Generating of Conditionally Exactly Soluble Potentials by Method of Supersymmetric Quantum Mechanics

This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials,and uses the variational supersymnetric WKB method to obtain the approximate wlues of the energy spectrum of the whole class.     

SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS

The present work describes the application of the method of fundamental solutions (MFS) along with the analog equation method (AEM) and radial basis function (RBF) approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson's equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition (SVD) technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric (MQ) are fully analyzed to provide useful reference.     

Method of array shape calibration based on time delay estimation using two auxiliary sources

As for a flexible horizontal array deployed in the sea, it is difficult to obtain each sensor's precise relative position. Therefore a method of array shape calibration is proposed. The method is described as follows. Firstly two separate auxiliary sources are deployed. Secondly tune delay of each sensor's received signal is estimated. Finally, with the aid of GPS location of the sources and the horizontal array, relative sensor positions of the horizontal array can be determined. The estimation of relative sensor positions is unbiased. Simultaneously, simulation analysis has been done to estimate its standard variance, and the optimal flare angle of the two sources has been derived. Data of 2001 Asian Sea International Experiment have been used to validate the method. After array calibration, measured source azimuth angle agrees with the real one, and measured array gain agrees with the theoretical gain. In conclusion, the theoretical and experimental results both show that the method can determine each sensor's relative position precisely.     

红外光谱微机数据库

PC-IR大型红外光谱微机数据库系统 ,包含了全套标准红外光谱集的 6万张光谱数据 ,是世界上最大的一种纯化合物红外光谱微机数据库。系统已通过省级鉴定。鉴定指出 :“其规模和性能已达到国际先进水平。”该成果先后获福建省医卫科技进步一等奖 ,福建省政府科技进步二等奖 ,卫生部优秀软件奖。按照未知样品的红外谱图 ,根据系统的屏幕提示 ,用户由键盘输入各主要吸收峰的波数和透过率值 ,即可进行自动检索。系统给出库中与样品光谱相同或最相近的若干种化合物的图谱序号 ,熔点状态 ,分子式及相似性得分。该系统可在 3 86,486,5 86等微机或 …     

解三角形中的高、中线、角平分线问题

在学习了《解三角形》这一章后,我们学会了怎样利用正弦定理和余弦定理来求三角形的边、角等问题．先让我们来回顾这部分主要内容：     

相声——说集合

甲：老朋友,好久不见,您近来可好! 乙：托您的福,吃得好,睡得香,身体棒得像头牛． 甲：牛好啊,今年是牛年,您也一定是牛劲十足!最近在忙点啥呀？ 乙：忙学习呀!学习能使人变得聪明,学习能使人变得文明,学习能使人掌握自己的命运．     

与抽屉原理相关的一道数学题的妙解

众所周知,抽屉原理（即鸽笼原理）是解决许多数学问题的有力工具．m个鸽子飞进n个笼子里,人们往往容易想到：“当m〉n时,至少有两个‘倒霉’的鸽子挤到同一个笼子里去”,而忽略另一个同样重要的事实：“当m〈n时,至少有n—m个‘幸运’的笼子是空的”．     

一道二元三角方程题的妙解

一个方程,两个未知数,在一般的情况下,解不是唯一的,而有些方程的解是唯一的．本文用构造的方法给出了一道三角方程题的两种妙解,与大家交流．     

我是这样利用“1”的

今天,老师给我们复习三角函数时出现这样一道题：已知tanθ=1/3,求cos2θ＋1/2sin2θ值．老师讲解时利用sin2θ＋cos2θ=1的条件,并由此布置了这样一道作业：“1”是我们最熟悉、最简单的数字,在日常生活中经常被用到．在解决数学问题过程中,如果能巧妙地利用这个简单的“1”,就可以避繁就简,轻松获解,取得意想不到的效果,回顾我们所学高中数学内容,对于“1”进行提炼,看看在哪些知识点中可以运用这个“1”．之后,我进行了总结,大致可以在如下几个方面：