A Simple Proof for a Property of the Vector Space Ⅴ Over the Field F

<正> In this paper we'll prove a fundameutal property of the vector space by means of the ex-tension field,i.e.the numbers of the elements of a basis of the vector space V over the field Fequal to the d imensions(V:F).     

Constructive and Destructive Two-Pulse Excitation Investigated with a White-Light Michelson Interferometer

Linear propagation of two pulses through methanol solution of aluminum phthalocyanine chloride is investigated using a modified white-light Michelson interferometer. The observed coherence time of the white light is 6 fs, and the separation between the two-excitation pulses is set to about 10 fs. The excitation is dependent on the phase-relation between the two pulses. We have observed an enhancement of the excitation when the two pulses are in-phase and strong suppression of the excitation when the two pulses are out of phase by π.     

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.     

Finite-Type Invariants of Cubic Complexes

The paper is for a general audience and may serve as a preliminary introduction to the theory of finite-type invariants.     

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.     

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.     

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.     

Optimality for set functions with values in ordered vector spaces

Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG() _D . The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably.     

有机磷酸酯类化合物气相色谱定量结构保留关系研究

采用分子电性距离矢量(MEDV)表征有机磷酸酯类化合物的分子结构,运用多元线性回归建立定量结构-色谱保留关系(QSRR)模型,同时采用逐步回归结合统计检测对模型进行变量筛选,建立了35个有机磷酸酯类化合物在3种不同固定相(OV-101,DB-1701和DB-WX)上气相色谱保留指数(RI)与MEDV的定量相关模型.在3种固定相上的QSRR模型的建模计算值复相关系数(R)、留一法(leave-one-out)交互校验复相关系数(QCV)分别为0.998 0和0.995 1(OV-101);0.996 3和0.989 6(DB-1701);0.993 7和0.984 1(DB-WX),表明模型具有良好估计能力与稳定性.     

苯丙氨酸改性树枝状聚赖氨酸的合成及表征

以双芴甲氧羰基赖氨酸(Di- Fmoc -Lysine)为支化单元采用固相多肽合成技术制备了一种树枝状聚赖氨酸.该聚合物表面活性氨基通过与芴甲氧羰基苯丙氨酸(Fmoc- Phe)反应获得表面完全替代的苯丙氨酸改性树枝状聚赖氨酸.产物的分子量和结构经MS和NMR进行了表征.研究结果表明,利用该方法得到的产物分子量单一,是一种潜在的理想非病毒治疗载体.