A multifractal decomposition according to rate of returns

For one‐dimensional simple symmetric random walk, the Hausdorff and packing dimensions of sets of sample paths with prescribed rate of returns to the origin are determined. This gives a multifractal decomposition of the underlying sample space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

模糊集单调型分解定理

模糊集的分解集定理有两种形式，第一种形式与模糊集的λ—截集有关：Ａ＝其中Ａ＿λ是的λ—截集￣［１］．第二种形式与集合套有关：其中Ｈ（λ）为集合套￣［２］或者Ａ＝其中Ｈ（λ）为集合套，Ｑ为（０，１）的可列稠密子集＿［３］，．其实，这两种形式在本文提出的基本模糊集的概念下，可以统一起来成为任何模糊集可以分解为一些（可数或不可数）基本模糊集的和。不仅如此，本文还提出简单模糊集的概念，并证明了任何模糊集都可以表示成为可数个单调上升的简单模糊集的和，或等价地，可以表示成可数个单调上升的简单模糊集的极限，所用的证明方法是构造性的，所以对模糊集的结构也得出了一个清晰的认识．     

On Two Theorems of Finite Solvable Groups

For a finite group G, let T（G） denote a set of primes such that a prime p belongs to T（G） if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions： （1） G has a p-complement for each p∈T（G）; （2）│T（G）│= 2： （3） the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T（G）; then G either is solvable or G/Sol（G）≌PSL（2, 7） where Sol（G） is the largest solvable normal subgroup of G.     

A Monte Carlo simulation of the heterogeneous adsorption of hydrogen ions on metal oxides: Effect of inert electrolyte

Charging of the surface of an oxide caused by the adsorption of hydrogen ions and ions of inert 1:1 electrolyte was investigated by using grand canonical Monte Carlo simulation technique. In particular, adsorption isotherms of protons as well as of ions of the electrolyte together with the resulting charge density of the surface were obtained for different system parameters. Also, the effect of the surface energetic heterogeneity and the concentration of the background electrolyte on the isotherms and the charge density curves was examined. Furthermore, lateral interactions in the mixed adsorbed phase were taken into account in the modeling of the system behavior. The obtained results, in general, suggest that the three factors mentioned above may have substantial influence on the charging mechanism at the liquid/oxide interface.     

A new class of Ornstein transformations with singular spectrum

It is shown that for any family of probability measures in Ornstein type constructions, the corresponding transformation has almost surely a singular spectrum. This is a new generalization of Bourgain's theorem [J. Bourgain, On the spectral type of Ornstein class one transformations, Israel J. Math. 84 (1993) 53–63], same result is proved for Rudolph's construction [D. Rudolph, An example of a measure-preserving map with minimal self-joining and applications, J. Anal. Math. 35 (1979) 97–122].     

Highly sensitive determination of haloperidol in human serum by capillary gas chromatography using a surface ionization detector

A method has been developed for highly sensitive determination of haloperidol in human serum involving a simple extraction procedure followed by gas chromatographic separation. Target components were separated from the extracting solvents with a Van den Berg type solventless sample injector before introduction Into a DB-1 capillary separation column. A surface ionization detector (SID), which has highly selective sensitivity for Substituted amines, was employed for quantitation using bromperidol as an internal standard. Chloroform proved to be the best extracting solvent, yielding a quantitative detection limit of 5 ng/ml (S/N = 2). Comparison of the response to target compounds obtained by the SID, FTD (flame thermionic detector), and FID (flame ionization detector) showed the SID to be superior.     

苯巴比妥的二次微分简易示波伏安法测定

利用苯巴比妥的示波特性 ,分别建立了在0.2mol/LKOH和1.0×10-4mol/LCd2 +-0.1mol/L硼砂底液中直接和间接测定苯巴比妥的二次微分简易示波伏安法 ;直接测定和间接测定的线性范围分别为1.0×10 -5mol/L～1.0×10 -4mol/L和4.0×10 -6mol/L～8.0×10 -5mol/L ;检出限分别为8×10 -6mol/L和2×10 -6mol/L;在直接测定中 ,对6.000×10 -5mol/L苯巴比妥进行10次测定的RSD为4.5 % ;间接测定中 ,对2.000×10 -5mol/L苯巴比妥进行10次测定的RSD为2.6 % ;这一研究表明对于一些在示波分析中灵敏度不高或本身没有示波活性的药物 ,可以利用其与金属离子生成沉淀的方法间接测定 ,从而提高药物测定的灵敏度、拓宽示波分析应用领域     

橡胶中简单剪切与纯剪切的关系

研究了简单剪切与纯剪切的关系，得出了：（１）简单剪切可看成纯剪切加转动，转动角θ有；（２）若简单剪切椭圆的长轴与坐标轴Ｘ的夹角为φ，相应的纯剪椭圆长袖与坐标轴ｙ的夹角为β０，则φ＝β０；（３）橡胶在双向拉伸时剪应变γ的一般表达式为，对简单剪切而言即为     

再论Pedoe不等式的高维推广及应用

本文对欧氏空间E~n中的两个n维单形,给出了著名的Pedoe不等式的一个实质性推广,并讨论了它的应用.     

Multi-objective optimal design of feedback controls for dynamical systems with hybrid simple cell mapping algorithm

This paper presents a study of multi-objective optimal design of full state feedback controls. The goal of the design is to minimize several conflicting performance objective functions at the same time. The simple cell mapping method with a hybrid algorithm is used to find the multi-objective optimal design solutions. The multi-objective optimal design comes in a set of gains representing various compromises of the control system. Examples of regulation and tracking controls are presented to validate the control design.