Limit cycles of a class of Liénard systems derived from state-dependent impulses

Discontinuous phenomena, in which objects may behave continuously and sometimes discretely are not only found in nature and under laboratory conditions but also in simple, familiar contexts. For example, this phenomenon is skillfully incorporated into the internal structure of mechanical wristwatches. Unless an extremely small amount of state-dependent impulse is applied intermittently, the reciprocating rotational movement of the balance and hairspring, which is the heart of the mechanical wristwatch, cannot be maintained. The small amount of state-dependent impulse, which is often overlooked, can make a significant difference; however, very few studies have examined this subject. This study assumes the underlying cause of discontinuous behaviors as impulses generated when an object reaches a particular state, assuming that the continuous behavior follows the Liénard system, which is widely studied in the field of electrical circuits. The main theorem provides the conditions under which the effect of the impulses causes a stable limit cycle in the Liénard system, even if no limit cycle exists when there are no impulses. The Poincaré–Bendixson theorem for discontinuous dynamical systems and phase plane analysis are used to prove the main theorem. Several examples and their simulations are provided to illustrate the main theorem.     

On Bahadur asymptotic efficiency in a semiparametric regression model

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Bahadur efficiency and robustness of studentized score tests

We derive the exact Bahadur slopes of studentized score tests for a simple null hypothesis in a one-parameter family of distributions. The Student's t-test is included as a special case for which a recent result of Rukhin (1993, Sankhy Ser. A, 55, 159–163) was improved upon. It is shown that locally optimal Bahadur efficiency for one-sample location models with a known or estimated scale parameter is attained within the class of studentized score tests. The studentized test has an asymptotic null distribution free of the scale parameter, and the optimality of likelihood scores does not depend on the existence of a moment generating function. We also consider the influence function and breakdown point of such tests as part of our robustness investigation. The influence of any studentized score test is bounded from above, indicating certain degree of robustness of validity, but a bounded score function is needed to cap the influence from below and to ensure a high power breakdown point. We find that the standard Huber-type score tests are not only locally minimax in Bahadur efficiency, but also very competitive in global efficiency at a variety of location models.     

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 .     

黑腔靶X光转换,输运的定量测量

为了测量黑腔靶X光引光效率、转换效率,我们设计了相应的分解靶(泄漏靶)实验,1989～1992年在″神光″装置上共进行了四次漏靶分解实验,利用灵敏度作了绝对标定的平响应X光二极管对漏靶注入孔、引光孔流出的X光角分布进行了测量,测出了x光角分布,得到了黑腔靶X光转换效率为50％～60％,引光效率约6％,为以后辐射驱动内爆研究的理论计算和靶的优化设计提供了重要的数据。     

Cyclical games with prohibitions

We consider a certain combinatorial game on a digraph for two cases of the price function. For one case the game in question extends the cyclical game studied in Ehrenfeucht and Mycielski (1979) and Gurvitch, Karzanov and Khachiyan (1988) which, in its turn, is a generalization of the well-known problem of finding a minimum mean cycle in an edge-weighted digraph. We prove the existence of optimal uniform stationary strategies for both cases and give algorithms to find such strategies.This work was partially supported by Chaire municipale, Mairie de Grenoble.     

光催化降解染料ZnO催化剂的性能

光催化法是20世纪70年代发展起来的新型水处理技术，即以某些半导体材料为催化剂，利用光催化法来降解环境污染物。该方法工艺简单，成本较低，在常温下能使大多数不能或难于生物降解的有毒有机物彻底氧化分解。近年来研究最多的是TiO2，由于其带隙较宽(3．2eV)，只能吸收波长λ≤387nm的紫外光，因此研制新型光催化剂仍是重要课题。     

Polyethylenimine （PEI）-g-comb-poly（ethylene glycol）-transferrin（Ⅰ）： Tumor-targeted Vector for Gene Delivery In.vitro

The work described the synthesis and evaluation of PEI-g-comb-PEG-transferrin as a potential system for gene therapy in vitro. The MW of PEG was 10KDa, and PEI was 2KDa. Its structure was identified by NMR, FT-IR and TGA spectroscopy. MTT assay found that at concentration up to 4000 n mol/L of the polymer, cell viability was over 85%. The bio-character of polymer/DNA complex was characterized by agarose gel electrophoresis, ethidium bromide exclusion and zeta-potential assay. The polymer could retardate DNA at N/P ratio 3.0-3.5 （mol/mol）. The particle size of the polymer/DNA complex was less than 300 nm. Transfection efficiency of the complex was studied in COS7 and NT2 cell lines.     

土壤环境中铅的化学

论述了环境中铅的背景值、来源、污染、质量标准、化学循环以及环境中铅的烷基化，为铅污染治理提供理论依据。     

Y掺杂对氢氧化镍电极高温性能的影响

合成了内掺稀土元素Y的β-Ni(OH)2和α-Ni(OH)2材料, 并通过XRD、TEM、CV 和充放电测试等方法研究了Y元素对这两种晶型活性材料的结构、形貌以及高温电化学性能方面的影响, 发现Y元素可显著提高β-Ni(OH)2和α-Ni(OH)2材料的高温性能, 且作用机理相同, 均是通过提高析氧过电位来改善镍电极的高温充电效率. 但是α-Ni(OH)2在高温下的相稳定性仍有待提高.