On the structure of similarity solutions of a differential equation arising from boundary layer problem

We consider an ordinary differential equation with f(0)=a, f^′(0)=1, f^′(∞):=limt→∞f^′(t)=0, where β is a real constant. The given problem may arise from the study of steady free convection flow over a vertical semi-infinite flat plate in a porous medium, or the study of a boundary layer flow over a vertical stretching wall. In this paper, the structure of solutions for the cases of β?−2 is studied. Combining the results of [B. Brighi, T. Sari, Blowing-up coordinates for a similarity boundary layer equation, Discrete Contin. Dyn. Syst. 5 (2005) 929-948; J.-S. Guo, J.-C. Tsai, The structure of solution for a third order differential equation in boundary layer theory, Japan J. Indust. Appl. Math. 22 (2005) 311-351; J.-C. Tsai, Similarity solutions for boundary layer flows with prescribed surface temperature, Appl. Math. Lett. 21 (1) (2008) 67-73], we conclude that the given problem may possess at most two types solutions for β∈R. Moreover, multiple solutions are also verified for various pairs of (a,β).     

One-mode three-way overlapping cluster analysis

The present paper introduces an overlapping cluster analysis model and an associated algorithm that can analyze one-mode three-way similarities. The present model is an extension of ADCLUS model, and the present algorithm is based on the MAPCLUS algorithm. In the present model, one-mode three-way similarities are represented by the sum of the numerical weights of clusters to which any triplet of objects belongs. The present model and algorithm were applied to joint purchase data, and compared the result with that of MAPCLUS to show that the present model is effective in representing one-mode three-way similarities.     

激光诱导击穿光谱元素谱线自动识别方法研究

根据激光诱导击穿光谱谱线展宽机制,对NIST标准谱线数据库中的发射谱线进行了模拟,并与实验光谱进行对比,在对比分析中引入相似性测度,得到模拟光谱和实验光谱的相似程度。对元素谱线的自动归属识别方法进行分析和研究,通过相似性计算对土壤样品340～345nm波段光谱进行了识别分析,利用最小二乘原理计算各谱线之间的比例系数,实现了光谱识别,实验结果验证了基于相似性测度的光谱识别方法的可行性及其自动识别的优越性。     

粗糙集的相似度量

在近似空间中,分别以集合的上下近似以及元素的隶属度定义了两个集合间的相似度度量,讨论了两种相似度的性质,并对两种相似度进行了比较．     

Exact vortex solitons in a quasi-two-dimensional Bose–Einstein condensate with spatially inhomogeneous cubic–quintic nonlinearity

The exact vortex soliton solutions of the quasi-two-dimensional cubic–quintic Gross–Pitaevskii equation with spatially inhomogeneous nonlinearities are constructed by similarity transformation. It is demonstrated that spatially inhomogeneous cubic–quintic nonlinearity can support exact vortex solitons in which there are two quantum numbers S and m. The radius structures and density distributions of these vortex solitons are studied, and it is shown that the number of ring structure of the vortex solitons increases by one with increasing the “radial quantum number” m by one.     

Structure–semantics interplay in complex networks and its effects on the predictability of similarity in texts

The classification of texts has become a major endeavor with so much electronic material available, for it is an essential task in several applications, including search engines and information retrieval. There are different ways to define similarity for grouping similar texts into clusters, as the concept of similarity may depend on the purpose of the task. For instance, in topic extraction similar texts mean those within the same semantic field, whereas in author recognition stylistic features should be considered. In this study, we introduce ways to classify texts employing concepts of complex networks, which may be able to capture syntactic, semantic and even pragmatic features. The interplay between various metrics of the complex networks is analyzed with three applications, namely identification of machine translation (MT) systems, evaluation of quality of machine translated texts and authorship recognition. We shall show that topological features of the networks representing texts can enhance the ability to identify MT systems in particular cases. For evaluating the quality of MT texts, on the other hand, high correlation was obtained with methods capable of capturing the semantics. This was expected because the golden standards used are themselves based on word co-occurrence. Notwithstanding, the Katz similarity, which involves semantic and structure in the comparison of texts, achieved the highest correlation with the NIST measurement, indicating that in some cases the combination of both approaches can improve the ability to quantify quality in MT. In authorship recognition, again the topological features were relevant in some contexts, though for the books and authors analyzed good results were obtained with semantic features as well. Because hybrid approaches encompassing semantic and topological features have not been extensively used, we believe that the methodology proposed here may be useful to enhance text classification considerably, as it combines well-established strategies.     

一种基于小波和矩阵型扩散的图像放大

提出了一种基于小波多分辨分析和矩阵型扩散的图像放大方法.该方法把原图像作为放大图像的小波低频子带,初始高频置零小波重构,用矩阵型扩散方程处理后小波分解,得到估计的高频再与原图像重构.在扩散中取矩阵型扩散的扩散系数,选择其特征根,使扩散在垂直于边缘方向梯度较大时为逆扩散以锐化边缘,而沿边缘方向为正向扩散以增强边缘;同时提出了放大图像与原图像的一种相似性标准.该方法在放大图像的同时既去除了噪音又有效保持了边缘.数值实验结果证实,此方法为一个有效地图像放大方法.