Trace class Toeplitz operators with unbounded symbols on weighted Bergman spaces

In this note we construct a function φ in L2（Bn,dμ） which is unbounded on any neighborhood of each boundary point of Bn such that Tφ is a trace class operator on weighted Bergman space Lα2（Bn,dμ） for several complex variables.     

Embeddings of Un(q2) and symmetric strongly regular graphs

In the geometric setting of the embedding of the unitary group U_n(q²) inside an orthogonal or a symplectic group over the subfield GF(q) of GF(q²), q odd, we show the existence of infinite families of transitive two‐character sets with respect to hyperplanes that in turn define new symmetric strongly regular graphs and two‐weight codes. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 248–253, 2010     

Rainbow and orthogonal paths in factorizations of Kn

For n even, a factorization of a complete graph K_n is a partition of the edges into n?1 perfect matchings, called the factors of the factorization. With respect to a factorization, a path is called rainbow if its edges are from distinct factors. A rainbow Hamiltonian path takes exactly one edge from each factor and is called orthogonal to the factorization. It is known that not all factorizations have orthogonal paths. Assisted by a simple edge‐switching algorithm, here we show that for n?8, the rotational factorization of K_n, GK_n has orthogonal paths. We prove that this algorithm finds a rainbow path with at least (2n+1)/3 vertices in any factorization of K_n (in fact, in any proper coloring of K_n). We also give some problems and conjectures about the properties of the algorithm. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 167–176, 2010     

Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kind

Periodic harmonic wavelets (PHW) were applied as basis functions in solution of the Fredholm integral equations of the second kind. Two equations were solved in order to find out advantages and disadvantages of such choice of the basis functions. It is proved that PHW satisfy the properties of the multiresolution analysis.     

Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations

This article presents a time-accurate numerical method using high-order accurate compact finite difference scheme for the incompressible Navier-Stokes equations. The method relies on the artificial compressibility formulation, which endows the governing equations a hyperbolic-parabolic nature. The convective terms are discretized with a third-order upwind compact scheme based on flux-difference splitting, and the viscous terms are approximated with a fourth-order central compact scheme. Dual-time stepping is implemented for time-accurate calculation in conjunction with Beam-Warming approximate factorization scheme. The present compact scheme is compared with an established non-compact scheme via analysis in a model equation and numerical tests in four benchmark flow problems. Comparisons demonstrate that the present third-order upwind compact scheme is more accurate than the non-compact scheme while having the same computational cost as the latter.     

正交回归和一般最小二乘回归的几何误差分析

线性回归分析中,一般最小二乘回归的目标函数只考虑一个方向的扰动,采用基于几何距离的正交回归能克服固定单方向最优带来的拟合稳定性差的弊端。本文分析和比较了正交回归和一般最小二乘回归的误差,并定量地给出了两者的几何误差与原始数据的方差、相关系数之间的关系,指出正交回归的几何误差小于一般最小二乘回归,并且正交回归具有旋转不变性。最后,以平面直线拟合为例验证了这个结论。     

Banach空间中渐近非扩张型半群的遍历定理

对带Opial条件的Banach空间中非扩张半群的不动点理论进行推广,得到了带Opial条件的Banach空间中渐近非扩张型半群的遍历收敛定理.     

X‐tended target projection (XTP)—comparison with orthogonal partial least squares (OPLS) and PLS post‐processing by similarity transformation (PLS + ST)

Target projection (TP) also called target rotation (TR) was introduced to facilitate interpretation of latent‐variable regression models. Orthogonal partial least squares (OPLS) regression and PLS post‐processing by similarity transform (PLS + ST) represent two alternative algorithms for the same purpose. In addition, OPLS and PLS + ST provide components to explain systematic variation in X orthogonal to the response. We show, that for the same number of components, OPLS and PLS + ST provide score and loading vectors for the predictive latent variable that are the same as for TP except for a scaling factor. Furthermore, we show how the TP approach can be extended to become a hybrid of latent‐variable (LV) regression and exploratory LV analysis and thus embrace systematic variation in X unrelated to the response. Principal component analysis (PCA) of the residual variation after removal of the target component is here used to extract the orthogonal components, but X‐tended TP (XTP) permits other criteria for decomposition of the residual variation. If PCA is used for decomposing the orthogonal variation in XTP, the variance of the major orthogonal components obtained for OPLS and XTP is observed to be almost the same, showing the close relationship between the methods. The XTP approach is tested and compared with OPLS for a three‐component mixture analyzed by infrared spectroscopy and a multicomponent mixture measured by near infrared spectroscopy in a reactor. Copyright © 2008 John Wiley & Sons, Ltd.     

基于扩展数学形态学的高光谱图像异常检测

提出了一种新型的基于扩展数学形态和光谱相似度测量的高光谱图像异常榆测方法.在日标与背景未知的情况下.同时利用光谱和空间信息实现日标的定位与检测,实现离光谱遥感数据的日标检测.通过扩展的膨胀和腐蚀操作实现目标特征提取;通过正交投影散度计算扩展形态学操作的累加距离确定排序关系并利用其融合特征提取结果实现特征提取结果的融合.算法性能通过合成的OMIS数据进行评价.与经典异常检测RX算法进行比较.并应用于具有相似光谱特征目标的区分.实验证明,本文提出的算法性能优于RX算法.具有低虚警率的异常目标检测结果,并且能够较好地区分了相似光谱特征的异常日标.