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 .     

Preparation of a novel self-assembling nonlinear optical (NLO) polymer film

A novel self-assembling crosslinking second harmonic generation nonlinear optical (SHG/NLO) film with high SHG coefficient (2×10-7 e.s,u.by IR dichroism) was prepared by morecular design and "in-situ poling and sol-gel process".The content of the NLO chromophore (S)-(-)-1-(4)-mtrophenyl-2-pyrrolidinemethanol (NPP) is as high as 50 mol% since NPP molecules probably disperse in the film at a molecular level The film is rigid,uni form and transparent.This designed clathrate supermolecular structure was poved by IR,atomic force microseopv (AFM) and differential scanning calorimetry (DSC) detection.The title film exhibits a long-term temporal stability with 95% of the initial value of SHG coefficient maintained even after 20 d at 65℃(by UV spectroscopy)     

O（^3P）原子与丙醛和正丁醛化学反应动力学研究

我们已对O(~3p)原子和酮类分子化学反应速率常数进行了系列测定,分析讨论了羰基对O(~3p)抽提氢原子反应速率的影响,关于O(~3p)与醛类分子反应速率的测定也有报道。本文用流动微波放电-化学发光光子计数方法测定O(~3p)原子与丙醛和正丁醛化学反应速率常数及其与温度的关系,并由动力学数据对醛基中C—H键的离解能进行了讨论。