几何基础

Moreover, multivariate splines are closely related with some topics in pure mathematics, such as, abstract algebraic, algebraic geometry and combinatorics.

另一方面，多元样条与基础数学的一些领域，如：抽象代数、代数几何、微分方程及组合数学等，亦有着密切关联。

On the basis of B-Rep of CAD data and ACIS library,a technology of surface filling based on loop feature handling and outlines smoothing is presented in the paper,filling for the surface with complex concave edges is also studied in the paper.

以CAD数据的边界表示法和ACIS几何开发库为基础，提出了基于环特征处理和外边界光顺的曲面填充技术，对含有复杂凹缘的汽车覆盖件曲面填充进行了研究。

In this dissertation, the mechanical behavior of the metal adhesively bonded composite joints under loading have been systematically investigated by numerical calculation methods and experiments, and effects of shape dimensions and physical parameters of joints on stress distribution and strength of adhesively bonded joints have been placed emphasis upon.

本文在对国内外关于金属-胶层复合材料接头力学性能数值研究及发展现状进行综述的基础上，运用有限元法并结合实验手段主要研究了胶接接头承载后的力学行为，综合考虑了几何尺寸和物性参数对接头强度和应力分布的影响，并运用层次分析法对胶接质量进行综合评估，综合考虑接头形式，制造工艺，操作人员素质等因素的影响。

The stress distribution of adhesively-bonded metal/metal single lap joints under tensile shear loading is analysed using elastic-plastic finite element method .The influence of lap length on the strength of adhesively bonded metal joints which are bonded with phenolic resin and acrylic resin respectively is discussed in detail. It is shown that adhesive has great influence on the stress distribution of the lap region. With the increment of lap length, the stress concentration of adhesive layer decreases.

本文在对国内外关于金属-胶层复合材料接头力学性能数值研究及发展现状进行综述的基础上，运用有限元法并结合实验手段主要研究了胶接接头承载后的力学行为，综合考虑了几何尺寸和物性参数对接头强度和应力分布的影响，并运用层次分析法对胶接质量进行综合评估，综合考虑接头形式，制造工艺，操作人员素质等因素的影响。

A new digital measure method was presented based on the three coordinate measuring machines. Compensation of sensor radius, establish part's measure reference frame, the best measuring layout and mix programmed scanning all those not only enhance measure precision and increase efficiency of scanning measure, but also the data can image geometrical characteristic of complex surface. The method was illuminate by a sample, and the digital data of the surface adumbration are obtained at last

在三坐标测量机的基础上给出了一种数字化测量曲面轮廓的方法，通过测球半径的补偿、坐标系的建立、最佳测量路径的规划以及混合编程扫描，提高了测量精度及扫描测量的效率，而且采集到的数据可以反映曲面的几何特征，并以实例对该方法进行说明，得到了数字化的曲面轮廓数据。

Typical remote imaging distortions are analyzed firstly. For sea area optical images, a Convex Hull of Extended Centroids target global invariant feature extraction method is proposed based on affine geometry theory.

论文在分析成像畸变误差的基础上，针对海域光学遥感图像数据，提出了基于仿射几何理论的扩展质心-凸包目标全局不变特征提取方法。

Compared with the invariant features of single parameter group, entirely global affine invariant features are more applicable, and chapter 4 introduces a new global affine invariant feature extraction method called EC-ARC, which is based on the invariance in affine geometry.

然后，提出了扩展质心(Extended Centroid， EC)和仿射区域划分(Affine Region Cutting， ARC)的新概念，并在EC和ARC的基础上，结合仿射几何性质，提出了构造具有完全仿射不变性的特征提取方法EC-ARC。

The main objects of study are algebraic varieties in an affine or projective space over an algebraically closed field; these are introduced in Chapter I, to establish a number of basic concepts and examples.

全书共分七章，前三章是基础知识部分；后四章是本书的核心部分，总结了近年来代数几何码的最新研究成果，并且包含了作者的一些尚未发表的结果。

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按"序"最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

In this paper, we summarize the foundations of Algebraic function fields, algebraic curves over finite fields and algebraic geometry codes, then we focus on the dimensions of codes on the quotient of the hermitian curves, by using the theory of weierstrass semigroup and the idea of Ho...

我们在系统地总结了代数函数域，有限域上的代数曲线和代数几何码的基本知识的基础上，利用Weierstrass子半群理论，使用Homma和Kim的方法，讨论了Hermite曲线商域上码的维数问题，得到的主要结果如下： 1。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。