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Abstract  

By introducing some parameters, we give new extensions of Hilbert inequality with best constant factors.

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Abstract  

The heats of hydration reactions for MgCl2⋅4H2O and MgCl2⋅2H2O include two parts, reaction enthalpy and adsorption heat of aqueous vapor on the surfaces of magnesium chloride hydrates. The hydration heat for the reactions MgCl2⋅4H2O+2H2O→MgCl2⋅6H2O and MgCl2⋅2H2O+2H2O→MgCl2⋅4H2O, measured by DSC-111, is –30.36 and –133.94 kJ mol–1,respectively. The adsorption heat of these hydration processes, measured by head-on chromatography method, is –13.06 and –16.11 kJ mol–1, respectively. The molar enthalpy change for the above two reactions is –16.64 and –118.09 kJ mol–1, respectively. The comparison between the experimental data and the theoretical values for these hydration processes indicates that the results obtained in this study are quite reliable.

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Local stability analysis of dynamical models of interacting populations predicted that food web connectance (C) is proportional to 1/S where S is species richness. This .hyperbolic connectance hypothesis. was initially supported by analyses of documented food webs. This study shows that the qualitative global asymptotic stability of the Lotka-Volterra cascade model with a finite number of species predicts a relationship between connectance and species richness that agrees closely with the hyperbolic connectance hypothesis predicted from the analysis of local asymptotic stability. Moreover, the threshold of the qualitative global asymptotic stability in the Lotka-Volterra cascade model separates food webs in constant environments from those in fluctuating environments. The obvious discrepancy between the C-S relationship based on some recent data and that predicted by the dynamical models could be due to the selection of data.

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Abstract  

The SHS route is based on the well-known thermite reaction, in which a strongly exothermic reaction can sustain itself and propagate in the form of a combustion wave until the reactants have been completely consumed. The successful application of the method to the synthesis of superconducting ceramics of stoichiometry RBa2Cu3Oy (R=Y, Er, Yb) is reported. The 123 phase was obtained when pellets of R2O3, BaO2 and Cu metal in the correct proportions were dropped into a heater held at 800°C in an oxygen atmosphere and left there for only 10 minutes. Thermal methods (DSC and DTA) are excellent techniques with which to investigate the dependence of the reaction on heating rate, atmosphere and starting composition.

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Summary

A high-performance liquid chromatographic (HPLC) technique coupled with photodiode array (PDA) detection has been proposed for simultaneous determination of five flavonoids, i.e. quercetin 3-O-β-d-glucopyranoside, quercetin 4′-methoxy-3-O-β-d-galactopyranoside, kaempferol 3-O-β-l-rhamnopyranoside, asebotin, and kaempferol 7-methxoy-3-O-α-l-rhamnopyranoside in extract of the whole plant of Saussurea mongolica Franch. The optimum conditions for separation were achieved on a 4.6 × 250 mm i.d., 5-μm particle, C18 column with acetonitrile and 1% acetic acid (20:80, v/v) as the mobile phase at a flow rate of 1.0 mL min−1. For all the analytes, a good linear regression relationship (r of >0.999) was obtained between peak area and concentration over a relatively wide range. The method was validated for repeatability, precision, stability, and accuracy. Seven different extraction procedures were investigated for preparation of the sample solution. The validated method was successfully applied to simultaneous analysis of these flavonoids in S. mongolica and was found to be simple and efficient.

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Abstract  

The present study explores the feasibility of the determination of phosphorus at the extreme trace levels in high-purity silicon by radioreagent method. After silicon dissolution with hydrofluoric and nitric acids and matrix volatilization, 12-molybdophosphoric acid (12-MPA) is formed by the addition of the radioreagent,99MoO 4 2– , in nitric acid medium and then extracted into isobutyl acetate. By plotting the phosphorus content against the radioactivity of99Mo in the organic phase, a linear relationship persisting down to 5 ng is obtained. Special effort has been made to the elimination of the unreacted99MoO 4 2– reagent and the optimal control of phosphorus blank introduced through the multistage analytical procedure in order to ensure reliable determination of phosphorus at the ppb level.

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Summary

A rapid, simple, and practical high-performance liquid chromatographic method (HPLC) was developed and validated for the simultaneous determination of norephedrine (NME), norpseudoephedrine (NMP), ephedrine (E), pseudoephedrine (PE), and methylephedrine (ME) in traditional Chinese medicines (TCM) which contained Ephedrae Herba (Ephedra). This analysis could be accomplished within 12.5 min with an Alltima Phenyl Column by isocratic elution using a mixture of KH2PO4 (20 mM)-acetonitrile (96:4, v/v) as the mobile phase at a flow-rate of 0.6 mL min−1 and a wavelength of 210 nm. This method was successfully applied to quantify ephedra alkaloids in both Ma-xing-gan-shi decoction and Ephedra decoction. The concentration of total ephedra alkaloids (4.62 mg mL−1) in Ma-xing-gan-shi decoction was much lower than that (7.10 mg mL−1) in Ephedra decoction. Furthermore, the concentration of NME, NMP, E, PE, and ME was significantly lower in Ma-xing-gan-shi decoction than that in Ephedra decoction, respectively. The method was easily acceptable and would be popular with most analytical laboratories.

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Abstract  

The radiochemical method has been used for investigation of the adsorption of radium on eighteen inorganic ion exchangers. The distribution coefficient of radium obtained are as follows: barite 2955, celestite 2420, BaSO4 4350, BaCrO4 5245, Ba3(PO4)2 5775, MnO2·nH2O 1681, La2O3·nH2O 4150, Zerolit S/F 2920, etc.

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Abstact  

The reduction process of silica supported cobalt catalyst was studied by thermal analysis technique. The reduction of the catalyst proceeds in two steps:

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$Co_3 O_4 + H_2 \to 3CoO + H_2 O, 3CoO + 3H_2 \to 3Co + 3H_2 O$$ \end{document}
which was validated by the TPR and in-situ XRD experiments. The kinetic parameters of the reduction process were obtained with a comparative method. For the first step, the activation energy, E a, and the pre-exponential factor, A, were found to be 104.35 kJ mol−1 and 1.18�106∼2.45�109 s−1 respectively. The kinetic model was random nucleation and growth and the most probable mechanism function was found to be f(α)=3/2(1−α)[−ln(1−α)]1/3 or in the integral form: g(α)=[−ln(1−α)]2/3. For the second step, the activation energy, E a, and the pre-exponential factor, A, were found to be 118.20 kJ mol−1 and 1.75�107∼2.45 � 109s−1 respectively. The kinetic model was a second order reaction and the probable mechanism function was f(α)=(1−α)2 or in the integral form: g(α)=[1−α]−1−1.

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Summary  

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $M^n$ \end{document} be a Riemannian \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n$ \end{document}-manifold with \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n\ge 4$ \end{document}. Consider the Riemannian invariant \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\sigma(2)$ \end{document} defined by
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sigma(2)=\tau-\frac{(n-1)\min \text{Ric}}{n^2-3n+4},$$ \end{document}
where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\tau$ \end{document} is the scalar curvature of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $M^n$ \end{document} and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $(\min \text{Ric})(p)$ \end{document} is the minimum of the Ricci curvature of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $M^n$ \end{document} at \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $p$ \end{document}. In an earlier article, B. Y. Chen established the following sharp general inequality:
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sigma(2)\le \frac{n^2{(n-2)}^2}{2(n^2-3n+4)}H^2$$ \end{document}
for arbitrary \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n$ \end{document}-dimensional conformally flat submanifolds in a Euclidean space, where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $H^2$ \end{document} denotes the squared mean curvature. The main purpose of this paper is to completely classify the extremal class of conformally flat submanifolds which satisfy the equality case of the above inequality. Our main result states that except open portions of totally geodesic \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n$ \end{document}-planes, open portions of spherical hypercylinders and open portion of round hypercones, conformally flat submanifolds satifying the equality case of the inequality are obtained from some loci of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $(n-2)$ \end{document}-spheres around some special coordinate-minimal surfaces.
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