高斯-谢尔模型光束通过光阑像散透镜传输轴上光谱变化

从部分相干光的传输理论出发,研究了高斯-谢尔模型(GSM)光束通过光阑像散透镜传输轴上的光谱变化规律.结果表明,与光源光谱相比,高斯-谢尔模型(GSM)光束通过光阑像散透镜传输轴上光谱发生了中心频率的移动,这种现象被称为光谱位移.详细分析了透镜的像散、光束的空间相关性和光阑的截断参量对光谱变化的影响.数值计算表明,这些参量会对光谱移动产生比较大的作用.     

高斯光束斜入射法布里-珀罗干涉腔后的反射光强分布

基于多光束干涉原理,推导了高斯光束斜入射法布里-珀罗干涉仪后的反射光强表达式.在此基础之上数值研究了入射角对高斯光束的反射特性的影响.研究结果表明:当法布里-珀罗干涉腔的腔长满足反共振时,随着入射角的增大,反射光的光强分散,峰值强度下降后呈现出幅度衰减的波动;峰值位置随着入射角的增大,呈现出幅度越来越小的振荡偏移;光斑大小随入射角的增大,呈现出幅度减小的振荡.     

色散介质中啁啾高斯脉冲的时间和光谱特性

对啁啾高斯脉冲光束在色散介质中的时间和光谱特性作了研究.给出了远场光谱蓝移和脉冲展宽的解析式.结果表明：通过选择适当的啁啾参量,啁啾高斯脉冲光束沿轴上传输色散长度时,脉冲可恢复到初始值.随啁啾参量增加,谱线宽度展宽,轴上光谱蓝移增加,在远场蓝移趋于一渐近值.随啁啾参量增加,离轴光谱红移增加.     

小波域高斯混合模型与中值滤波的混合图像去噪研究

基于高斯混合模型的小波去噪方法并结合中值滤波法对脉冲噪音有较好滤除效果的特点,将这两种方法结合起来,对含有高斯脉冲混合噪音图像进行去噪处理.该算法采用Matlab语言进行仿真.实验结果表明,这种混合去噪方法的效果要优于单纯使用中值滤波或者小波去噪的效果.     

Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects

Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.     

Local Lead–Lag Relationships and Nonlinear Granger Causality: An Empirical Analysis

The Granger causality test is essential for detecting lead–lag relationships between time series. Traditionally, one uses a linear version of the test, essentially based on a linear time series regression, itself being based on autocorrelations and cross-correlations of the series. In the present paper, we employ a local Gaussian approach in an empirical investigation of lead–lag and causality relations. The study is carried out for monthly recorded financial indices for ten countries in Europe, North America, Asia and Australia. The local Gaussian approach makes it possible to examine lead–lag relations locally and separately in the tails and in the center of the return distributions of the series. It is shown that this results in a new and much more detailed picture of these relationships. Typically, the dependence is much stronger in the tails than in the center of the return distributions. It is shown that the ensuing nonlinear Granger causality tests may detect causality where traditional linear tests fail.     

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is applied to calculations of the nuclear excitations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that is successful in the mean-field calculations. The RPA results obtained by the GEM are compared with those obtained by several other available methods in Ca isotopes, by using a density-dependent contact interaction along with the Woods–Saxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM with good precision, for the 1⁻, 2⁺ and 3⁻ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the E1 response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in ⁶⁰Ca are investigated in some detail.     

Circular partially coherent flattened Gaussian beam

An alternative theoretical model called circular partially coherent flattened Gaussian beam (FGB) is developed to describe a circular partially coherent beam with a flat-topped spatial profile. Explicit expression for the propagation factor of a circular partially coherent FGB is derived. We drive the analytical formulae for the cross-spectral density and mean-squared beam width of a circular partially coherent FGB propagating through a paraxial ABCD optical system based on the generalized Collins formula. The intensity, spreading and directionality properties of a circular partially coherent FGB propagating in free space are studied as numerical examples. The propagation properties of a circular partially coherent FGB agree well with those of a partially coherent flat-topped beam reported in the literature. Thus, our model provides an alternative but reliable model for describing a circular partially coherent beam with flat-topped profile.     

On Pseudo-Holomorphic Curves from Two-Spheres into a Complex Grassmannian G（2, 5）

Let s ： S2 → G（2, 5） be a linearly full totally unramified pseudo-holomorphic curve with constant Gaussian curvature K in a complex Grassmann manifold G（2, 5）. It is prove that K is either 1 4 1 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/3 if and only if s is totally real. We also prove that the Gaussian curvature K is either 1 or -4/3 if s is a non-degenerate holomorphic curve under some conditions.     

Relativistic correlating basis sets for 57La and 89Ac

Developed and reported are compact yet efficient correlating basis sets for the ₅₇La and ₈₉Ac atoms, missing in the literature. Good performance of these correlating sets is exemplified in molecular applications to diatomic oxides and fluorides. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010