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 .     

原子吸收光谱测定Sm-Eu-Gd富集物中Sm、Eu、Gd

本文制定了N_2O-C_2H_2焰原子吸收光谱直接测定Sm-Eu-Gd富集物中Sm、Eu和Gd的分析方法。采用氧化镧溶液作为缓冲剂消除干扰提高灵敏度。此法不需要复杂的分离过程。方法简便、快速、成本低、适合工厂采用。     

Flow injection analysis methods for determination of diffusion coefficients

Two flow injection analyses (FIA) methods for the determination of diffusion coefficients in a straight single tube FIA system were developed. Based on the analytical solution of the convection-diffusion equation, linear relationships of the logarithmic values of the dispersion coefficient (D) and the half-peak width (W_1/2) with the diffusion coefficient (D_m) were obtained. Experiments were designed to verify these methods. For example, for potassium hexacyanoferrate (III) a D_m value of 0.72 × 10⁵ cm² s⁻¹ was found versus a literature value of 0.76 × 10⁵ cm² s⁻¹ (error, 5%). For potassium hexacyanoferrate (II) a D_m value of 0.67 × 10⁵ cm² s⁻¹ was obtained versus a literature value of 0.63 × 10⁵ cm² s⁻¹ (error, 6%). The diffusion coefficients of some important biomedical compounds, such as dopamine, epinephrine, norepinephrine and ascorbic acid, were then determined. The values of 10⁵ D_m/cm² s⁻¹ are 0.60 ± 0.03, 0.44 ± 0.02, 0.60 ± 0.01 and 0.68 ± 0.06, respectively.     

原位氧化还原沉淀水热合成法制备LixMn2O4尖晶石

Li xMn2O4尖晶石是新一代的锂离子二次电池正极材料 [1], 其合成方法对材料的电化学性质影响很大[2].常规合成大多采用高温固相反应法, 此法具有反应温度高, 反应时间长, 容易产生缺陷和产物不纯净等缺点, 导致所合成的锂离子二次电池正极材料的性能较差. 目前用水热合成法制备电池正极材料Li xMn2O4尖晶石尚未见文献报道. 本文在常规水热合成法的基础上采用原位氧化还原沉淀水热合成法 [3]制备前驱物, 该法合成条件更温和, 而且使材料的综合性能得到了改善和提高.      

Facile Total Synthesis of (±)‐Nimbiol

A facile total synthesis of (±)‐nimbiol 1 has been achieved. In order to decrease the dioxo byproduct 2a , an improved oxidation system of CrO₃/H₂O/HOAc/NaOAc was used.     

Total synthesis of methyl protodioscin: a potent agent with antitumor activity

Methyl protodioscin (1), otherwise known as 3-O-[alpha-L-rhamnopyranosyl-(1-->2)-[alpha-L-rhamnopyranosyl-(1-->4)]-beta-d-glucopyranosyl]-26-O-[beta-D-glucopyranosyl]-22-methoxy-25(R)-furost-5-ene-3 beta,26-diol, has been synthesized for the first time from diosgenin through nine steps in an overall yield of 7.8%.