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For a general parametric curve/surface, we usually cannot compute its exact implicit form. Even though its exact implicit form can be computed, the curve/surface implicitization involves relatively complicated computation and the degree is higher. Moreover, it may have unexpected components and self-intersections. All these unsatisfied properties limit the applications of the exact implicitization. So finding curve/surface approximate implicitization has become a practical problem. In this paper, we present an algorithm to solve the approximate implicitization of a given parametric curve by using a quadratic algebraic spline curve.

由于精确隐式化过程不一定可以实现，即使可以实现隐式曲线曲面的阶数高计算复杂，并且具有不希望的自交点和奇异分支，从而限制了隐式化的运用，所以寻求参数曲线曲面的近似隐式化问题成为很实际又重要的问题，提出利用二次代数样条曲线来实现一般平面参数曲线近似隐式化的一种算法。

And the methods how to combine them with the discretized algebraic eigenvalue equation for generalized Rayleigh and Love waves are also given.

推导了这三种边界条件的公式，并且给出了它们进入离散化后的Rayleigh波与Love波的代数特征方程方法。

And the induced normal curvature along the normal of contact line between the worm and the planet is obtained. The algebraic expression of the induced normal curvature at the top point of the ball-tooth is given.

另外，对行星轮与环面蜗杆沿接触线法线方向的诱导法曲率进行了求解和分析，给出了诱导法曲率在球齿齿面顶点时的代数式显式表达。

This is borne out by the name - Bijaganitam, which was given to the algebraic form of computation.

这是由比杰甘尼坦——这个名字而来，给予和计算的代数形式。

A pressure correction equation is established by use of the finite volume method on nonorthogonal collocated grids, and its algebraic form is also given. The equation is applied to simulation of the flow field in an equilateral cavity and an inclined cavity with a tilt angle of 45°.

利用有限体积法建立了非正交同位网格系统中的压力校正方程，详细给出了压力校正方程的离散形式，并对正方腔及倾斜角为45°的斜方腔内流场进行了数值模拟计算。

Given a planar point set,the moving least squaremethod is adopted to denoise and resample it so that the resulting point set is with low noise and uniform sampling density.Then the reliable signed distance field of the preprocessed point set is constructed by using the Level Set method.Finally,an algebraic B-spline function is adopted to fit the signed distance field by solving a linear equation system.

首先给定一个表示封闭曲线、可能带有噪音且分布不均匀的平面点云，采用移动最小平方(moving least square，简称MLS)方法对点云去噪、重采样，得到一个低噪音、分布均匀的"线状"点云，再通过Level Set方法建立该"线状"点云的离散几何距离场，最后用一个代数B-样条函数光顺拟合该离散距离场，代数函数的零点集即为重建曲线。

It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.

这基于在赖斯大学在计算的代数学的几何学方面在过去5 年中在一个大的跨学科的计划里给的课程，包括数学，计算机科学，biomathematics和生物信息科学。

Based on the proper segmentation of algebraic curves,the convex hull of curve segment was given.

基于代数曲线的合理分割，给出了曲线段的三角形凸包的描述。

The appliance of polynomial symbolic algebraic in formal verification ,people have given two polynamial denotative module WGLs and TEDs,and gives the corresponding equivalence checking algorithms .

关于多项式符号代数理论在形式化验证方面的研究，人们给出了WGLs和TEDs两个多项式表示模型，并给出了相应的等价性验证算法。

In this paper, we have made a systemic theoretic research on modelling and reshaping several types of spline curves/surfaces in CAGD. And some creative productions are given as follows. At first, the uniform C-B-spline basis is proved to be a normalized totally positive basis, and can be extended to a normalized B-basis. C-B-spline and C-Bézier basis, similar to B-spline basis and Bézier basis in algebraic space, are two bases in algebraic trigonometric space.

本文围绕着CAGD中常用的几种曲线曲面造型和形状调整进行了深入的研究，主要获得了以下一些成果：首先，证明了代数三角空间中的n次均匀C-B-spline基是一组标准全正基，并进一步扩充为一组标准B基。C-B-spline基与C-Bézier基是多项式与三角混合空间中的两组基，是适应工程实践中设计特殊曲线曲面的需要而产生的，类似于多项式空间中的B-spline基与Bézier基，是CAGD中重要的造型工具。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！