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.     

Gating processes in Na-channel of biological membrane from the standpoint of superionic phase transition

The method of condensed matter physics is applied to reason out the problem of Na transport through a biological membrane. A similiarity of gating process in Na ion channel to the superionic phase transition is discussed. A possible microscopic mechanism is suggested.     

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.     

麻黄中伪麻黄碱在小鼠组织中的分布研究

为了解麻黄(Herba ephedrae,简称HE)中伪麻黄碱(Pseudoephedrine,简称PE)在小鼠脑、肺、心、肝、肾的分布变化,探讨HE的归经,用GC-MS/SIM法,分析了用药后30、60、120 min PE在小鼠脏器分布量。结果表明,PE于不同时间点在小鼠脏器的分布由多到少的顺序是:30 min时,肺脏(肾脏、肝脏、脑),心脏;60 min时,肾脏,心脏(肝脏),脑,肺脏;120 min时,脑,肾脏,心脏,肝脏(肺脏)。本试验从PE在小鼠体内脏器的分布量初步反映了HE的归经趋势。     

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.     

Suppression of red cell diffusional water permeability by lipophilic solutes

The inhibitory effect of a series of neutral lipophilic solutes (methanol, ethanol, n-propanol, iso-propanol, n-butanol, iso-amylalcohol, n-hexanol, diethylether, nitrobenzene, and pyridine) on the diffusional water permeability (Pd, tot) of bovine erythrocyte membrane at 25 degrees C was studied in comparison to that of p-chloromercuri benzoate (pCMB). Permeability data were obtained by measuring the transmembrane diffusional water exchange time tau(exch) using an 1H-T2 NMR technique. Maximal inhibition by approximately 50% of Pd, tot was produced by 2 mM pCMB which completely blocked the membrane water channels in 20 min, hence suggesting the channel-to-lipid diffusional water permeability ratio of about 1:1. Furthermore, the maximal inhibitory effect of pCMB in combination with the lipophilic solutes was lower than that of pCMB alone. As pCMB does not interfere with the lipid bilayer, and provided that it blocks the water channels in solute presence as well, this confirms that the solutes induce an increase in the lipid-mediated background water permeability contribution (Pd, lipid) by the formation of aqueous leaks in the membrane hydrophobic barrier. However, faster but less efficient in permeability inhibition than pCMB (either alone or combined with solutes) were the lipophilic solutes alone. Taken together, the results indicate that the lipophilic solutes suppress the membrane total permeability Pd, tot by two opposing effects: a reduction of its channel-mediated part (Pd, channel) to the extent exceeding that of a simultaneous Pd, lipid increase. The inhibitory potency of the solutes tested appears to be correlated with their solubility in the membrane medium.     

Photoinduced electron transport process in electrochemical cell I. Phenomenological description

The process of electron transport plays an essential role in the fundamental phenomena of life like photosynthesis, respiration and vision as well as in photoelectronic devices. However, the molecular mechanisms of the electron way and factors governing the transport rate in such systems are still unclear. Several groups have reported theoretical approaches for searching the mechanisms by using statistical mechanics, coherent dynamics and quantum mechanics. The current density vector inside the semiconducting layer is determined. In this paper we consider the problem of transport of electron promoted in the electrochemical cell constructed of two electrodes with the dye molecules immersed in. We describe the process of electron promotion by refractive light wave on the vacuum–semiconductor boundary as well as on the semiconducting electrode and the dye molecule layer in terms of extended phenomenological electrodynamics formalism. The results of our theoretical model show that such a theoretical approach will give more information on the mechanism of electron transport and will give insight in the determination of some electric features of materials.     

Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.