光学工程分析中的镜面面形处理新方法

光学系统在载荷的作用下会发生变形。基于干涉检验理论,提出了一种先调整后再拟合的处理方法。首先利用下山法计算光学镜面在法线方向的变形;然后利用Zernike多项式拟合变形曲面得到Zernike系数;最后去除刚体位移,作等高线图。新的数据处理方法可以更好的与干涉检验保持一致。对某相机的主镜进行仿真试验,结果表明,下山法计算效率较高,先调整后再拟合的处理结果与干涉检验结果的一致性较好。     

线性与非线性波的Chebyshev广义有限谱模拟

给出求解二维线性与非线性波的Chebyshev广义有限谱模拟方法.结合时间层次的高精度预报-校正方法，模拟了二维线性浅水驻波和波在浅滩的非线性变形.方法能够准确模拟水波的物理特征. 关键词： Chebyshev广义有限谱 线性波 非线性波     

含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔

讨论简谐激励作用下含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔现象.首先用Chebyshev 多项式逼近法将随机Duffing-van der Pol系统化成与其等价的确定性系统，然后通过等价确定性系统来探索该系统的倍周期分岔现象.数值模拟显示随机Duffing-van der Pol 系统与均值参数系统有着类似的倍周期分岔行为，同时指出，随机参数系统的倍周期分岔有其自身独有的特点.文中的主要数值结果表明Chebyshev 多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法. 关键词： Chebyshev多项式 随机Duffing-van der Pol系统 倍周期分岔     

Spectrum is periodic for n-intervals

In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set Ω is periodic, with the period an integral multiple of the measure of Ω. As a consequence we get a structure theorem for such spectral sets and observe that the generic case is that of the equal interval case.     

Laguerre Polynomials, Restriction Principle, and Holomorphic Representations of SL(2,R)

The restriction principle is used to implement a realization of the holomorphic representations of SL(2,R) on L ² (R ⁺,t dt) by way of the standard upper half plane realization. The resulting unitary equivalence establishes a correspondence between functions that transform according to the character e^–i(2n++1); under rotations and the Laguerre polynomials. The standard recursion relations amongst Laguerre polynomials are derived from the action of the Lie algebra.     

On the Right-Definite and Left-Definite Spectral Theory of the Legendre Polynomials

In this paper, we further develop the left-definite and right-definite spectral theory associated with the self-adjoint differential operator A in L²(-1,1), generated from the classical second-order Legendre differential equation, having the sequence of Legendre polynomials as eigenfunctions. Specifically, we determine the first three left-definite spaces associated with the pair (L²(-1,1),A). As a consequence of these results, we determine the explicit domain of both the associated left-definite operator A₁, first observed by Everitt, and the self-adjoint operator A^1/2. In addition, we give a new characterization of the domain D(A) of A and, as a corollary, we present a new proof of the Everitt-Mari result which gives optimal global smoothness of functions in D(A).