查询词典 algebraic branch point

Two-phase-learning is adopted. The strongpoint is that intuitionistic knowledge can be used to control the segmentation by using input-weight and distant-weight. Examples prove that segmentation using SOFM network is right and efficient. Surface fitting is an absolutely necessarily process in REGM. Surface fitting includes algebraic and parametric surface fitting. Algebraic surface fitting has not extra requirement for data distribute format and boundary shape.

第三种方法把人工智能用于反向工程的数据分区，因为数据分区的实质是相似特征的聚类，而神经网络可以实现自组织特征映射，在本论文中第一次把自组织特征映射神经网络用于多视图点云的数据分区，通过神经网络对数据点的坐标、法向量等几何特征进行聚类，并且运用了快速稳定的训练方法——两阶段训练算法，最重要的是，通过距离权值和输入权值可以把用户观察所得的直观知识加入聚类过程。

If the surface isrepresented by an implicit algebraic equation,the mapping can be constructed bythe theory of parametrization of algebraic surfaces;If the surface is represented byan parametric equation,the parameter values on the parameter plane can be solvedby numerical method or Grobner Basis method.

若曲面由代数隐式方程给出，可通过代数曲面参数化理论构造映射；若曲面由参数方程给出，可通过数值方法或Grobner基方法求解参数型值点。

OR-coincidence algebraic system has close relationship with modular algebraicsystem, so it is necessary to study this algebraic system.

或-符合代数系统与模代数系统有着密切的关系，对它的研究也成为热点。

In this paper, we present a method to solve system of algebraic equations or system of parametric algebraic equations by computing the normal zero decomposition of polynomial systems.

本文提出一种利用多项式系统的正规零点分解的算法来求解代数方程组以及带有参数的代数方程组的方法。

As thezeros of multivariate splines, the piecewise algebraic variety is a generalization of theclassical algebraic variety.

分片代数簇作为多元样条的公共零点集合，是经典代数簇的推广，它不仅和许多实际问题如多元样条插值，CAD和CAGD等有关，而且还为研究经典代数几何提供理论依据。

Applying the techniques of real radical ideal, P-radical ideal , decomposition of semi-algebraic set in ( [72] ), affine Hilbert polynomial and B-net form of polynomials on simplex, this paper obtains two theorems of real C〓 piecewise algebraic variety dimensions and the real Nullstellensatz in C〓 spline ring.

4：应用多项式在单纯形上的B-网形式以及文献（[72]）中的实根理想，锥根理想，半代数簇分解定理，本文得出了实C〓分片代数簇的二个维数定理和C〓样条空间的实零点定理。

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

By using the solutions of a new auxiliary elliptic equation,a direct algebraic method is proposed to construct the exact solutions of some nonlinear evolution equations.The main difference between this method and previous auxiliary elliptic equation methods is that the balance order becomes smaller after using the new auxiliary elliptic equation.Therefore,the derived algebraic equations are greatly simplified.

利用一个新的辅助椭圆方程将求解非线性发展方程精确解的问题转化为一个代数方程组进行求解，与已有的辅助椭圆方程法的主要不同是，应用这一新的辅助椭圆方程后降低了平衡次数，减少了所得的代数方程组的个数和方程的项数，从而大大地简化了代数方程组的求解。

By analyzing the relationship between the algebraic degree and characteristic matrix of a Boolean function,the relationship between the algebraic immunity and characteristic matrix of a Boolean function is obtained.

通过分析布尔函数的代数次数与特征矩阵的关系，得到了布尔函数的代数免疫度与特征矩阵的关系。

The course contains four sections as follows: mathematical logic (including basic concepts of propositional logic and predicate logic, propositional calculuses and inference theories), set theory (including set algebras, relations, functions and cardinal numbers), algebraic structure (including algebraic systems, semigroups and groups, rings and fields, lattices and Boolean algebras), graph theory (including basic concepts of graph, Euler graphs and Hamiltonian graphs, trees, planar graphs and coloring graphs, some special vertex subsets and edge subsets).

本课程包含四部分内容：数理逻辑（包含命题逻辑与一阶逻辑的基本概念、等值演算以及推理理论），集合论（包含集合代数、二元关系、函数和基数），代数结构（包含代数系统、半群与群、环与域、格与布尔代数），图论（包含图的基本概念、欧拉图与哈密顿图、树、平面图及图的着色、图的某些特殊的顶点子集与边子集）。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。