一些新的数论函数及其均值公式

对于给定的自然数m,我们利用最大公约数和最小公倍数定义数论函数(m,n)和[m,n]/m.本文主要目的是研究这两个新的函数的渐近性质,利用解析方法得到这两个函数的几个渐近公式.     

Fast neighborhood search for the single machine total weighted tardiness problem

Most successful heuristics for solving 1||∑w_jT_j are based on swap moves. We present an algorithm which improves the complexity of searching the swap neighborhood from O(n³) to O(n²). We show that this result also improves the complexity of the recently developed dynasearch heuristics.     

Vector Lattices on a Set of Two Generators

It is proved that the center of an automorphism group Aut(FVL2) of a free vector lattice FVL2 on a set of two free generators is isomorphic to a multiplicative group of positive reals. It is shown that the free vector lattice FVL2 has an isomorphic representation by continuous piecewise linear functions of the real line; as a consequence, the ideal lattice and the root system for rectifying ideals in FVL2 are amply described. Similar results are obtained for a free vector lattice FVL2 _Q 2 generated by two elements over a field of rational numbers.     

Least‐squares finite element method on adaptive grid for PDEs with shocks

We apply the least‐squares finite element method with adaptive grid to nonlinear time‐dependent PDEs with shocks. The least‐squares finite element method is also used in applying the deformation method to generate the adaptive moving grids. The effectiveness of this method is demonstrated by solving a Burgers' equation with shocks. Computational results on uniform grids and adaptive grids are compared for the purpose of evaluation. The results show that the adaptive grids can capture the shock more sharply with significantly less computational time. For moving shock, the adaptive grid moves correctly with the shock. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

回归系数的混合估计与最小二乘估计的一个新的相对效率

本文对具有附加信息的线性回归模型中的混合估计与最小二乘估计给出了一种新的相对效率,研究了新的相对效率与其它几种相对效率的关系,得出了新的相对效率的上、下界.     

The Essential Component of the Solution Set for Vector Equilibrium Problems

In the paper, by using Ky Fan’s section theorem, we obtain an existence theorem for vector equilibrium problems. Motivated by the ideas of Kinoshita and McLennan, we introduce the concept of the essential component of the solution set for vector equilibrium problems, and we prove that there exists at least one essential component of the solution set for every vector equilibrium problem satisfying some conditions. Research was partially supported by the Natural Science Foundation of Guangdong Province, P. R. China.     

广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

Electroencephalogram (EEG) time series classification: Applications in epilepsy

Epilepsy is among the most common brain disorders. Approximately 25–30% of epilepsy patients remain unresponsive to anti-epileptic drug treatment, which is the standard therapy for epilepsy. In this study, we apply optimization-based data mining techniques to classify the brain's normal and epilepsy activity using intracranial electroencephalogram (EEG), which is a tool for evaluating the physiological state of the brain. A statistical cross validation and support vector machines were implemented to classify the brain's normal and abnormal activities. The results of this study indicate that it may be possible to design and develop efficient seizure warning algorithms for diagnostic and therapeutic purposes. Research was partially supported by the Rutgers Research Council grant-202018, the NSF grants DBI-980821, CCF-0546574, IIS-0611998, and NIH grant R01-NS-39687-01A1.     

New reals: Can live with them,can live without them

We give a self‐contained proof of the preservation theorem for proper countable support iterations known as “tools‐preservation”, “Case A” or “first preservation theorem” in the literature. We do not assume that the forcings add reals. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diffusion in three-dimensional random systems at their percolation thresholds

Extensive Monte Carlo simulations of theant-in-the-labyrinth problem on randomL* L* L simple cubic lattices are performed, forL up to 960 on a CRAY-YMP supercomputer. The exponentk for the rms displacementr witht inrt ^k is found to bek=0.190±0.003. As a second approach, large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality. The diffusion equation is then solved by using the exact enumeration technique. The corresponding critical exponentd ^w is found to be 1/d ^w =0.250±0.003.On leave from I. Institut für Theoretische für Physik, Universität Hamburg, D-2000 Hamburg, Federal Republic of Germany.