黑体辐射公式的量纲分析

量纲分析是研究物理问题的重要方法之一.本文对量纲分析的解题步骤做了梳理归纳,并对于黑体辐射公式进行了量纲分析.     

Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles.We also prove how to construct various tight frames for L2(Rd) by replac-ing some mother framelets.     

Exploring Microstructures and Interphase Properties of Surface- Grafted Diblock Copolymers in a Homopolymer Melt by Self-Consistent Field Theory Simulations

Polymeric self-consistent field theory is used to investigate microstructures and interphase properties of diblock copolymers grafted onto solid surfaces in a homopolymer melt. The calculations show that the grafted diblock copolymers can self-assemble into hemispherical microstructures at low grafting densities of the diblock copolymers. The morphology transforms into hemicylinder-like and sandwich-like lamellar microstructures with an increase in the chain-grafting density. The effective thickness of the grafted block layer and the interphase width between the homopolymer melt and the grafted copolymers strongly depend on the physicochemical parameters of the system, such as the composition of the grafted copolymer, the chemical incompatibility between the different components, the length ratio of grafted copolymer to homopolymer, and the grafting density of the diblock copolymers. In addition, the above computational results of microphase-separated structures and interphase properties are qualitatively compared with our previous experimental observations. The comparison indicates that our theoretical results not only reproduce the general feature of the experimental observations, but also elucidate the internal structural information and complement the findings in the region of high grafting densities of diblock copolymers.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.     

Blind separation of fluorescence spectra using sparse non‐negative matrix factorization on right hand factor

Sparse non‐negative matrix factorization on right side factor (SNMF/R) has better performance in feature extraction than non‐negative matrix factorization. In this work, SNMF/R was first used to separate the overlapped three‐dimensional fluorescence spectra of polycyclic aromatic hydrocarbons mixtures in pure water, lake water, and river water, respectively. It is found that the similarity coefficients between the acquired three‐dimensional spectra and the corresponding reference spectra with random initials are all above 0.80; the recognition rate of SNMF/R is higher than that of PARAFAC and non‐negative matrix factorization algorithms, especially in the case of lake water and river water samples. In addition, SNMF/R does not need any initialization scheme designing during spectra separation. These results demonstrate that SNMF/R is an appropriate algorithm to separate the overlapped fluorescence spectra of polycyclic aromatic hydrocarbons in aquatic environment accurately and effectively. Copyright © 2015 John Wiley & Sons, Ltd.     

Explicit–implicit mapping approach to nonlinear blind separation of sparse nonnegative dependent sources from a single mixture: pure component extraction from nonlinear mixture mass spectra

The nonlinear, nonnegative single‐mixture blind source separation problem consists of decomposing observed nonlinearly mixed multicomponent signal into nonnegative dependent component (source) signals. The problem is difficult and is a special case of the underdetermined blind source separation problem. However, it is practically relevant for the contemporary metabolic profiling of biological samples when only one sample is available for acquiring mass spectra; afterwards, the pure components are extracted. Herein, we present a method for the blind separation of nonnegative dependent sources from a single, nonlinear mixture. First, an explicit feature map is used to map a single mixture into a pseudo multi‐mixture. Second, an empirical kernel map is used for implicit mapping of a pseudo multi‐mixture into a high‐dimensional reproducible kernel Hilbert space. Under sparse probabilistic conditions that were previously imposed on sources, the single‐mixture nonlinear problem is converted into an equivalent linear, multiple‐mixture problem that consists of the original sources and their higher‐order monomials. These monomials are suppressed by robust principal component analysis and hard, soft, and trimmed thresholding. Sparseness‐constrained nonnegative matrix factorizations in reproducible kernel Hilbert space yield sets of separated components. Afterwards, separated components are annotated with the pure components from the library using the maximal correlation criterion. The proposed method is depicted with a numerical example that is related to the extraction of eight dependent components from one nonlinear mixture. The method is further demonstrated on three nonlinear chemical reactions of peptide synthesis in which 25, 19, and 28 dependent analytes are extracted from one nonlinear mixture mass spectra. The goal application of the proposed method is, in combination with other separation techniques, mass spectrometry‐based non‐targeted metabolic profiling, such as biomarker identification studies. Copyright © 2015 John Wiley & Sons, Ltd.     

等效相移光栅反射光谱特性的研究

等效相移光栅的原理是,通过对取样光纤布拉格光栅在特定点进行毫米尺度的“位移”,经过傅里叶变换,在各频率通道产生“等效相移”。首先利用光栅的Turan传输矩阵进行数值模拟,验证了真实相移光栅的各种性质在等效相移光栅中的实现,然后针对当前关于等效相移光栅的报道中,-2级光栅反射率都很低,并且没有出现“等效相移”的情况,提出了一种实现-2级等效相移光栅的方法,并进行了仿真验证。最后给出了等效相移光栅反射率随长度变化的曲线。     

基于传输矩阵法的纵向啁啾体光栅衍射特性

为了研究纵向啁啾体光栅的光谱衍射特性,采用传输矩阵方法进行了分析,研究了光栅的厚度、折射率调制系数和啁啾波长范围对纵向啁啾体光栅中心衍射效率的影响。结果表明,随着光栅厚度的增加,中心衍射效率随之增大;随着光栅折射率调制系数的增大,中心衍射效率也随之逐渐增加;而随着啁啾波长范围的增大,纵向啁啾体光栅的中心衍射效率则逐渐减小。此研究结果对大尺寸啁啾体光栅的设计制作有一定的参考价值。     

基于RPCA的SAR图像纹理特征去噪

合成孔径雷达(SAR)图像具有丰富的纹理信息,这些纹理信息能反映地物空间结构关系。当前纹理特征被广泛应用于SAR图像分类和SAR图像分割中。受成像因素影响,直接采用从SAR图像中提取的纹理特征效果不够好。为避免传统先滤波再提取纹理特征的方法对纹理、边缘信息造成损失,提出了一种先提取SAR图像纹理特征,再利用Robust PCA方法对纹理特征去噪的新方法,最后采用Kmeans聚类方法检验RPCA处理后的纹理特征表达效果。实验结果表明该方法能将聚类正确率从82%提高到84%。     

基于证据空间有效性指标的聚类选择性集成

首先针对距离空间在描述数据复杂结构信息方面的不足给出证据空间的概念。然后基于证据空间扩展有效性指标Davies-Bouldin,同时利用聚类成员的类别相关矩阵度量差异性。最后以较高有效性和较大差异性为目标选择聚类成员并用于集成。实验结果显示所提方法能够有效提高聚类集成算法的有效性。