曲线的结点

The multivariate polynomial interpolation problem is a classical mathematical problem that is widely used in many fields, such as multivariate function list, surface design and finite element method. In recent years, multivariate polynomial interpolation has been focused by many people, of which the geometric topological struction of sets of interpolation nodes is also much concerned by us.

多元多项式插值问题是一个十分具有研究意义和实际应用价值的数学问题，它广泛应用于多元函数列表，以及曲面的外形设计和有限元法等诸多领域，近年来多元多项式插值越来越受到人们的广泛关注，其中有关插值结点组的几何拓扑结构问题也是人们十分关注的内容。1998年，梁学章和吕春梅在文献[2]中借助代数几何中的有关理论，进一步讨论了沿无重复分量平面代数曲线上的Lagrange插值问题，并应用Cayley ？

They are cardinal splines and the linear combination of freedom in adjusting curves and surfaces.

多结点参数的改变增加了曲线交互调节的自由度。

In this paper, thereare four sections. In the first section, we introduce the basic theory. Inthe second section, we give out the recent main results of multivariateLagrange interpolation. In the third section, we get some theories ofno posed set of nodes from a kind of recursive method of constructingposed set of nodes for bivariate Lagrange interpolation, and we get akind of abnormal posed set of nodes for interpolation form the reversethought of that theory.

本文共分为四章，第一章介绍了有关多元插值的基本理论和方法，第二章讲述了有关多元Lagrange插值和多元切触插值的近期主要结果，第三章我们从有关适定结点组的添加曲线法考虑，得到了一些有关Lagrange插值不适定的结论，并从该结论的反方向思考，得到了一种非常规型插值适定结点组。

The liquid-liquid equilibrium binodal curves and the tie-line data of an epoxy cotton seed oil/acetic acid/water ternary system.

测定了环氧棉籽油－醋酸－水三元系分别在30℃，40℃，50℃，60℃下的液－液平衡双结点曲线，以及在40℃，50℃，60℃下的液－液平衡系线数据；分别应用物料衡算法和系线中点轨迹法对实验数据进行了检验。

Applying soil's nonlinear stress-stran relationships (the skelton curve adopts Hadin's hyperbola model and the loaded/unloaded curve adopts the Masing's law revised by Pyke), and taking the viscous boundary as flank artificial boundary, 2D dynamic analysis of the foundation is programed by FEM. It contains an automatic dividing-element subroutine. It could be employed to calculate the horizontal and vertical seismic responses of the soil and foundation.

本文按照土体的非线性应力—应变模式，即将Hadin的双曲线模式作为骨架曲线，加卸荷采用Pyke等修正的广义Masing二倍法则，采用粘性边界作为侧面人工边界，用八结点等参数有限元法在微机上编写了二维地基的动力分析程序，该程序含有网络自动剖分模块，能较好地模似地基和基础在水平方向和竖向的地震反应。

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。