The two-dimensional minimum-bias window function

Using the criterion of minimization of the bias integral, by means of a quantum-mechanical analogy, the optimum two-dimensional window function for spectral estimates is determined. The optimum window and its two-dimensional Fourier transform are numerically evaluated. A comparison is carried out with some other standard windows. A three-dimensional generalization is briefly outlined.     

A new method of spectral decomposition of covariance matrix in mixed effects models and its applications

For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare with the two methods in literature, the decomposition can not only give the actual number of all distinct eigenvalues and their expression, but also show clearly the relationship between the design matrices of random effects and the decomposition. These results can be applied to the problems for testifying the analysis of the variance estimate being a minimum variance unbiased under all random effects models and some mixed effects models with balanced data, for finding the explicit solution of maximum likelihood equations for the general mixed effects model and for showing the relationship between the spectral decomposition estimate and the analysis of variance estimate.     

Estimates and Spectral Asymptotics for Systems with Multiplicities

We consider elliptic and hyperbolic systems with diagonalizable principal part. Characteristics are allowed to have variable multiplicities. Assuming that the characteristics are generic, we give estimates for solutions of a hyperbolic Cauchy problem in L ^p spaces. The first and second terms of the spectral asymptotics are obtained for the corresponding elliptic system.     

Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory

We have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces. For the special case of a Duffing oscillator (a damped anharmonic oscillator with a cubic nonlinearity) driven by Gaussian white noise and by a sinusoidal force, explicit expressions for the renormalized (linearized) frequency, the autocorrelation function, and the spectral density of the oscillator displacement in terms of all the system parameters have been derived. We have determined the region of the parameter space in which the applied periodic force has a significant influence on the second-order statistics of the oscillator.This research was supported by the Office of Naval Research, by the National Science Foundation under grant No. CHE78-21460 and by a grant from Charles and Reneé Taubman.     

Intensity fluctuations in thermal light with orthogonally polarised multiple-peak spectrum

The moment generating function of the integrated light intensity of thermal radiation having multiple peak spectrum is obtained. Cases of two-peak and three-peak spectra where different peaks are in orthogonal states of polarisation are considered. The moment generating function is shown to be the product of two simpler generating functions.     

谱问题、发展方程族及Lax表示的等价性

讨论了四对谱问题、相应的保谱方程族以及它们Ｌａｘ表示的等价住，并利用这种等价关系可导出一些方程的Ｌａｘ表示．     

部分相干光的轴外点频移

本文研究了普通热光源（不相干光源）通过消色差傅里叶变换系统后，二次光源产生的远场轴外点频移，数值计算结果表明，轴外点的频谱分布有微小的调制，且频移量与轴上点不同。     

Stochastic LQ-optimal control for 2-D systems

Stochastic LQ-optimal control problem is solved for linear 2-D systems via 2-D polynomial techniques. All stabilizing controllers are parameterized and then minimizing one is obtained. Its transfer function results from two 2-D spectral factorizations and a couple of linear equations in formal power series. A practically useful sub-optimal controller is also considered that results from truncated spectral factorizations and a couple of 2-D polynomial equations.     

光照光谱功率分布的估计和颜色分割

提出了应用有限维线性模型和双色反射模型和双色反射模型抽表示而物体颜色的本征特性的方法，首先估计出光照的光谱功率分布，再获取物体的表面光谱反射率，从而得到和光照与几何条件无关的归一化偏差光谱反射率，它仅反映物体的表面反射特性，可作为颜色分割和识别的可靠特征。     

悬置槽线行波相位调制器的特性分析

提出一种新颖的集成光波导行波相位调制器结构，它利用悬置槽线作为调制器的外调制电路，减小了光波和调制波之间的速度失配，提高了相位调制器的调制带宽。采用谱域等效传输线法分析了悬置槽线的传播特性．