Zero divisors and

Let be a discrete group, the group ring of over and the Lebesgue space of with respect to Haar measure. It is known that if is torsion free elementary amenable, and , then . We will give a sufficient condition for this to be true when , and in the case we will give sufficient conditions for this to be false when .

     

On the non-existence of -uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems

In this paper fitted finite difference methods on a uniform mesh with internodal spacing , are considered for a singularly perturbed semilinear two-point boundary value problem. It is proved that a scheme of this type with a frozen fitting factor cannot converge -uniformly in the maximum norm to the solution of the differential equation as the mesh spacing goes to zero. Numerical experiments are presented which show that the same result is true for a number of schemes with variable fitting factors.

     

On boundary properties of the components of polyharmonic functions

The following two classes of functions are introduced forp0: the classCU ^p (G) of uniformly continuous functions of orderp in a domainG , and the classM ^p (G) of functions of the boundedness of orderp inG. Criterions are established for ann-analytic function to belong to each of these classes.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 821–834, June, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-013766     

Baire and

Let be a locally compact Hausdorff space and let be the Banach space of all bounded complex Radon measures on . Let and be the -rings generated by the compact subsets and by the compact subsets of , respectively. The members of are called Baire sets of and those of are called -Borel sets of (since they are precisely the -bounded Borel sets of ). Identifying with the Banach space of all Borel regular complex measures on , in this note we characterize weakly compact subsets of in terms of the Baire and -Borel restrictions of the members of . These characterizations permit us to give a generalization of a theorem of Dieudonné which is stronger and more natural than that given by Grothendieck.

     

Convergence of random walks on the circle generated by an irrational rotation

Fix . Consider the random walk on the circle which proceeds by repeatedly rotating points forward or backward, with probability , by an angle . This paper analyzes the rate of convergence of this walk to the uniform distribution under ``discrepancy' distance. The rate depends on the continued fraction properties of the number . We obtain bounds for rates when is any irrational, and a sharp rate when is a quadratic irrational. In that case the discrepancy falls as (up to constant factors), where is the number of steps in the walk. This is the first example of a sharp rate for a discrete walk on a continuous state space. It is obtained by establishing an interesting recurrence relation for the distribution of multiples of which allows for tighter bounds on terms which appear in the Erdös-Turán inequality.

     

用支持向量机建立中药有效成分聚集体的预测模型

化合物可以形成聚集体, 这种分子聚集体可能对靶点具有混杂抑制活性. 在中药中已经发现这种现象, 为了进一步研究这种现象,使用支持向量机(SVM)方法建立了分子形成聚集体的分类预测模型. 研究表明, 这个模型具有良好的预测能力, 并且具有稳定性. 通过使用现有化合物对该模型进行验证, 发现该模型具有良好的推广能力. 这个模型被用于对中草药有效成分三维结构与性质数据库(CHDD)中的分子的预测.     

2,2'－联吡啶桥连的双－4,4'-联吡啶哑铃型化合物的合成

二甘醇2与对甲苯磺酰氯在CH_2Cl_2中，0 ℃～r.t.及Et_3N存在下反应得2－ （羟乙氧基）乙醇对甲苯磺酸酯（3），收率88％。化合物3与对叔丁基苯甲酰氯在 CH_2Cl_2中0～5 ℃及吡啶存在下反应得2－（对叔丁基苯甲酰氧基乙氧基）乙醇对 甲苯磺酸酯（4），收率96％。4与对羟苯甲醇在乙腈中及CsF/K_2CO_3存在下70 ℃ 反应得2－（对叔丁基苯甲酰氧基乙氧基）乙氧苄醇（5），收率98％。5与NBS及 PPh_3在THF中，室温下反应得化合物2－（对 丁基苯甲酰氧基乙氧基）乙氧苄溴 （6），收率95％。6与4,4'－联吡啶在乙腈中，60 ℃反应1h得N－[2－（对叔丁基 苯甲酰氧基乙氧基）乙氧苄基]－4,4'－联吡啶六氟磷酸盐（7），收率85％。7与 α,α－二（溴甲基）－2,2'－联吡啶在乙腈中，油浴60 ℃反应36h，得到标题化 合物，产率为45％。     

Prediction by support vector machines and analysis by Z-score of poly-l-proline type II conformation based on local sequence

In recent years, the poly-L-proline type II (PPII) conformation has gained more and more importance. This structure plays vital roles in many biological processes. But few studies have been made to predict PPII secondary structures computationally. The support vector machine (SVM) represents a new approach to supervised pattern classification and has been successfully applied to a wide range of pattern recognition problems. In this paper, we present a SVM prediction method of PPII conformation based on local sequence. The overall accuracy for both the independent testing set and estimate of jackknife testing reached approximately 70%. Matthew's correlation coefficient (MCC) could reach 0.4. By comparing the results of training and testing datasets with different sequence identities, we suggest that the performance of this method correlates with the sequence identity of dataset. The parameter of SVM kernel function was an important factor to the performance of this method. The propensities of residues located at different positions were also analyzed. By computing Z-scores, we found that P and G were the two most important residues to PPII structure conformation.     

工件有到达时间及可拒绝下的同类平行机排序问题的近似算法

本文研究工件有到达时间且可拒绝下的同类平行机排序问题。在该问题中, 给定一个待加工工件集, 每个工件在到达之后, 可以被选择安排到$m$台同类平行机器中的某一台机器上进行加工, 也可以被选择拒绝加工, 但需支付一定的拒绝惩罚费用。目标函数是最小化接受工件集的最大完工时间与拒绝工件集的总拒绝费用之和。当$m$为固定常数时, 设计了一个伪多项式时间动态规划精确算法; 当$m$为任意输入时, 设计了一个近似算法, 当接受工件个数大于$(m-1)$时, 该算法近似比为3, 当接受工件个数小于$(m-1)$时, 该算法近似比为$(2+\rho)$, 其中$\rho$为机器加工速度最大值和最小值的比值。最后通过算例演示了算法的运行。     

带惩罚的相同容量k-均值问题的局部搜索算法

经典$k$-均值问题是一类应用广泛的聚类问题,它是指给定$\mathbb{R}^d$中观测点集合$D$和整数$k$,目的是在空间中寻找$k$个点作为中心集合$S$,使得集合$D$中的每个观测点到$S$中离它最近的中心的距离平方求和最小。这是个NP-难问题。经典$k$-均值问题有很多推广,本文研究的带惩罚的相同容量$k$-均值问题就是其中之一。与经典$k$-均值问题相比,惩罚性质是指每个观测点都给定惩罚费用,当某个观测点到最近中心的距离大于惩罚费用时,其对目标函数的贡献就用该观测点的惩罚费用来代替最近的距离的平方,相同容量约束要求每个中心至多连接$U$个观测点。针对这种问题,我们设计了局部搜索算法,该算法在至多选取$（3+\alpha）k$个中心的情况下,可以达到$\beta$-近似,其中,参数$\alpha>34$,$\beta>\frac{\alpha+34}{\alpha-34}$。