共查询到20条相似文献,搜索用时 78 毫秒
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利用奇性流形的任意性,选用不同的展开函数及非标准截断展开于KdV方程,得到了许多用复杂隐函数表示的精确解 相似文献
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利用高阶窗函数结合连分式展开等技术研究并建立一种水平层状各向异性介质中电磁场并矢Green函数的快速有效算法. 首先借助于高阶窗函数将构成并矢Green函数的Sommerfeld积分转化成广义快速下降路径上积分,并给出高阶窗函数Hankel变换的一种新的更高阶幂级数展开式以及严格的Lommel函数表达式,以满足在全空间上高精度计算并矢Green函数的要求. 在此基础上,用Bessel函数的零点将积分路径划分成一系列小区间并通过改进的自适应Gauss求积公式确定各个小区间上的积分值,然后引入连分式展开法对各个区间上的积分值求和,从而使整个积分的收敛效率得到大大提高. 最后通过数值结果验证本方法的有效性.
关键词:
高阶窗函数
连分式展开
并矢Green函数
层状各向异性介质 相似文献
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本文发展了使用幂次式展开收敛域中含有支点的复变函数的方法.在无穷阶支点下,函数的展开式化为积分的形式,称之为洛朗变换.文章还探讨了部分典型函数的展开结果及其完备性问题,并提出了使用连续复幂次代替实幂的方法.最后,举出一例简释了该方法在信号系统中的实际应用,展望了应用前景. 相似文献
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比较了节块展开法(NEM),节块格林函数法(NGFM)和节块傅立叶展开法(NFEM)的偏中子通量展开技术,证明了NFEM的精度高于任何有限阶NEM,而与NGFM相当。 相似文献
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提出了一种用于分析椭圆孔光子晶体光纤的正交函数模型.发展了一种新型超格子的构造方法,将光子晶体光纤的横向介电常数表示为两种周期性结构叠加,这两种周期性结构分别用余弦函数展开;同时将横向电场以Hermite-Gaussian函数展开.利用正交函数的性质,将全矢量波动方程转化为矩阵本征值问题,求得两偏振模式传输常数.利用此模型可以研究圆孔及椭圆孔光子晶体光纤的模式特性、色散特性、偏振特性等.
关键词:
光子晶体光纤
超格子
正交函数
本征值问题 相似文献
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We develop the theory of operators defined on a space of holomorphic functions. First, we characterize such operators by a suitable space of holomorphic functions. Next, we show that every operator is a limit of a sequence of convolution and multiplication operators. Finally, we define the exponential of an operator which permits us to solve some quantum stochastic differential equations. 相似文献
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Du?an?Popov Nicolina?Pop Viorel?Chiritoiu Ioan?Luminosu Marius?Costache 《International Journal of Theoretical Physics》2010,49(4):661-680
In the paper we examine some properties of the generalized coherent states of the Barut-Girardello kind. These states are
defined as eigenstates of a generalized lowering operator and they are strongly dependent on the structure constants. Besides
the pure coherent states we focused our attention on the mixed states one, which are characterized by different probability
distributions. As some examples we consider the thermal canonical distribution and the Poisson distribution functions. We
calculate for these cases the Husimi’s Q and quasi-probability P-distribution functions. 相似文献
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Reflection amplitudes are defined as two-point functions of certain class of conformal field theories where primary fields are given by vertex operators with real couplings. Among these, we consider (Super-) Liouville theory and simply and non-simply laced Toda theories. In this paper we show how to compute the scaling functions of effective central charge for the models perturbed by some primary fields which maintains integrability. This new derivation of the scaling functions are compared with the results from conventional TBA approach and confirms our approach along with other non-perturbative results such as exact expressions of the on-shell masses in terms of the parameters in the action, exact free energies. Another important application of the reflection amplitudes is a computation of one-point functions for the integrable models. Introducing functional relations between the one-point functions in terms of the reflection amplitudes, we obtain explicit expressions for simply-laced and non-simply-laced affine Toda theories. These nonperturbative results are confirmed numerically by comparing the free energies from the scaling functions with exact expressions we obtain from the one-point functions. 相似文献
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S. Youssef 《The European Physical Journal C - Particles and Fields》2000,15(1-4):202-204
Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed
by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring
probability density functions. 相似文献
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借助于符号计算软件Maple,对方程的种子解作适当的未知函数替换,然后利用Backlund 变 换通过具体的符号演算获得了(2+1)维Boussinesq方程的一系列精确解.这些解包括类孤子解 和有理解,其中有的解中含有任意函数,当任意函数取特殊函数时,这些解具有丰富的结构 ,有些结构可能对物理现象的研究是有意义的.
关键词:
(2+1)维Boussinesq方程
Backlund 变换
精确解
类孤子解 相似文献
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In this paper, we use our method to solve the extended Lotka--Volterra equation and
discrete KdV equation. With the help of Maple, we obtain a number of exact solutions
to the two equations including soliton solutions presented by hyperbolic functions
of \sinh and \cosh, periodic solutions presented by trigonometric functions of
\sin and \cos, and rational solutions. This method can be used to solve some
other nonlinear difference--differential equations. 相似文献
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We calculate some simplest n-point functions in supersymmetric Yang-Mills theories contributed by instantons. The result is not vanishing and we discuss some implications of this. In particular, the dynamics of the supersymmetric theories must exhibit some unusual features. 相似文献
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利用数值计算的方法求解了一维理想双势阱模型的基态及低激发态能级和相应的波函数,将双势阱之间的间距、双势阱的相对深度和双势阱的宽窄与实际的物理问题建立了联系,并分析了它们对一维双势阱的能级和相应波函数的影响,定性地模拟了双原子分子和原子中的双势阱问题. 相似文献
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We summarize and deepen existing results on systems of orthogonal pure states in the context of Jordan–Banach (JB) algebras
and C* algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact
spaces such as exposing points by continuous functions, separating sets by continuous functions, and multiplicativity of pure
states. 相似文献
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Spectral reflectance is a significant physical property of materials. It plays an important role in color constancy, illumination modeling, and color reproduction. Spectral reflectance basis functions are the most important impact factors for spectral reflectance recovery. Previous methods mainly calculated basis functions for the reflectance spectra data sets by employing the principle component analysis (PCA) and its improved methods. In this paper, we present a new method to solve this problem. Specifically, we propose a new cost function and some constraint conditions to convert the problem into an optimization problem by minimizing the cost function. Unlike the PCA method which yields the orthogonal basis functions for approximating the reflectance spectra, our method yields the nonorthogonal basis functions for better approximating the reflectance spectra. Experimental results show that our derived basis functions are better than those obtained by the PCA method for reflectance spectra recovery. 相似文献