On the criteria for integrability of the Liénard equation

The Liénard equation is of a high importance from both mathematical and physical points of view. However a question about integrability of this equation has not been completely answered yet. Here we provide a new criterion for integrability of the Liénard equation using an approach based on nonlocal transformations. We also obtain some of the previously known criteria for integrability of the Liénard equation as a straightforward consequence of our approach’s application. We illustrate our results by several new examples of integrable Liénard equations.     

On the Center of Continuous Maps of Dendrites

The structure and the depth of the center of a continuous map of a dendrite with a closed countable set of branch points of a finite order are studied. It is proved that the center of that map coincides with the closure of the set of periodic points. It is shown also that for an arbitrary natural number n S 2 there are the dendrite X n with a closed countable set of branch points of a finite order and the continuous map f n : X n M X n with n as the depth of the center.     

The Different,but Interesting Behaviors of Benzyl Systems in the Willgerodt-Kindler Reaction under Solvent-Free Conditions

On the benzyl system, bearing various functional groups, have been carried out the Willgerodt-Kindler reaction to obtain thiobenzmorpholide ( 1 ). The reactions, under solvent-free conditions, were performed in both classical (reflux, room temperature) and nonclassical (microwave) conditions to attempt our elucidation of the reactions pathways. Unlike benzylamine and benzyl mercaptan, benzyl halides give poor result due to the type of amine. The experimental results suggest that the proposed reaction pathway involves the oxidation coupling of benzylic substrates, followed by a thiolation step and an attack of the amine on the thiolated product to give ( 1 ).     

One ligand capable of in situ reaction in a mixed-ligand system with two new different frameworks

The in situ ligand 2,3-pyrazinedicarboxylic acid (2,3-H₂pzdc) mixed with 1,1′-(1,4-butanediyl)bis(benzimidazole) (bbbi) is used to form two coordination polymers ([Cd(2,3-pzdc)(bbbi)] (1) and [Cd₂Cl₃(2-pzc)(bbbi)₂] (2)) under hydrothermal conditions. Complex 1 was obtained in the absence of in situ reaction and 2 was synthesized with 2,3-H₂pzdc in situ generating 2-pyrazinecarboxylate (2-pzc^?). The structural details reveal that 1 has a 3D framework with dia topology, and 2 is a 2D layer structure and develops a 3D supramolecular structure via strong π?π stacking interactions. The ligand effects were compared for the two frameworks. In addition, fluorescence properties and thermal stabilities of 1 and 2 in the solid were studied.     

非经典碳正离子简介

非经典碳正离子作为一种特殊的反应中间体,具有重要的理论和实际研究的意义。本文以碳正离子理论的发展为主线,以历史上非经典碳正离子(特别是降冰片基正离子)之争为中心,简要综述了Winstein、Brown和Olah三人的观点,并结合最新进展进行评述。此外,还对除降冰片基正离子之外的非经典碳正离子进行了适当的讨论。     

Simultaneous derivatization and air-assisted liquid–liquid microextraction of some aliphatic amines in different aqueous samples followed by gas chromatography-flame ionization detection

The paper presents a new method based on simultaneous derivatization and air-assisted liquid–liquid microextraction (AALLME) for the extraction and preconcentration of some aliphatic amines prior to gas chromatography-flame ionization detection (GC-FID). Primary aliphatic amines are derivatized and extracted simultaneously by a fast reaction with butylchloroformate (derivatization agent/extraction solvent) under mild conditions. The mixture of butylchloroformate and aqueous sample solution is rapidly sucked into a 10-mL glass syringe and then is injected into a test tube with conical bottom and the procedure is repeated seven times. After centrifuging the resulted cloudy solution, the derivatized analytes in the sedimented phase are determined by GC-FID. The influence of main factors on the efficiency of derivatization/extraction procedure is studied. Under the optimal conditions, the enrichment factors (EFs) for aliphatic amines are obtained in the range of 248–360 and limits of detection (LODs) are between 0.30 and 2.6 μg L⁻¹. The obtained extraction recoveries ranged from 50 to 72% and the relative standard deviation (RSD) was less than 4.8% for intra-day (n = 6) and inter-days (n = 4) precision. The method is successfully applied to determine some aliphatic amines in environmental water samples.     

CATALASE MIMIC WITH Fe (II) METALLOMICELLE

The effect of Fe (II) metallomicelle as a model of catalase, which was formed by adding surfactants (CTAB, SDS, LSS, Brij35) in Fe (II) -trien complex of molar ratios 1: 500 on the decomposition of hydrogen peroxide was investigated at 20°C and 30°C in pH 10 using KI-color and UV Spectrophotometry. A kinetic model for metallomicellar catalysis was proposed. The association constant of the ternary complex K and the rate constant of the decomposition of hydrogen peroxide k3 were obtained. The results indicate that the metallomicelles making up of Fe (II) metal complex and cationic or nonionic surfactants have obvious catalysis on the decomposition of hydrogen peroxide, but the metallomicelles making up of Fe (II) metal complex and anionic or zwitterionic surfactants have inhibition on this reaction.     

航空通信网络中复杂干扰过滤技术研究

航空通信环境中存在复杂的干扰信号,对正常的通信信号造成强烈的干扰。利用传统算法进行干扰信号过滤,无法避免由于干扰信号过于复杂导致过滤不充分的缺陷。提出一种基于加权残差优化算法的航空通信网络中复杂干扰过滤方法。对原始信号进行降频处理,能够消除峰值干扰信号,提高了信号的准确性。根据加权残差修正优化算法的相关原理,对通信信号进行残差优化处理,经过处理后的通信信号在受到干扰时会形成零陷,实现了对复杂干扰信号的过滤。实验结果表明,利用该算法进行航空通信网络中复杂干扰信号过滤,能够有效提高过滤的准确性,效果令人满意。     

夜视战场环境视觉传感信息采集系统设计

夜视战场环境视觉传感信息的实时获取是跟踪夜视战场图像处理分析的前提,针对夜视战场环境的复杂特征,设计了夜视战场环境视觉传感信息采集系统,分析了系统的总体结构,系统硬件主要包括视觉传感器、传感器控制卡和扩展卡、图像采集与存储以及信号调理电路,给出了系统采集节点的程序设计流程以及传感信息采集的具体程序代码实现过程。实验结果说明,所设计系统可有效采集到夜间军事战场中的传感信息,并且具有较高的采集精度。     

An explicit counter-example for the shephard problem of convex bodies in ℝ n

Comparing the volume of the projection body of a double cone and that of the projection body of a ball, we give an explicit counter-example for the Shephard problem of convex bodies in Rⁿ (n ≥ 3) and an affirmative answer to the question of Zhang.