Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture

By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems.     

一阶形式系统K~*及其完备性

模糊命题演算的形式系统L＊已经在模糊逻辑与模糊推理的结合研究中得到了成功的应用.本文考虑与系统L＊相应的一阶逻辑理论,建立了一阶形式系统K＊,并证明了这个系统的完备性.     

基于MATLAB(SIMULINK)的电弧炉电极调节系统FUZZY-PD控制器的仿真

介绍了采用MATLAB V5.2提供的模糊逻辑工具箱来设计研究电孤纺电极调节系统中的模糊－－PD控制器，讨论了在SIMULINK环境下模糊－PD控制器的参数自调速原理、结构、建立模糊控制规则库和模糊推论方法，并给出仿真结果与结论。     

醇+N-甲基哌嗪二元体系的体积性质

采用振荡管式数字密度计分别测定甲醇、乙醇、正丙醇、异丙醇、丁正醇和异丁醇与N-甲基哌嗪组成的二元体系在298.15K下的密度，计算了超额摩尔体积、超额偏摩尔体积、表观摩尔体积、偏摩尔体积等体积性质，从分子相互作用角度讨论了这些二元体系的体积性质的变化规律，为N-甲基哌嗪的开发和研究提供基础数据和信息。     

Algorithms for flattened Gaussian beams passing through apertured and unapertured paraxial ABCD optical systems

The propagation property of flattened Gaussian beams (FGBs) is studied based on the Collins formula, and analytical propagation equations for FGBs with and without an aperture are derived. It is shown that the closed-form expressions for the FGB of order N passing through paraxial ABCD optical systems without an aperture can be written as the combinations of Confluent Hyper-geometric Functions, and that the analytical equations for the FGB of order N passing through apertured paraxial ABCD optical systems may involve Error Functions. The proposed algorithms for the considered beams can save computing time, provide intuitive physical insights, and help to design optical systems. Our results are confirmed and illustrated with numerical examples.     

用于波分复用系统的多峰干涉滤光片

介绍了用于波分复用系统的多峰干涉滤光片的设计原理,提出了滤光片透射峰位置的确定方法,讨论了影响滤光片半宽度和截止度的因素,给出了滤光片的膜厚容差分析结果,表明透射率监控标准偏差在<0.5%范围内,可以得到波形良好的多峰滤光片,最后给出了实验结果.     

ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.     

Preparation, structure and properties of novel 1,3-dithiol-2-ylidene derivatives containing bis(ethynylpyridine) units

1,3-Dithiol-2-ylidene derivatives containing bis(ethynylpyridine) units were synthesized using a Pd-catalyzed reaction of the corresponding dibromide. X-Ray crystal analysis revealed unique crystal structures depending on the aromatic groups. The absorption spectra and redox properties indicated intramolecular charge-transfer interactions between the 1,3-dithiole unit and the pyridyl parts.     

一类NLS-mKdV方程族的扩展可积系统

利用代数变换，构造了与文献［５］中的loop代数₂的子代数等价的loop代数1的一个子 代数₁.再将₁扩展为一个高维的loop代数.利用设计了一个等谱问题 ，结合子代数间的直 和运算和同构关系，得到了NLS_mKdV方程族的一类扩展可积系统.作为约化情形，求得了著 名的Schrdinger方程与mKdV方程的可积耦合系统. 关键词： loop代数 可积系统 等谱问题     

Hypernormal form theory: foundations and algorithms

Hypernormal forms (unique normal forms, simplest normal forms) are investigated both from the standpoint of foundational theory and algorithms suitable for use with computer algebra. The Baider theory of the Campbell-Hausdorff group is refined, by a study of its subgroups, to determine the smallest substages into which the hypernormalization process can be divided. This leads to a linear algebra algorithm to compute the generators needed for each substage with the least amount of work. A concrete interpretation of Jan Sanders’ spectral sequence for hypernormal forms is presented. Examples are given, and a proof is given for a little-known theorem of Belitskii expressing the hypernormal form space (in the inner product style) as the kernel of a higher-order differential operator.