代数学的拓扑是透过代数空间的全球特性的研究。
Algebraic topology is the study of the global properties of Spaces by means of algebra.
该算法的特点是将能量最小法则和奇异值分解结合起来，在代数空间中建立了一种自适应的图像降噪算法。
Comparing with the adaptive denoising algorithm based on compression ratio and SVD, it avoids calculating the function of image compression ratio and its knee point.
单极本征函数在不同动力学0(2,1)基底中的代数规律性表明径向相空间的对称性。
The algebraic regularity of monopole eigenfunctions in various dynamical0 (2, 1) basis shows the symmetry in radial phase space.
数量和空间在解析几何，微分几何和代数几何中都发挥作用。
Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry.
关于线性子空间的研究，普通的高等代数教材已有许多好的结论。
As for the research on linear space, good conclusions are attained in the General High Algebra Course.
最后，基于数学工具———代数系统，给出了空间数据立方体严格的数学定义。
At last, based on a mathematical tool: algebraic system, this paper gives definition of spatial data cube.
本文证明了强可的极大三角代数的同构是空间实现的。
In the paper, we proved that every isomorphism of strohglyreducible triangular algebras is spatial.
接着对速度空间提出一种类似的网格转移算子，并给出W循环的多重网格法来解对应的代数方程组。
Then a similar intergrid transfer operator is given for the spaces of velocity, and the W-cycle multigrid method is presented for solving the algebraic equations.
把量纲概念与矢量空间联系起来，提出用线性代数进行量纲分析的方法，并举例说明。
The concept of dimension is connected with vector space, a linear algebraic method for dimensional analysis is proposed, some examples are given.
本文主要讨论了线性拓扑空间中集合的固有代数边界点集的性质。
The properties of the proper algebraic boundary point sets of the sets in topological linear Spaces were discussed.
用定性模空间和区间代数刻划了定性定量相结合的求解方法。
Used qualitative model space and interval algebra to depict the solving method combining the quality and quantity.
本文给出了三维射影空间上对合透视的代数表达式。
In this paper we discuss the algebraic expression of involutory perspective in three-dimensional projective space.
最后求出多项式角动量代数的单玻色实现及其在有限维多项式函数空间的微分实现。
At last the deformed algebra's single boson operator realization and one differential realization under finite_dimensional spaces are deduced.
将李群李代数理论成功地拓展应用于空间柔性机构系统的分析，验证了该方法的有效性。
The Lie groups and Lie algebras is successfully extended to study the mechanical system with spatial compliant links.
本课程主要内容包括：向量代数与空间解析几何、多元函数微积分、无穷级数等。
This course mainly includes: vector algebra and analytic geometry in space, multivariable calculus and infinite series.
李三系作为一种代数体系，最初源于对黎曼流形的一类特殊子空间——全测地子流形的研究。
As an algebraic system, Lie triple systems arise upon consideration of certain sub-spaces of Riemannian manifolds, the totally geodesic submanifolds.
讨论了阶化向量空间和李超代数的基本性质。
The general properties of graded vector space and Lie superalgebras are discussed.
数学方法：线性代数，赋范空间，分布，积分。
Mathematical Methods: Linear Algebra, Normed Spaces, Distributions, Integration.
主要内容有：向量代数、空间的平面和直线、特殊曲面和二次曲面、一般二次曲面和一般二次曲面。
The main content: vector algebra, plane and linear space, special surfaces and secondary surfaces, general quadratic surfaces and general quadric surface.
引入对个体的代数保护策略，即在它发生变异前保证有足够的演化，可以避免对新空间不成熟的开发。
Aprotectionstrategyfortheevolvedgenerationsfor individuals is introduced to guarantee enough evolution before the mutation occur, which avoids immature exploitation for new Spaces.
举例来说，一个学生可能在代数方程序的学习上有困难，但他可能在空间几何方面有天赋。
A student who has trouble with algebraic equations, for instance, may have a talent for spatial geometry.
状态空间分析方法的数学基础是线性代数和矩阵论，能控性和能观性是状态分析方法的根本问题。
The mathematical foundation of state space analysis method is linear algebra and matrix theory, whose essential issues are controllability and observability.
本文简单分析了满足GIS空间查询代数的一般要求，然后形式化地定义了一种适合于GIS空间查询的变量查询代数。
General requirements of spatial query in GIS are briefly outlined in this paper. A Variable query Algebra is formally defined for spatial query of GIS.
与在向量空间上构造的方法比，有限域上置换多项式的代数次数等性质更容易研究。
Compared to the construction over vector space, it is easier to study the properties of permutation polynomials, like algebraic degree.
利用黎曼对称空间同正交对称李代数之间的密切关系及一个矩阵不等式给出了一个复流形上截面曲率的上界的精确估计。
We used the relationship of the Riemann symmetric space and the symmetric algebra, a matrix inequality to provided a estimate sectional curvature of a complex manifold.
讨论近似空间中的孤点对其代数结构以及粗相等的清晰集刻画的影响。
The influences of isolated points on algebraic structure of approximate space and description of rough equality by crisp sets are discussed.
课程内容包括常微分方程、空间解析几何与向量代数、多元函数微分学、多元函数积分学和无穷级数等几大板块。
This course consists of several major parts such as ordinary differential equation vectors and analytic geometry derivatives integration and series.
身体重要思想的载体，推广到向量空间，研究了线性代数。
The physically important concept of vectors, generalized to vector Spaces, is studied in linear algebra.
模式识别；可视化；多元数据；图表示；几何代数；子空间坐标；优化。
Pattern Recognition; Visualization; Multivariate Data; Graphical Representation; Geometric Algebra; Subspace Coordinates; Optimization.
模式识别；可视化；多元数据；图表示；几何代数；子空间坐标；优化。
Pattern Recognition; Visualization; Multivariate Data; Graphical Representation; Geometric Algebra; Subspace Coordinates; Optimization.
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