Irregularities of distribution with respect to strips

Summary A lower bound is established for the strip discrepancy of a broad class of point distributions. The bound implies unbounded strip discrepancy for equally weighted point distributions under favorable conditions. The methods of proof use notions from integral geometry.     

A Characterisation of Posets that Are nearly Antichains

We present a characterisation of posets of size n with linear discrepancy n − 2. These are the posets that are “furthest” from a linear order without being an antichain. This revised version was published online in September 2006 with corrections to the Cover Date.     

The set of toric minimal log discrepancies

We describe the set of minimal log discrepancies of toric log varieties, and study its accumulation points. This work is supported by a 21st Century COE Kyoto Mathematics Fellowship, and a JSPS Grant-in-Aid No 17740011.     

An implicit method for linear ill‐posed problems with perturbed operators

An implicit iterative method is applied to solving linear ill‐posed problems with perturbed operators. It is proved that the optimal convergence rate can be obtained after choosing suitable number of iterations. A generalized Morozov's discrepancy principle is proposed for the problems, and then the optimal convergence rate can also be obtained by an a posteriori strategy. The convergence results show that the algorithm is a robust regularization method. Copyright © 2006 John Wiley & Sons, Ltd.     

关于不含k-C-圈的n阶r-一致超图的若干结果

主要讨论了不含k-C-圈的n阶r-一致超图,对不同的k,分别得出了它的极大边数的一个下界,并且得出在有些情况下它的下界是最大的.另外,我们得到了Krn含k-C-圈的一个充分必要条件.     

Uniform random number generation

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject.     

用ATRP法构筑核壳型梯度极性的多羟基多臂星状超支化聚合物及聚合物刷——双层聚合物刷的合成与表征

设计并通过原子转移自由基聚合方法 (ATRP)合成了核壳型多羟基多臂星状超支化聚合物刷 .以 2 溴异丁基酰溴封端的超支化聚 (3 乙基 3 羟甲基氧杂环丁烷 ) (HP Br)作为大分子引发剂 ,采用Cu(I)Br和N ,N ,N′ ,N′ ,N″ 五甲基二乙基三胺 (PMDETA)催化体系 ,在丁酮与丙醇的混和溶液中 ,通过甲基丙烯酸羟乙酯(HEMA)的ATRP溶液聚合 ,得到了一系列含有大量羟基的多臂星状超支化聚合物刷 (HP g PHEMA) ,并考察了其羟基的活性 ,发现羟基还可以与苯甲酰氯发生反应 .产物的结构和热性能用1 H NMR、FTIR、GPC、TGA、DSC等进行了表征和测试 .     

高聚物亚浓溶液区标度律的蒙特卡洛模拟

利用蒙特卡洛模拟方法对线形链和星形键在亚浓溶液区的标度律作了验证与讨论。我们的计算结果证明线形链渗透压Π与体积分数Φ在亚浓溶液区的标度规律是与德热纳的理论结果相一致的。同时还证明了星形链在亚浓溶液区具有与线形链相同的标度行为。     

水溶性含C_(60)聚电解质的制备及其与重氮树脂自组装膜AFMFFM的初步研究

通过BPO引发的溶液聚合 ,合成了水溶性的星状C6 0 苯乙烯 苯乙烯磺酸钠的三元共聚物 [Star shapedC6 0 poly(St SS) ],运用自组装技术 ,在水溶液中 ,含C6 0 的三元共聚物与重氮树脂 (Diazoresin)通过正负离子间的吸附力在云母基片上交替一层一层有序地组装成固体膜 .自组装膜经紫外光幅照反应 ,通过重氮基的分解 ,层间连接的离子键转变成共价键 ,从而增加薄膜的稳定性和堆砌密度 .用原子力显微镜 摩擦力显微镜(AFM FFM)考察了C6 0 在膜中的承载作用及比较不同链结构、不同链长、不同层数自组装膜的表面形貌和微摩擦性能 .初步的研究结果显示了聚合物薄膜的微摩擦性能与聚合物的化学结构、链长和膜的层数有密切关系