标量衍射理论的非傍轴近似及其有效性

当光束束腰（或衍射孔孔径）可与波长相比拟或光束具有较大的发散角时，傍轴近似不再成立.在标量瑞利.索末菲衍射积分的基础上，进一步研究了衍射场的非傍轴近似解，并详细分析了解的有效性.以平面波圆孔衍射为例，对衍射场的精确解、非傍轴近似解以及菲涅耳近似解进行了详细的数值计算和比较研究.结果表明，非傍轴近似对微小孔衍射非常精确、有效.     

Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws

We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalues are allowed to have constant multiplicity and corresponding characteristic fields to be linearly degenerate. The approach is based on our careful construction of more accurate auxiliary approximation to weakly nonlinear geometric optics, the properties of wave front-tracking approximate solutions, the behavior of solutions to the approximate asymptotic equations, and the standard semigroup estimates. To illustrate this approach more clearly, we focus first on the Cauchy problem for the hyperbolic systems with compact support initial data of small bounded variation and establish that the L ¹-estimate between the entropy solution and the geometric optics expansion function is bounded by O(?²), independent of the time variable. This implies that the simpler geometric optics expansion functions can be employed to study the behavior of general entropy solutions to hyperbolic systems of conservation laws. Finally, we extend the results to the case with non-compact support initial data of bounded variation.     

Conditional tests for elliptical symmetry

In this paper, we suggest the conditional test procedures for testing elliptical symmetry of multivariate distribution. The conditional tests are exactly valid if the symmetric center and the shape matrix are given and are asymptotically valid if they are unknowns to be estimated. The equivalence, in the large sample sense, between the conditional tests and their unconditional counterparts is established. The power behavior of the tests under global as well as local alternatives is investigated theoretically. A small simulation study is performed.     

茶叶掺糖含量检测算法中光谱数据有效性及冗余度研究

基于近红外光谱(NIRS)技术和遗传算法-反向传播(GA-BP)神经网络建立模型，分析茶叶掺蔗糖样品的1～2.5 μm原始光谱数据的有效性及冗余度。固定样本数据，对模型的参数优化选择后建立茶叶蔗糖含量定量检测模型。将1～2.5 μm原始数据分1～1.7，1～1.3，1.3～1.7，1.7～2.5和2～2.2 μm。利用建立的模型对同一分辨率下的不同波段进行模型训练。预测结果表明，1～1.7和1～2.5 μm波段存在数据冗余。仅使用1.3～1.7或1.7～2.5 μm波段即可有效建立模型。预测模型对同一波段下的不同分辨率进行研究，从2 nm到20 nm改变分辨率，当波段范围为1～2.5 μm时，模型的R均介于0.9和0.95之间，且RMSEP也在1.7和2.1之间。当波段范围为1～1.7 μm时，模型的R均在0.9和0.93之间，且RMSEP也在1.95和2.25之间。结果表明，1～2.5 μm原始数据中确实存在波长范围和光谱分辨率的冗余。通过光谱特征分析和算法建模，可以显著提高光谱数据获取的有效性；对于茶叶中蔗糖含量的检测，可以采用更窄的波长范围和更低的光谱分辨率。     

Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances

The nonlinear Schrödinger (NLS) equation can be derived as an amplitude equation describing slow modulations in time and space of an underlying spatially and temporarily oscillating wave packet. The purpose of this paper is to prove estimates, between the formal approximation, obtained via the NLS equation, and true solutions of the original system in case of non-trivial quadratic resonances. It turns out that the approximation property (APP) holds if the approximation is stable in the system for the three-wave interaction (TWI) associated to the resonance. We construct a counterexample showing that the NLS equation can fail to approximate the original system if instability occurs for the approximation in the TWI system. In the unstable case we give some arguments why the validity of the APP can be expected for spatially localized solutions and why it cannot be expected for non-localized solutions. Although, we restrict ourselves to a nonlinear wave equation as original system we believe that the results hold in more general situations, too.     

基于样本最大分类信息的聚类有效性函数

根据每一样本的最大分类信息，对Bezdek定义的划分系数进行修改，提出了一个新的聚类有效性函数，讨论了该函数的若干性质。实验结果表明在某些情形该函数的判决效果优于划分系数。     

基于万有引力定律的数据分类效果评价

针对模糊C-均值聚类算法对初始化分类参数的选择比较敏感而导致分类结果差异性较大的不足，提出基于万有引力定律的分类效果好坏的评价准则。实验结果表明。本文定义的分类效果评价准则是可行的。     

Comparing the validity of numerical judgements elicited by direct rating and point allocation: Insights from objectively verifiable perceptual tasks

Two popular methods for assigning numerical values to a set of to-be-judged objects in order to capture their relative standing are Direct Rating (DR) and Point Allocation (PA). People using PA distribute a fixed sum of 100 points among the objects, while people using DR rate each object on a fixed scale, typically 0–10, later rescaled to sum to 100. Prior research shows that these methods exhibit distinct profiles when values are ranked from largest to smallest, with DR being more test–retest reliable. But which method best translates people’s inner judgments into outer numerical values (is more valid)? Instead of examining subjective or abstract stimuli, we use objectively verifiable perceptual tasks, namely judgments of line length presented using bar charts. We show that (i) DR is more inter-rater reliable than PA; (ii) DR is more accurate than PA at the individual level; (iii) but there is no difference in accuracy when individual judgments are combined to form group-level estimates; and (iv) DR judgments were improved by using prior knowledge of method bias, whereas PA judgments were not.