矩形校正公式的误差分析

This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively.It also displays an analysis on convergence order of compound corrector formulas for rectangular rule.Examples of numerical calculation have validated theoretical analysis.     

Indépendance algébrique sur les T-modules

We study the transcendence degree (of the values at algebraic points) of the coordinate functions of a given one parameter subgroup on a simple g dimensional T-module. In such a situation, we obtain a lower bound for this transcendence degree depending on g and on the growth order of the parameter subgroup. As a particular case, one gets the finite characteristic analogue of a result of Siegel on the algebraic independence for the values of the classical Bessel function. Résumé. Nous obtenons une minoration du degré de transcendance d'un ensemble de valeurs en des points algébriques des fonctions coordonnées d'un sous-groupe à un paramètre d'un T-module simple, en fonction de l'ordre de croissance de ces dernières et de la dimension du T-module. Un cas particulier de ce résultat permet d'obtenir en caractéristique finie un analogue d'un résultat de Siegel sur l'indépendance algébrique des valeurs de la fonction de Bessel usuelle.     

Weierstrass points and their impact in the study of algebraic curves: a historical account from the “Lückensatz” to the 1970s

In this note we give a historical account of the origin and the development of the concept of Weierstrass point. We also explain how Weierstrass points have contributed to the study of compact Riemann surfaces and algebraic curves in the century from Weierstrass’ statement of the gap theorem to the 1970s. In particular, we focus on the seminal work of Hürwitz that raised questions which are at the center of contemporary research on this topic.      

Parameterization and algebraic structure of 3-band orthogonal wavelet systems

In this paper, a complete parameterization for the 3-band compact wavelet systems is presented. Using the parametric result, a program of the filterbank design is completed, which can give not only the filterbanks but also the graphs of all possible scaling functions and their corresponding wavelets. Especially some symmetric wavelets with small supports are given. Finally an algebraic structure for this kind of wavelet systems is characterized.     

Iteration 2-theories

The axioms of iteration 2-theories capture, up to isomorphism, the equational properties of iteration in conjunction with horizontal and vertical composition in all algebraically complete categories. We give a concrete representation of the free iteration 2-theory generated by a 2-signature.     

Investigation of self-adaptive algebraic tomography for gas reconstruction in larger temperature range by multiple wavelengths absorption spectroscopy

We develop a self-adaptive algebraic tomography algorithm （SAATA） to investigate the simultaneons reconstruction of concentration and temperature distributions in larger temperature range from two views. The simplified optical arrangement with fewer projections is realized by extension of spectral information at multiple wavelengths, resulting in great potential in applications of practical combustion diagnosis. Tile results show SAATA can perform much better reconstructions in 300 3000 K temperature range than genetic simulated annealing algorithm and least-square orthogonal-triangular decomposition method with two- wavelength scheme. More phantoms are created to demonstrate the capability of SAATA to capture the peaks and adapt for both flat and sharp temperature distributions. Meanwhile, the advantage of high stability ensures better reconstruction performance at noise levels from 0.1% to 10% in projections.     

On the geometry of null hypersurfaces in Minkowski space

The present work is divided into three parts. First we study the null hypersurfaces of the Minkowski space ${\mathbb{R}}_1^{n+2}$, classifying all rotation null hypersurfaces in ${\mathbb{R}}_1^{n+2}$. In the second part we start our analysis of the submanifold geometry of the null hypersurfaces. In the particular case of the $(n+1)$-dimensional light cone, we characterize its totally umbilical spacelike hypersurfaces, show the existence of non-totally umbilical ones and give a uniqueness result for the minimal spacelike rotation surfaces in the $3$-dimensional light cone. In the third and final part we consider an isolated umbilical point on a spacelike surface immersed in the 3-dimensional light cone of ${\mathbb{R}}_1^4$ and obtain the differential equation of the principal configuration associated to this point, showing that every classical generic Darbouxian principal configuration appears in this context.     

多重网格法与Newton-Raphson法耦合求线弹流数值解

利用多重网格算法,在最粗网格上,采用Newton-Raphson迭代法模式精解线接触弹流非线性方程组,充分利用了多重网格法与Newton-Raphson法各自的优点,计算实践表明,求解弹流问题的数值解过程在收敛与稳定性方面均有较大改善,且有相当宽的载荷参数适用范围。     

再论约束最小二乘法

本文介绍的约束最小二乘法如同经典的最小二乘法一样,也普遍适用于各种科学领域。然而,这一方法仅在“模型修正”一类论文的附录中出现过。鉴于约束最小二乘法在计算力学和工程问题中愈来愈重要的作用,本文将作者十多年前提出的这一方法稍加扩展（如引入加权因子和讨论了自然权因子的应用等）后,再做一系统的介绍,并随意设计了一个简单考例,证实了约束最小二乘法的有效性。     

Some Remarks on Real and Algebraic Cobordism

We investigate connections between Real cobordism, algebraic cobordism, quadratic forms, the Rost Motive, Morava K(n)-theories and analogues of homotopy classes of Hopf invariant 1.