Accurate bending analysis of rectangular plates with two adjacent edges free and the others clamped or simply supported based on new symplectic approach

The symplectic geometry approach is introduced for accurate bending analysis of rectangular thin plates with two adjacent edges free and the others clamped or simply supported. The basic equations for rectangular plates are first transferred into Hamilton canonical equations. Using the symplectic approach, the analytic solution of rectangular thin plate with two adjacent edges simply supported and the others slidingly supported is derived. Accurate bending solutions of title problems are then obtained using the superposition method. The approach used in this paper eliminates the need to pre-determine the deformation function and is hence more reasonable than conventional methods. Numerical results are presented to demonstrate the validity and efficiency of the approach as compared with those reported in other literatures.     

An exploration of a novel strategy for superposing several flexible molecules

Summary This paper describes a computational strategy for the superposition of a set of flexible molecules. The combinatorial problems of searching conformational space and molecular matching are reduced drastically by the combined use of simulated annealing methods and cluster analysis. For each molecule, the global minimum of the conformational energy is determined by annealing and the search trajectory is retained in a history file. All the significantly different low-energy conformations are extracted by cluster analysis of data in the history file. Each pair of molecules, in each of their significantly different conformations, is then matched by simulated annealing, using the difference-distance matrix as the objective function. A set of match statistics is then obtained, from which the best match taken from all different conformations can be found. The molecules are then superposed either by reference to a base molecule or by a consensus method. This strategy ensures that as wide a range of conformations as possible is considered, but at the same time that the smallest number of significantly different conformations is used. The method has been tested on a set of six angiotensin II antagonists with between 7–11 rotatable bonds.     

迭加态的量子统计特性

本文利用量子力学迭加原理,讨论了相干态与Fork态的迭加产生的压缩和反聚束效应.结果表明在一些迭加态中存在两个压缩区,两个压缩区之问的区域反聚束效应较强,压缩效应及反聚束效应的强弱与相干态的平均光子数|α|~2及Fork态|m>的光子数m密切相关.文章最后一节讨论了在实验室如何实现这一压缩迭加态.     

材料力学用叠加法求梁变形个别例题的商榷

在现行的某些材料力学教材中,用叠加法求梁变形一节的个别例题,其解题方法并不符合所在教材定义的叠加原理。我们认为,这些例题不利于学生掌握叠加原理,有可能在他们的头脑中形成关于这个原理的模糊概念。鉴于叠加原理是固体力学中比较重要的原理,因此,将此问题提出,以供广大教师及力学工作者探讨。     

驻波振幅分布研究

本文研究了入射波与经固定界面一次、二次及多次反射所生的反射波迭加而成的驻波的振幅分布规律，并得出了一些有意义的结果。     

Lipschitzian Operators of Substitution in the Algebra ΛBV

We present necessary and sufficient conditions on the generating functions of operators of substitution (=Nemytskii superposition operators), which map the Waterman space v BV of functions of v -bounded variation on the interval into another space of this type and satisfy the Lipschitz condition.     

试谈英语句子结构中的纲与目

有的人学英语时为时不短，可仍觉得句子结构复杂、神秘。本文在对英语的句子进行了剖析后，指出句子就其成分来说，也有其主次之分、纲目之别。在阅读时，应搞清句子的内部结构及各个分句之间的逻辑关系，合句的意思也就能够明白了。     

一种新的非线性叠加相干态的相位特性

根据Pegg-Barnett 相位定义,计算了一种新的非线性叠加相干态的相位概率分布函数和光子数-相位压缩效应,并进行了数值模拟.     

Multiple beam Fizeau interferometer with filtered frequency comb illumination

Real wedge interferometers of the Fizeau-type do not allow for fringes in case of a spectral broadband source - or in short: for white light fringes. Here, the use of a suitable frequency comb source will help to overcome this limitation on the one hand and on the other will offer the capability for enhanced phase sensitivity in high precision measurements of surface deviations. Frequency combs can be produced either by using a pulse train from a fs-laser or by passive filtering of the light emitted by a broadband source as a superlum-diode or a fs-laser. The frequency comb produced by a common fs-laser is extremely fine, i.e., the frequency difference of consecutive peaks is very small or the distance of consecutive pulses of the pulse train might be of the order of 1 m. Therefore, the pulse train produced by passive filtering of a broadband source is better adapted to the needs of surface testing interferometers. White light fringes are either applied for the profiling of discontinuous surfaces and/or can serve as an indication for the correct choice of multiplication factors in superposition interferometry. During the last decennium it became more and more clear that spatially incoherent sources provide better measuring accuracy in surface measurements due to the reduced influence of dust diffraction patterns. The advantage of laser illumination can nevertheless be maintained if the laser light is made spatially incoherent through moving scatterers in the light path. Here, we will discuss the application of spatially incoherent broadband light frequency filtered through a Fabry-Perot filter. The main applications are in the following fields: (1) surface profiling applications using two-beam Fizeau interferometers, (2) selection of single cavities out of a series of interlaced cavities, and (3) sensitivity enhancement for multi-beam interferometers for planeness or sphericity measurements. Some of the discussed possibilities will be experimentally demonstrated.     

Monotonicity properties of the superposition operator and their applications

We establish some properties of the superposition operator which are associated with monotonicity. Those properties are expressed in terms of the notion of degree of decrease or degree of increase. An application of the obtained results to the study of solvability of a quadratic Volterra integral equation is also derived.