Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.     

Perturbed recurrence relations II the general case

In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations are given.     

Constructing orthogonal pandiagonal Latin squares and panmagic squares from modular n‐queens solutions

In this article, we show how to construct pairs of orthogonal pandiagonal Latin squares and panmagic squares from certain types of modular n‐queens solutions. We prove that when these modular n‐queens solutions are symmetric, the panmagic squares thus constructed will be associative, where for an n × n associative magic square A = (a_ij), for all i and j it holds that a_ij + an?i?1,n?j?1 = c for a fixed c. We further show how to construct orthogonal Latin squares whose modular difference diagonals are Latin from any modular n‐queens solution. As well, we analyze constructing orthogonal pandiagonal Latin squares from particular classes of non‐linear modular n‐queens solutions. These pandiagonal Latin squares are not row cyclic, giving a partial solution to a problem of Hedayat. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 221–234, 2007     

Evaluation of gap length fluctuation with harmonic analysis method

Gap length (GL) of reading head is one of the most critical parameters for high-density magnetic recording systems. A novel method is proposed for quantitative evaluation of the GL fluctuation among a batch of magneto-resistive/giant magneto-resistive heads with same structure design. The method works at head-gimbal assembly level and the evaluation can be done with any read/write analysis equipment. The testing process is based on harmonic analysis of the readback signal. The testing system consists of a selected reference head and sample heads for evaluation. A GL variation function is introduced for the evaluation of GL deviation between the reference head and sample head. This method proved to be easy for implementation and results suggest that variation of GL is considerable and has obvious effect on recording performance in high recording density systems.     

On inequalities of Lieb-Thirring type

Applying the method proposed by Kashin for proving inequalities of Lieb-Thirring type for orthonormal systems, we prove a similar inequality in the multidimensional case.     

COMPLETENESS OF THE PARABOLIC SUBGROUPS OF PROJECTIVE ORTHOGONAL GROUPS

All parabolic subgroups and Borel subgroups of PΩ(2m 1, F) over a linear-able field F of characteristic 0 are shown to be complete groups, provided m > 3.     

Asymmetry in the Multiprotein Systems of Molecular Biology

Signaling in living systems needs to achieve high specificity, to be reversible, and to achieve high signal to noise. Signaling mediated by multiprotein systems has evolved that avoids the requirement for high-affinity binary complexes that would be difficult to reverse and which, in the overcrowded cell, would lead to excessive noise in the system. Symmetrical structures are only occasionally formed. When they are, it is principally to colocate components, for example, the tyrosyl kinases of growth factors, where dimers form. Symmetry is, however, often broken, presumably to create more sensitivity and specificity in the signaling system by assembling other components, into higher-order multiprotein systems. The binding of a single heparin to two 1:1 FGF:FGFR complexes is an example, as is the binding of a single ligase to the Xrcc4 dimer, perhaps so creating a further DNA-binding site.     

The Generalized West Decomposition of Operators and Other Compact Perturbation Problems

This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space： （a） Every generalized Riesz operator has the generalized West decomposition; （b） Every operator makes strong Stampfli theorem true; Every operator has Apostol＇s compact correction.     

描述光伏效应的新解析模型

 对陆启生等人提出的描述光伏效应的解析模型涉及的边界条件进行了讨论，提出了一个适用性更宽的解析模型。通过对新模型、陆的模型以及另一个解析模型的比较，对前两个模型能够描述光伏型光电探测器在强光辐照时的信号饱和效应的原因进行了解释。     

书籍扫描图像畸变参数自动计算方法的研究

为实现书籍扫描图像的畸变自动校正,提出用多项式来描述各像素的理论灰度g(zi)与页面上对应点到扫描仪工作平面距离zi二者之间的关系。为确立该多项式,在畸变参数已知条件下扫描一幅图像,根据已知畸变参数求出zi,即可按最小二乘法原理由各像素灰度的实际值求出多项式的各个系数。实验证明,采用4阶多项式已能满足一般要求,并求出了各系数。对任意扫描图像,自动计算畸变参数的方法为:首先利用扫描图像上页边空白处各像素的灰度,对畸变参数进行估计,并求出zi的估计值;然后代入所确立的多项式,可求得g(zi);通过调整各畸变参数的估计值,直到g(zi)与gi最为接近,即得最佳畸变参数。用于图像校正实验,获得了较好的校正效果,最大误差由不校正时的41%下降到了6.9%。这使得无需用户测量并输入有关畸变参数即可进行自动校正。