Efficient integration for a class of highly oscillatory integrals

This paper presents some quadrature methods for a class of highly oscillatory integrals whose integrands may have singularities at the two endpoints of the interval. One is a Filon-type method based on the asymptotic expansion. The other is a Clenshaw-Curtis-Filon-type method which is based on a special Hermite interpolation polynomial and can be evaluated efficiently in O(N log N) operations, where N + 1 is the number of Clenshaw-Curtis points in the interval of integration. In addition, we derive the corresponding error bound in inverse powers of the frequency ω for the Clenshaw-Curtis-Filon-type method for the class of highly oscillatory integrals. The efficiency and the validity of these methods are testified by both the numerical experiments and the theoretical results.     

Computation of generalized differentials in nonlinear complementarity problems

Let f and g be continuously differentiable functions on R ⁿ . The nonlinear complementarity problem NCP(f,g), 0≤f(x)⊥g(x)≥0, arises in many applications including discrete Hamilton-Jacobi-Bellman equations and nonsmooth Dirichlet problems. A popular method to find a solution of the NCP(f,g) is the generalized Newton method which solves an equivalent system of nonsmooth equations F(x)=0 derived by an NCP function. In this paper, we present a sufficient and necessary condition for F to be Fréchet differentiable, when F is defined by the “min” NCP function, the Fischer-Burmeister NCP function or the penalized Fischer-Burmeister NCP function. Moreover, we give an explicit formula of an element in the Clarke generalized Jacobian of F defined by the “min” NCP function, and the B-differential of F defined by other two NCP functions. The explicit formulas for generalized differentials of F lead to sharper global error bounds for the NCP(f,g).     

基于Vague集的水电工程方案模糊综合评价

水利工程建设方案决策是多目标综合评价问题,系统指标信息具有复杂、多变,模糊、不确定等特点,采用Vague集相似度量评价模型构建水利工程建设方案综合决策模型,建立基于Vlague集的指标隶属度计算方法,构造基于Vague集相似度的多目标方案评价.针对建设方案决策评价指标的不确定性,通过肯定、踌躇、否定的Vague集相似度量概念延伸了传统模糊集的评价、分析方式.将方法应用于水利工程建设方案决策实例,取得较为满意的结果,表明了方法的合理可行性,为水利工程的建设方案评价提供了科学决策的新途径.     

改进模糊一致矩阵及其在工程评标中的应用

基于模糊一致矩阵的决策方法的不足之处,对模糊优先关系矩阵的构造、模糊一致矩阵的转化、排序方法等方面进行了改进.将改进后的决策方法用于建筑工程的综合评价,将决策者的思维量化,由定性向定量进行转化,构造出建筑工程的综合评价方案优选的改进模糊一致矩阵数学模型,为建筑工程评标数学模型的建立提供了影响因素量化排序的分析方法.实证分析结果表明,改进后的决策方法能更好地反映参评对象的实际情况.     

Oxidation of Au by surface OH: nucleation and electronic structure of gold on hydroxylated MgO(001)

The nucleation and electronic structure of vapor-deposited Au on hydroxylated MgO(001) surfaces has been investigated under ultrahigh vacuum conditions. Hydroxylated MgO(001) surfaces with two different hydroxyl coverages, 0.4 and 1 monolayer, respectively, were prepared by exposure to water (D(2)O) at room temperature. Scanning tunneling microscopy experiments show significantly higher gold particle densities and smaller particle sizes on the hydroxylated MgO surface as compared to gold deposited on clean MgO(001). Infrared spectroscopy and X-ray photoelectron spectroscopy experiments were performed to reveal details about the initial nucleation of gold. Gold atoms are found to chemically interact with a specific type of hydroxyl groups on the MgO surface, leading to the formation of oxidized gold particles. The enhanced adhesion of Au particles, which is due to the formation of strong Au-O interfacial bonds, is responsible for the observed higher stability of small Au clusters toward thermal sintering on hydroxylated MgO surfaces. The results are compared to similar studies on Au/TiO(2)(110) model systems and powder samples prepared by the deposition-precipitation route.     

Examining the mechanism of action of a kinesin inhibitor using stable isotope labeled inhibitors for cross-linking (SILIC)

It is difficult to determine a chemical inhibitor's binding site in multiprotein mixtures, particularly when high-resolution structural studies are not straightforward. Building upon previous research involving photo-cross-linking and the use of mixtures of stable isotopes, we report a method, Stable Isotope Labeled Inhibitors for Cross-linking (SILIC), for mapping a small molecule inhibitor's binding site in its target protein. In SILIC, structure-activity relationship data is used to design inhibitor analogues that incorporate a photo-cross-linking group along with either natural or 'heavy' stable isotopes. An equimolar mixture of these inhibitor analogues is cross-linked to the target protein to yield a robust signature for identifying inhibitor-modified peptide fragments in complex mass spectrometry data. As a proof of concept, we applied this approach to an ATP-competitive inhibitor of kinesin-5, a widely conserved motor protein required for cell division and an anticancer drug target. This analysis, along with mutagenesis studies, suggests that the inhibitor binds at an allosteric site in the motor protein.     

New Phenylphenalene Derivatives from Water Hyacinth (Eichhornia crassipes)

Water hyacinth (Eichhornia crassipes) is a cause of great concern in terms of environmental and agricultural impacts in many parts of the world. Phytochemical investigation of water hyacinth led to the isolation of six new phenylphenalenes, 2,3‐dihydro‐3,9‐dihydroxy‐5‐methoxy‐4‐phenyl‐1H‐phenalen‐1‐one ( 1 ), 2,3‐dihydro‐8‐methoxy‐9‐phenyl‐1H‐phenalene‐1,4‐diol ( 2 ), 2,3‐dihydro‐4,8‐dimethoxy‐9‐phenyl‐1H‐phenalen‐1‐ol ( 3 ), 2,3‐dihydro‐9‐(4‐hydroxyphenyl)‐8‐methoxy‐1H‐phenalene‐1,4‐diol ( 4 ), 2,6‐dimethoxy‐9‐phenyl‐1H‐phenalen‐1‐one ( 5 ), and 7‐(4‐hydroxyphenyl)‐5,6‐dimethoxy‐1H‐phenalen‐1‐one ( 6 ), together with the four known compounds 7 – 10 . Their structures were elucidated by spectrometric methods including 1D‐ and 2D‐NMR, and MS analysis. These compounds may be involved in allelopathic interactions of water hyacinth with neighboring plants.     

Two Antioxidant Alkaloids from Portulaca oleracea L.

Two alkaloids, oleraceins F and G, were isolated from Portulaca oleracea L., and their structures were determined as methyl (2S)‐6‐[(β‐D ‐glucopyranosyl)oxy]‐2,3‐dihydro‐5‐hydroxy‐1‐[(2E)‐3‐(4‐hydroxy‐3‐methoxyphenyl)prop‐2‐enoyl]‐1H‐indole‐2‐carboxylate and methyl (2S)‐6‐[(β‐D ‐glucopyranosyl)oxy]‐2,3‐dihydro‐5‐hydroxy‐1‐[(2E)‐3‐(4‐hydroxyphenyl)prop‐2‐enoyl]‐1H‐indole‐2‐carboxylate, based on their spectroscopic data. Oleraceins F and G exhibited scavenging activity against 1,1‐diphenyl‐2‐picrylhydrazyl (DPPH) radical, with EC₅₀ values of 21.00 and 37.69 μM , respectively.     

Sesquiterpenoids from the Aerial Parts of Inula japonica

Fourteen sesquiterpenoids with an eudesmane C‐atom skeleton, including four new ones, (1β,5α,7β,8β,11β)‐5‐hydroperoxy‐1‐hydroxyeudesm‐4(15)‐eno‐12,8‐lactone ( 1 ), (1β,5α,7β,8β)‐8‐(acetyloxy)‐5‐hydroperoxy‐1‐hydroxycostic acid methyl ester ( 12 ), and a mixture of (1β,3β,4β,7β,8β)‐1,3‐dihydroxyeudesma‐5,11(13)‐dieno‐12,8‐lactone ( 7 ) and (1β,3β,4β,7β,8β,11β)‐1,3‐dihydroxyeudesm‐5‐eno‐12,8‐lactone ( 8 ), were isolated from the aerial parts of Inula japonica (Asteraceae). Their structures were determined by extensive spectroscopic methods, and those of 7 and 12 confirmed by means of single‐crystal X‐ray diffraction analysis.