非线性分析广义增量法算法研究

本文推导出广义增量法极值点与非临界点的统一形式解，首次指出增量解与增广矩阵零空间基的关系，从而可直接由零空间基得到增量解。首次研究了在Matlab IDE环境下，基于广义增量法的非线性有限元分析实现方法，指出其在数值分析中类似位移增量法的特征。最后，数值分析算例结果表明了该算法与程序的正确性和有效性。  

F/1.3抛物面零检验补偿器设计

根据会聚光路中使用的Offner补偿器和平行光路中使用的两片式补偿器的要求,设计出了四个针对F/1.3抛物面的补偿器,并从剩余波像差、公差要求、加工工艺性、装调等方面对它们的性能做出比较,确定了三个可用于实际补偿检验的设计结果,其剩余波像差均小于/35。所述补偿器的设计方法和要求具有普遍性,设计结果也可用于同类型主镜补偿器的设计。  

Nonparametric inference with generalized likelihood ratio tests

The advance of technology facilitates the collection of statistical data. Flexible and refined statistical models are widely sought in a large array of statistical problems. The question arises frequently whether or not a family of parametric or nonparametric models fit adequately the given data. In this paper we give a selective overview on nonparametric inferences using generalized likelihood ratio (GLR) statistics. We introduce generalized likelihood ratio statistics to test various null hypotheses against nonparametric alternatives. The trade-off between the flexibility of alternative models and the power of the statistical tests is emphasized. Well-established Wilks’ phenomena are discussed for a variety of semi- and non-parametric models, which sheds light on other research using GLR tests. A number of open topics worthy of further study are given in a discussion section. This invited paper is discussed in the comments available at: , , , , , , , , . The work was supported by the NSF grants DMS-0354223, DMS-0532370 and DMS-0704337. The paper was initiated when Jiancheng Jiang was a research fellow at Princeton University.  

基于极小准则的完备正交判别局部保持算法

以无监督判别投影算法为理论基础,提出了一种基于极小准则的完备正交判别局部保持投影算法.算法首先根据同类样本的空间信息重新定义了类内局部保持散度矩阵与类问局部保持散度矩阵,然后借鉴无监督判别投影算法的目标函数,推导出一个基于极小准则的目标函数,该目标函数通过投影到总体散度矩阵的非零空间中有效地解决小样本问题,最后给出了该算法基于QR分解的正交投影矩阵的求解方法.人脸库上的实验结果表明了所提方法的有效性.  

Torsional rigidity of a circular bar with multiple circular inclusions using the null-field integral approach

In this article, a systematic approach is proposed to calculate the torsional rigidity and stress of a circular bar containing multiple circular inclusions. To fully capture the circular geometries, the kernel function is expanded to the degenerate form and the boundary density is expressed into Fourier series. The approach is seen as a semi-analytical manner since error purely attributes to the truncation of Fourier series. By collocating the null-field point exactly on the real boundary and matching the boundary condition, a linear algebraic system is obtained. Convergence study shows that only a few number of Fourier series terms can yield acceptable results. Finally, torsion problems are revisited to check the validity of our method. Not only the torsional rigidities but also the stresses of multiple inclusions are also obtained by using the present approach.  

大口径非球面Ronchi光栅测量方法

在对非球面加工过程中常用检测方法的优缺点进行比较的基础上,介绍了Ronchi光栅法的系统组成、工作原理和数据处理方法,并进行了光栅频率和灵敏度分析.通过对Ronchi光栅的频率、灵敏度的分析比较,发现可以通过改变其频率来实现大口径非球面不同加工阶段2～200 μm范围内的误差检测.该方法制作简单,使用方便.它的深入研究,将为大口径非球面精磨和初抛光阶段提供一种有效、可靠的定量检测手段.  

Reconciling Bayesian and frequentist evidence in the point null testing problem

For the point null hypothesis testing problem it is shown that, in some situations, the classical evidence againstH ₀, expressed in terms of the p-value, is in the range of Bayesian measures of evidence. In these situations, it is therefore possible to reconcile measures of evidence between Bayesian and frequentist approaches. More specifically, for the class of unimodal, symmetric and nonincreasing prior distributions, it is shown that the infimum of the posterior probability ofH ₀ is numerically equal to thep value. The discrepancy which appears in the literature dedicated to this subject until now, is due to the form of the mixed distribution and not due to its use as a prior.  

Probe model implementation in the null field approach to crack scattering

A model of a compressional ultrasonic transducer is implemented into a T-matrix method-based solution to a crack scattering problem. The probe can act both as a receiver and as a transmitter, and it is modeled as an acoustic piston-like source. A previous solution by the null field approach is applied and is here used to model a crack that is partly closed due to an external background pressure. Numerical calculations of the signal response when the crack is penny-shaped are performed and compared with results from a program based on the Geometrical Theory of Diffraction, and the agreement is generally found to be very good.  

Elastodynamic scattering by fluid-filled nonplanar cracks

A recent modification of the null field approach is adapted to the study of scattering of elastic waves by fluid-filled nonplanar cracks. The fluid-filled crack is modeled as a surface over which friction-free boundary conditions apply. A closed surface is formed by adding a fictitious surface, on which latter surface boundary conditions of welded contact are applied. The surface fields on the closed surface are expanded in vector spherical harmonics in a manner which takes the edge conditions into account. Some numerical results on farfield quantities, such as scattering cross sections and backscattering amplitudes (both in the frequency and time domains), are presented for rotationally symmetric cracks.  

Null-ellipsometry investigations of the optical properties and diffusion processes in spin-valve structures based on Co and Cu

The influence of annealing temperature (T_a = 300-900 K) on optical properties of the Au (4 nm)/Co (3 nm)/Cu (6-12 nm)/Co (20 nm)/SiO₂/Si spin-valve structures was studied. The model of Co, Au, and Cu atom interdiffusion was proposed based on the experimental data analysis. The formation of solid solutions at the thin layer interfaces Au/Co and Cu/Co was studied, and as a result the most intensive formation of solid solutions was identified at annealing temperature of T_a = 750 K. The optical parameters of the samples were calculated using the genetic algorithm. The spin-valve systems remain relatively unperturbed until 750 K, but the optical properties change significantly from 750 to 900 K. It can be explained by the formation of the interphase in multilayer thin film systems.