Setting local rank constraints by orthogonal projections for image resolution analysis: Application to the determination of a low dose pharmaceutical compound

Raman chemical imaging provides chemical and spatial information about pharmaceutical drug product. By using resolution methods on acquired spectra, the objective is to calculate pure spectra and distribution maps of image compounds. With multivariate curve resolution-alternating least squares, constraints are used to improve the performance of the resolution and to decrease the ambiguity linked to the final solution. Non negativity and spatial local rank constraints have been identified as the most powerful constraints to be used.     

Stereo matching cost computation based on nonsubsampled contourlet transform

A new matching cost computation method based on nonsubsampled contourlet transform (NSCT) for stereo image matching is proposed in this paper. Firstly, stereo image is decomposed into high frequency sub-band images at different scales and along different directions by NSCT. Secondly, by utilizing coefficients in high frequency domain and grayscales in RGB color space, the computation model of weighted matching cost between two pixels is designed based on the gestalt laws. Lastly, two types of experiments are carried out with standard stereopairs in the Middlebury benchmark. One of the experiments is to confirm optimum values of NSCT scale and direction parameters, and the other is to compare proposed matching cost with nine known matching costs. Experimental results show that the optimum values of scale and direction parameters are respectively 2 and 3, and the matching accuracy of the proposed matching cost is twice higher than that of traditional NCC cost.     

Bilateral generating functions and operational methods

Bilateral generating functions are those involving products of different types of polynomials. We show that operational methods offer a powerful tool to derive these families of generating functions. We study cases relevant to products of Hermite polynomials with Laguerre, Legendre and other polynomials. We also propose further extensions of the method which we develop here.     

双轴晶体主平面上倍频的相位匹配

从折射率椭球方程和折射率椭球面出发，讨论光束在双轴晶体中传播及偏振的特性、主平面倍频共线相位匹配（PM）问题，得到了双轴晶体主平面内激光所有可能PM倍频的8种偏振组合及其相应的PM角公式、有效非线性（NL）系数deff的一般表达式。结果表明：得到的公式简单，可大大简化PM参数计算及优化设计；折射率椭球面是单层曲面，比双层的折射率面简单；基于折射率椭球面寻找所有可能PM的类型、偏振组合的方法物理图像简明，易于理解，大大降低了双轴晶体PM问题分析的难度。     

一类图的特征多项式与匹配多项式

本文对一类具有对称轴的图A_n(n≥0),得到了它的特征多项式及匹配多项式的精确表达式;同时还得到A_(?)的完美匹配数。     

On the Zeros of Orthogonal Polynomials: The Elliptic Case

Constructive Approximation - Let E = [–1, α] \cup [β, 1], –1 &;lt; α &;lt; β &;lt; 1, and let (pn) be orthogonal on E with respect to the weight function...     

New inequalities from classical Sturm theorems

Inequalities satisfied by the zeros of the solutions of second-order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among other properties obtained, Szegő's bounds on the zeros of Jacobi polynomials for , are completed with results for the rest of parameter values, Grosjean's inequality (J. Approx. Theory 50 (1987) 84) on the zeros of Legendre polynomials is shown to be valid for Jacobi polynomials with |β|1, bounds on ratios of consecutive zeros of Gauss and confluent hypergeometric functions are derived as well as an inequality involving the geometric mean of zeros of Bessel functions.     

混合位级正交试验设计的极差分析方法

本文指出，在混合位级的正交试验设计中，以往的极差分析方法存在着不足。本文给出了极差的修正方法，并用大量实例做了数值验证，说明这个修正确实很有效