Limit cycle analysis of a class of strongly nonlinear oscillation equations

The limit cycle of a class of strongly nonlinear oscillation equations of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqadwhagaWaaiabgUcaRmXvP5wqonvsaeHbbjxAHXgiofMCY92D% aGqbciab-DgaNjab-HcaOiaadwhacqWFPaqkcqWF9aqpcqaH1oqzca% WGMbGaaiikaiaadwhacaGGSaGabmyDayaacaGaaiykaaaa!50B8!\[\ddot u + g(u) = \varepsilon f(u,\dot u)\] is investigated by means of a modified version of the KBM method, where is a positive small parameter. The advantage of our method is its straightforwardness and effectiveness, which is suitable for the above equation, where g(u) need not be restricted to an odd function of u, provided that the reduced equation, corresponding to =0, has a periodic solution. A specific example is presented to demonstrate the validity and accuracy of our 09 method by comparing our results with numerical ones, which are in good agreement with each other even for relatively large .     

二硫代氨基甲酸螯合树脂化学修饰电极的制备及银离子的测定

将纯石墨电极经三氧化二铝抛光与浓硝酸和浓硫酸(1+1)混合酸使其极性化,之后于1 g·L-1聚氯乙烯(PVC)环己酮溶液10μL中浸渍片刻,取出,用红外灯照射烘干30 min,冷却后,将电极置于含有哌嗪、K3PO4及二甲基甲酰胺(DMF)(2:1:8)的混合液中使其反应;最后在氢氧化钠存在下与二硫化碳反应,用水洗至中性,即制成修饰有二硫代氨基甲酸螯合树脂的石墨电极,将其用于银的测定。与未修饰的电极相比此电极具有较高的灵敏度和较好的选择性,在1．0×10-8～1．0×10-5mol·L-1范围内,峰电流与浓度呈线性关系,检出限为5．0×10-9mol·L-1。     

Preparation and properties of insoluble films of cyclodextrin condensation polymers

The preparation and properties of smooth and stable films of cyclodextrin polymers are described. The commercially available water soluble prepolymers of-, -, and-cyclodextrin of low molecular masses were crosslinked with glutaric dialdehyde. Side-chain unreacted aldehyde groups were reduced with sodium borohydride. For the-cyclodextrin polymer, optimum film performance was found for a 1:10 mass ratio of glutaric dialdehyde to prepolymer, which corresponds to a molar ratio of glutaric dialdehyde to cyclodextrin units of about 1.75: 1. Such films, of thickness 2.4 µm, were prepared on metallic or glassy-carbon substrates for characterization by scanning-electron microscopy, and for studies with the electrochemical quartz-crystal microbalance.     

Characterization of immobilized catalases and their application in pasteurization of milk with H2O2

The catalase (fromAspergillus niger) has been immobilized by a chemical method on the pous SiO₂ modified with γ-aminopropyltrietoxysilane, followed with glutaraldehyde and by a physical method in alginate and γ-carrageenan gel. Optimum support:enzyme ratios and pH values were determined for modified SiO₂ in a series of immobilization reactions of catalase in the presence of the crosslinking agent glutaraldehyde, and for alginate and γ-carrageenan in the presence of hemoglobin and bovine serum albimine. pH and temperaturedependent activity variations and the stability properties of immobilized catalase preparations were investigated. Rate constants for H₂O₂ decomposition and catalase deactivation were determined. The decomposition rate of H₂O₂ used in the cold pasteurizatioan of milk were investigated in a discontinuous batch type reactor system. Activity half-lives of immobilized catalase were determined.     

RECENT PROGRESS OF NANO-MECHANICAL MAPPING

 Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale. To date, the Hertzian theory was used for analyzing force-distance curves as the simplest model among several contact mechanics between elastic bodies. However, the preexisting methods based on this theory do not consider the adhesive interaction in principle, which cannot be neglected in the ambient condition. A new analytical method was introduced to estimate the elasticity and the adhesive energy simultaneously by means of the JKR theory, describing adhesive contact between elastic materials. Poly(dimethylsiloxane) (PDMS) and isobutylene-co-isoprene rubber (IIR) were analyzed to verify the applicable limit of the JKR analysis. For elastic samples such as PDMS, the force-deformation plots obtained experimentally were consistent with JKR theoretical curves. Meanwhile, for viscoelastic samples, especially for IIR, the experimental plots revealed large deviations from JKR curves depending on scanning velocity and maximum loading force. Some nano-rheological arguments were employed based on the difference between these specimens.     

THE COMPARISON OF LANZHOU LOESS PROFILE WITH VOSTOK ICE CORE IN ANTARCTICA OVER THE LAST GLACIATION CYCLE

Loess near Lanzhou in the late Pleistocene is very sensitive to climatic fluctuations. The Beiyuan terrace profile in Linxia City, of which the curve of susceptibility tallies with the trend of isotopic curves of Vostok 2083 m ice core in Antarctica, is 35m thick. There are five layers of paleosols under Malan loess(L_1). Upper three layers (S_(1-a),S(1-b)and S_(1-c) correspond to three warm stages in last interglaciation, Interstadial of Last Glacial (C stage in Antarctic ice core)was clearly recorded in the Beiyuan profile, in which three layers of paleosols and two of loess were formed. The lowest section of the profile belongs to penultimate glaciation, in which fossils of cold-drought-resistant mammal and mollusc have been discovered.     

Asymptotic expansions of the distributions of some test statistics

Summary A modified Wald statistic for testing simple hypothesis against fixed as well as local alternatives is proposed. The asymptotic expansions of the distributions of the proposed statistic as well as the Wald and Rao statistics under both the null and alternative hypotheses are obtained. The powers of these statistics are compared and its is shown that for special structures of parameters some statistics have same power in the sence of order . The results obtained are applied for testing the hypothesis about the covariance matrix of the multivariate normal distribution and it is shown that none of the tests based on the above statistics is uniformly superior. Research supported by the National Science Foundation Grant MCS 830149.     

Direct Electrochemistry of Cytochrome C on the Glassy Carbon Electrode Modified with 1-Pyrenebutyric Acid/MWNTs

With 1-Pymnebutyric acid （PBA） and multiwalled carbon nanotubes （MWNTs）, glassy carbon electrode modified was successfully prepared. In phosphate buffer solution （pH 7,0）, the direct electrochemistry of cytochrome C （Cyt C） was realized. In the cyclic voltammetry experiment two pairs of redox peaks ofCyt C were observed at 0.018 V and -0.314 V （vs. SCE）, respectively. The redox reaction at 0.018 V was diffusion controlled, while the redox reaction at -0.314 V was adsorption controlled.     

Eastman-Kodak AQ膜修饰电极阴极溶出伏安法测定痕量铁

本文用热处理法成功地制备了性能稳定的Eastman-Kodak AQ/GC修饰电极,对Fe~(3+)/Fe~(2+)及其络合阳离子在该电极上的行为进行了研究。表明AQ膜对Fe~(3+)和Fe~(2+)具有相近的交换能力,可用于Fe~(3+)或Fe~(2+)及其总量的阴极溶出伏安法测定。线性范围分别为2.0×10~(-7)～2.2×10~(-5)mol/L(Fe~(3+))和5.0×10~(-7)～2.0×10~(-5)mol/L(Fe~(2+)),检出限为1.0×10~(-7)mol/L(Fe~(3+))。文中对电极反应和再生进行了探讨。     

Nafion化学修饰圆盘预富集-石墨炉 原子吸收联用法对牛血超氧化物歧化酶中铜、锌分布状态的研究

本文研究了Nafion化学修饰钨丝圆盘预富集-石墨炉原子吸收(GFAAS)方法测定牛血超氧化物歧化酶(SOD)中游离态Cu～(2+)及Zn～(2+)的方法,并用GFAAS法直接测定SOD中铜、锌的总量,证实了牛血SOD中金属辅基铜、锌原子个数比为1:1,初步探讨了一定浓度的牛血SOD中Cu～(2+)、Zn～(2+)的表观离解平衡常数。为提高SOD的活性和稳定性的研究,提供了一种有效的方法。