Weakly dependent chains with infinite memory

We prove the existence of a weakly dependent strictly stationary solution of the equation _Xt=F(_Xt−1,_Xt−2,_Xt−3,…;_ξt)$X_t=F(X_{t-1},X_{t-2},X_{t-3},\dots ;{\xi }_t)$ called a chain with infinite memory. Here the innovations  _ξt${\xi }_t$ constitute an independent and identically distributed sequence of random variables. The function F$F$ takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments, the rate of decay of the Lipschitz coefficients of the function F$F$ and the weak dependence properties. From these weak dependence properties, we derive strong laws of large number, a central limit theorem and a strong invariance principle.     

A note on non-reduced Picard schemes

The Picard scheme of a smooth curve and a smooth complex variety is reduced. In this note we discuss which classes of surfaces in terms of the Enriques-Kodaira classification can have non-reduced Picard schemes and whether there are restrictions on the characteristic of the ground field. It turns out that non-reduced Picard schemes are uncommon in Kodaira dimension κ≤0, that this phenomenon can be bounded for κ=2 (general type) and that it is as bad as can be for κ=1.     

Global convergence of the nonmonotone MBFGS method for nonconvex unconstrained minimization

In this paper, we propose a new nonmonotone Armijo type line search and prove that the MBFGS method proposed by Li and Fukushima with this new line search converges globally for nonconvex minimization. Some numerical experiments show that this nonmonotone MBFGS method is efficient for the given test problems.     

Development and Validation of Nonaqueous Capillary Electrophoresis Method for Simultaneous Estimation of Icariin,Icariside II,and Epimedin K in Epimedium Leaves

This paper describes a novel nonaqueous capillary electrophoresis method for the separation and determination of Icariin, Icariside II, and Epimedin K in Epimedium leaves. Three flavonoids were extracted by ultrasonication with EtOH-H₂O (70:30) followed by a HP 20 resin column cleanup procedure. The optimized electrophoretic conditions were obtained with the running solution of 8 mM borate MeCN/H₂O (60:40, v/v) (pH 11.40), separation voltage of +20 kV and detection wavelength of 270 nm. The limits of quantification ranged from 0.24 to 0.84 mg/kg (signal/noise = 3) for three flavonoids. Three flavonoids in 10 Epimedium leaves were successfully measured and evaluated.     

Ru(III), Cr(III), Fe(III) complexes of Schiff base ligands bearing phenoxy Groups: Application as catalysts in the synthesis of vitamin K3

Two polydentade Schiff base ligands and their Ru(III), Cr(III) and Fe(III) complexes were synthesized and characterized by elemental analysis (C, H, N), UV/Vis, FT IR, ¹H and ¹³C NMR, LC–MS/MS, molar conductivity and magnetic susceptibility techniques. The absorption bands in the electronic spectra and magnetic moment measurements verified an octahedral environment around the metal ions in the complexes. The thermal stabilities were investigated using TGA. The synthesized complexes were used in the catalytic oxidation of 2-methyl naphthalene (2MN) to 2-methyl-1,4-naphthoquinone; vitamin K₃, menadione, 2MNQ; using hydrogen peroxide, acetic acid and sulfuric acid. L₁-Fe(III) complex showed very efficient catalytic activity with 58.54% selectivity in the conversions of 79.11%.     

A green route for the synthesis of 2-substituted benzoxazole derivatives catalyzed by Al-exchanged K10 clay

A new, simple, and efficient protocol is developed for the synthesis of 2-substituted benzoxazole derivatives through N–C–O bond formation using Al³⁺-exchanged K10 clay (Al³⁺-K10) as catalyst. A wide range of benzoxazole derivatives are synthesized in high yields without affecting many functional groups. Hot filtration experiments showed the absence of metal leaching and catalyst can be reused for five times with only a slight decrease in yield.     

Threshold Al KLL Auger spectra of oxidized aluminium foils

Threshold Al KLL Auger electron spectroscopy and K‐edge x‐ray absorption fine structure spectroscopy have been used to examine technical purity (99.5%) aluminium foil before and after chemical treatment that altered the thickness and degree of hydroxylation of the oxidized layer. Comprehensive surface chemical characterization was effected by means of monochromatized Al Kα‐excited photoelectron spectroscopy. Threshold Al KL_{2, 3}L_{2, 3} spectra were obtained for three of the foils investigated and these spectra were in broad agreement with those observed previously for pure Al foil. The relative intensities of the spectral components for two of the foils were clearly consistent with the previously proposed assignment of the resonantly enhanced Auger component, situated between those arising from the metal and Al(III) oxide, to a thin interfacial layer. The threshold Auger spectra from the aluminium foil bearing the thickest and most hydroxylated oxidized layer were not obviously consistent with the interfacial layer model but O K‐edge spectra revealed that this surface layer was fundamentally different from the others and could have had a greater interfacial surface area. Copyright © 2003 John Wiley & Sons, Ltd.     

K Ratio H-Point Standard Additions Method

Abstract

A modification of H-point standard additions method is proposed in order to obtain an unbiased analyte concentration when both analyte and interferent are present in a sample. The method is called “K ratio H-point standard additions method.” The method uses the analytical signal data at two selected wavelengths and the K ratio of an interferent determined by using the method proposed by Ni Yongnian et al. at the same wavelengths, giving two straight lines that have a common point H with coordinates (-C_H, A_H), where C_H is the unknown analyte concentration and A_H is the absorbance of an interferent at one of the two selected wavelengths, which depends on the calculating method of K ratio. Examples of application of the proposed method are given.     

Two new compounds from Melodinus suaveolens

Two new compounds, 19-hydroxy-melodinine K (1) and melodiside (2), and 25 known compounds were isolated from leaves and twigs of Melodinus suaveolens. Their structures were elucidated based on 1- and 2-D NMR, FTIR, UV and MS spectroscopic data. 19-hydroxy-melodinine K showed cytotoxic activity against MDA-MB-231 breast, BCG-823 gastric, SW480 colon and Hela cancer cells.     

Effect of hydration andpH on the thermal stability of proteinase K

The effect of hydration andpH on the thermal stability of proteinase K was studied in the temperature range 310–450 K by differential scanning calorimetry. The dependences of the denaturation temperatureT _d, the specific enthalpy of denaturation H _d and the maximum of excess apparent specific heat capacityC _ex ^max upon the degree of hydrationh and thepH of the buffers used are presented. The relation betweenT _d andh is of the Flory-Garrett's type. By means of Ooi's model, the two components of the denaturation enthalpy arising from hydration and conformational change, respectively, were estimated. The fact that the specific denaturation enthalpy of proteinase K is very low may be attributed to its very low enthalpy of conformational change per heavy atom.Dedicated to Prof. Menachem Steinberg on the occasion of his 65th birthdayThis major project was supported by the National Natural Science Foundation of China.