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。  

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.  

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.  

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.  

抑制运动强干扰的稳健波束域目标方位估计方法

为了减小来自旁瓣区快速运动的强干扰对波束域高分辨方位估计方法的影响,提出一种稳健的波束域高分辨方位估计方法。该方法在形成多波束时,将稳健自适应波束形成与零陷扩宽技术相结合,有效地抑制了运动强干扰所造成的快拍失效和扫描方向误差引起的自适应波束图畸变,从而保证波束域方法能准确地估计目标方位。仿真结果验证了该方法的有效性。  

五臂阵的自适应波束零点展宽方法的理论研究

针对水下声纳浮标系统中扩展性较好的五臂阵,为提高其自适应波束形成器的稳健性,引入了一种零点展宽的方法,主要包括Mailloux的基阵协方差矩阵扩展法和Zatman的频散合成法。两者用多个虚拟干扰源替代实际干扰源,从而共同作用形成宽的零陷。并进行了详细的理论推导,还通过仿真实验验证了其应用在实际声纳系统中的可行性和有效性。  

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.  

A note on Lindley's paradox

Lindley's paradox epitomizes the conflict between Bayesian and frequentist evidences in hypothesis testing. We scrutinize the point null approximation assumption using the interval null and the smooth formulations. Along with numerical calculation, under the smooth null formulation, we have found that Lindley's paradox prevails relatively independent of smoothness of the target function. However, it is less drastic as suggested earlier. The research is supported by Taiwan NSC 91-2118-M-259-003