearest-neighbour sites, u_AA<0, the system belongs to the universality class of the two-dimensional Ising model. However, when u_AA>0, the system exhibits a non-universal critical behaviour. We have evaluated the dependences of the critical point characteristics on the value of u_AA.     

弱(L_1,L_2)-BLD映射的正则性

本文首先将文［１］中的ＢＬＤ映射推广为弱（Ｌ１，Ｌ２）－ＢＬＤ映射，并证明了如下正则性结果：存在两个可积指数 Ｐ１＝Ｐ１（ｎ，Ｌ１，Ｌ２）＜ｎ＜ｑ１＝ｑ１（ｎ，Ｌ１，Ｌ２），使得对任意弱（Ｌ１，Ｌ２）－ＢＬＤ映射ｆ∈（Ω，Ｒｎ），都有ｆ∈（Ω，Ｒｎ），即ｆ为（Ｌ１，Ｌ２）－ＢＬＤ映射．     

Asymptotique de la norme $L^2$ d'un cycle géodésique dans les revêtements de congruence d'une variété hyperbolique arithmétique

Let M be an arithmetic hyperbolic manifold and be a codimension 1 geodesic cycle. In this paper, we study the asymptotic growth of the -norm of the lifts of F in the congruence tower above M. We obtain an explicit value for the growth rate of this norm. In particular, we provide a new proof of a celebrated result of Millson [Mi] on the homology of the arithmetic hyperbolic manifolds. The method is quite general and gives a new way of getting non zero homology classes in certain locally symmetric spaces. Received: 20 April 2001; in final form: 26 September 2001 / Published online: 28 February 2002     

Biodegradable/biocompatible ABC triblock copolymer bearing hydroxyl groups in the middle block

New biodegradable/biocompatible ABC block copolymers, poly(ethylene oxide)‐b‐poly(glycidol)‐b‐poly(L ,L ‐lactide) (PEO‐PGly‐PLLA), were synthesized. First, PEO‐b‐poly(1‐ethoxyethylglycidol)‐b‐PLLA was synthesized by a successive anionic ring‐opening copolymerization of ethylene oxide, 1‐ethoxyethylglycidyl ether, and L ,L ‐lactide initiated with potassium 2‐methoxyethanolate. In the second step, the 1‐ethoxyethyl blocking groups of 1‐ethoxyethylglycidyl ether were removed at weakly acidic conditions leaving other blocks intact. The resulting copolymers were composed of hydrophilic and hydrophobic segments joined by short polyglycidol blocks with one hydroxyl group in each monomeric unit. These hydroxyl groups may be used for further copolymer transformations. The PEO‐PGly‐PLLA copolymers with a molecular weight of PLLA blocks below 5000 were water‐soluble. Above the critical micellar concentration (ranging from 0.05 to1.0 g/L, depending on the composition of copolymer), copolymers formed macromolecular micelles with a hydrophobic PLLA core and hydrophilic PEO shell. The diameters of the micelles were about 25 nm. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3750–3760, 2003     

贝克曼AllegraTM21R型超高速离心机故障排除一例

贝克曼Allegra^TM 21R型超高速离心机开机后，操作面板上出现错误代码“28”，离心机不旋转。离心机的电机采用无刷感应驱动，由电机驱动电源模块BSMl0GD60DN2驱动离心机的电机。故障是由于电源模块BSMl0GD60DN2损坏引起的。采用东芝三相桥式IGBT电源模块MG25Q6ES42代替BSMl0GD60DN2，并更换已烧毁的栅极电阻后。开机试验，仪器恢复正常。     

Crystallization and morphology of poly(vinylidene fluoride)/poly(3‐hydroxybutyrate) blends. I. Spherulitic morphology and growth by polarized microscopy

The development of the poly(3‐hydroxybutyrate) (PHB) morphology in the presence of already existent poly(vinylidene fluoride) (PVDF) spherulites was studied by two‐stage solidification with two separate crystallization temperatures. PVDF formed irregular dendrites at lower temperatures and regular, banded spherulites at elevated temperatures. The transition temperature of the spherulitic morphology from dendrites to regular, banded spherulites increased with increasing PVDF content. A remarkable amount of PHB was included in the PVDF dendrites, whereas PHB was rejected into the remaining melt from the banded spherulites. When PVDF crystallized as banded spherulites, PHB could consequently crystallize only around them, if at all. In contrast, PHB crystallized with a common growth front, starting from a defined site in the interfibrillar regions of volume‐filling PVDF dendrites. It formed by itself dendritic spherulites that included a large number of PVDF spherulites. For blends with a PHB content of more than 80 wt %, for which the PVDF dendrites were not volume‐filling, PHB first formed regular spherulites. Their growth started from outside the PVDF dendrites but could later interpenetrate them, and this made their own morphology dendritic. These PHB spherulites melted stepwise because the lamellae inside the PVDF dendrites melted at a lower temperature than those from outside. This reflected the regularity of the two fractions of the lamellae because that of those inside the dendrites of PVDF was controlled by the intraspherulitic order of PVDF, whereas that from outside was only controlled by the temperature and the melt composition. The described morphologies developed without mutual nucleating efficiency of the components. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 873–882, 2003     

2-乙酰氨基-3,4,6-三乙酰葡萄糖的合成

细菌内毒素(ＬＰＳ)是革兰氏阳性阴性菌细胞外膜层的主要成分,由其引起的革兰氏阴性杆菌脓度症和休克是导致战创伤病人死亡的主要原因之一。而从类脂Ａ(ＬｉｐｉｄＡ)的结构出发,以非肽类物质拮抗内毒素受体ＣＤ-14为治疗手段的研究在国外刚刚起步。2-乙酰氨基-3,4,6-三乙酰葡萄糖是合成ＬｉｐｉｄＡ结构类似物的重要中间体[1,2]。它的合成一般是通过氨基葡萄糖五乙酸酯的选择性水解[3-6]脱去一个乙酰基得到。氨基葡萄糖五乙酸酯是通过氨基葡萄糖的乙酰化反应得到的,由于氨基葡萄糖不稳定,一般是用氨基葡萄糖的盐酸盐作为起始原料。由于…