Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations

This paper gives a modification of a class of stochastic Runge-Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

Fuzzy closure systems on L—ordered sets

In this paper, notions of fuzzy closure system and fuzzy closure L —system on L —ordered sets are introduced from the fuzzy point of view. We first explore the fundamental properties of fuzzy closure systems. Then the correspondence between fuzzy closure systems (fuzzy closure L —systems) and fuzzy closure operators is established. Finally, we study the connections between fuzzy closure systems and fuzzy Galois connections. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

基于未确知测度理论的工业企业经济效益评价

介绍了工业企业经济效益评价的经济指标,建立了基于未确知测度理论的多属性综合评价方法.在确定各评价对象的属性权重时,采用熵值法这一客观性方法来确定.通过实例,将这种方法应用于具体的工业企业经济效益的评价,为评价企业经济效益提供了一种量化处理的方法,从而能够更直观、更合理地分析评价企业的经济效益状况.     

C~n上Fock空间之正交补空间上的对偶Toeplitz算子的紧性

讨论C~m上Fock空间之正交补空间上以平方可积函数为符号的对偶Toeplitz算子,并给出其有界性与紧性的等价判别条件.     

Lebesgue积分几何意义的推广

证明了非负有界函数的Lebesgue上积分等于函数下方图形的Lebesgue外测度,其Lebesgue下积分等于函数下方图形的Lebesgue内测度,从而将积分的几何意义从可测情形推广到一般情形.     

Bruceines K and L from the Ripe Fruits of Brucea javanica

Bruceine K ( 1 ), a pentacyclic C₂₀‐quassinoid bearing a unique 12,20‐epoxy moiety, and bruceine L ( 2 ), along with the ten known compounds (6S,7E)‐6,9,10‐trihydroxy‐ and (6S,7E)‐6,9‐dihydroxymegastigma‐4,7‐dien‐3‐one ( 3 and 4 , resp.), cleomiscosins A–C, luteoline, quercetine, bruceantinol, pinoresinol, and thevetiaflavone, were isolated from the ripe fruits of Brucea javanica. Bruceines K ( 1 ) and L ( 2 ) were determined to be (1β,2α,11β,12β,14ξ,15β)‐12,20‐epoxy‐1,2,11,13,14,15‐hexahydroxypicras‐3‐en‐16‐one and (1β,2α,11β,12β,15β)‐13,20‐epoxy‐1,2,11,12‐tetrahydroxy‐16‐oxo‐15‐(senecioyloxy)picras‐3‐en‐21‐oic acid methyl ester (senecioic acid=3‐methylbut‐2‐enoic acid), respectively, on the basis of NMR (¹H‐ and ¹³C‐NMR, DEPT, ¹H,¹H‐COSY, NOESY, HMQC, and HMBC) and ESI‐MS data. Among the known compounds, (6S,7E)‐6,9,10‐trihydroxy‐ and (6S,7E)‐6,9‐dihydroxymegastigma‐4,7‐dien‐3‐one ( 3 and 4 , resp.), cleomiscosin C, luteoline, quercetine, and thevetiaflavone were isolated for the first time from the Brucea plants.     

The statistical overlap theory of chromatography using power law (fractal) statistics

The chromatographic dimensionality was recently proposed as a measure of retention time spacing based on a power law (fractal) distribution. Using this model, a statistical overlap theory (SOT) for chromatographic peaks is developed that estimates the number of peak maxima as a function of the chromatographic dimension, saturation and scale. Power law models exhibit a threshold region whereby below a critical saturation value no loss of peak maxima due to peak fusion occurs as saturation increases. At moderate saturation, behavior is similar to the random (Poisson) peak model. At still higher saturation, the power law model shows loss of peaks nearly independent of the scale and dimension of the model. The physicochemical meaning of the power law scale parameter is discussed and shown to be equal to the Boltzmann-weighted free energy of transfer over the scale limits. The scale is discussed. Small scale range (small β) is shown to generate more uniform chromatograms. Large scale range chromatograms (large β) are shown to give occasional large excursions of retention times; this is a property of power laws where "wild" behavior is noted to occasionally occur. Both cases are shown to be useful depending on the chromatographic saturation. A scale-invariant model of the SOT shows very simple relationships between the fraction of peak maxima and the saturation, peak width and number of theoretical plates. These equations provide much insight into separations which follow power law statistics.