余维数

基本解释 (translations)

codimension

与余维数相关的网络例句 [注：此内容来源于网络，仅供参考]

If a n-dimensional unoriented cobordism class α_n containing a representative that admits a (Z_2)~k-action with fixed point set of constant codimension r,we may say that α∈is an ideal of the unoricnted cobordism ring MO_*=.

若n维未定向协边类α_n的一个代表元M~n上有不动点集为常余维数r的(Z_2)~k光滑作用，则记α_n∈J_~r.J_~=∑_n≥r_J_(n，k~r是未定向上协边环MO_+=∑_(n≥0)MO_n的理想。

In the first chapter,we discuss the problem of (Z_2)~k-actions with fixed point set of constant codimension.

在第一章中，我们对具有常余维数不动点集的(Z_2)~k作用进行了研究。

The main advantages of the methodare that(1)this method is valid for all kinds of bifurcation pointswith the codimension ≤3;(2)it does not use any informations forsecond order derivatives and does not need the bifurcation point to beknown accurately in implementation;(3)it is sufficient to implementthe method that a standard continuation procedure is only used;and(4)derivation of the method is independent on the asymptotic expan-sions of the bifurcation solutions.

这种方法的主要优点是：(1)适应于一切余维数不超过3的分支点；(2)不需要任何二阶导数的信息，也不必精确地知道分支点的位置；(3)只需使用标准延拓软件就可以实现；(4)方法不依赖于分支解的渐近展式。

For higher codimension, the situation becomes more complicated. Due to the counterexample of Lawson-Osserman [31], the higher codimension Bernstein type result is not expected to be true in the most generality.

在余维数为1的情况，这个结果以被推广到(n+1)-维欧氏空间中(n≤7)，以及在某种增长性限制下，这个结果被推广到任意维数欧氏空间中，这些结果可以参考[17]及其参考文献中所提到的文献。

The injective rings play an important role in the study of rings and categories of modules . First , we introduce the notion of ann-injective rings and CT-injective modules .Second,we make an inquiry into a series of their properties.Third,we give the definition of homological dimension of CT-injective modules.At last,we give the definition of FGT rings which is the extension of cogenerator rings.

本文对环与模范畴中一重要的模类—内射模进行了延拓，引入了ann -自内射环以及CT -内射模的概念，探讨了它们一系列的性质，并定义了CT -内射模的同调维数，最后对余生成子环进行推广得到了FGT -环，讨论了它与CT -内射环的关系以及它的一些性质。

The Pinching problems are discussed on the sectional curvature of compact space-like pseudo-umbilical submanifolds M~n with parallel mean curvature vector in De Sitter space S~_p, and the theory of reduction of the codimension is obtained in De Sitter space through evaluating the Laplacian of square of the length.

讨论了De Sitter空间Snp+p中，具有平行平均曲率向量的紧致类空伪脐子流形Mn的截面曲率的拼挤问题，通过估计第二基本形式模长平方的Laplacian，得到了De Sitter空间中的余维数压缩定理。

For example, Keyfitz made the classification of the bifurcations in one state variable, without symmetry up to codimension 7; Golubitsky and Schaeffer obtained the classification of the bifurcation problems in one state variable with Z_2 symmetry, in one parameter up to codimension 3; Golubitsky and Roberts studied the classification of degenerate Hopf bifurcation in two state variables with dihedron D_4 symmetry, in one parameter up to topological codimension 2; Melbourne obtained the classification of bifurcations in three state variables with octahedral symmetry, in one parameter, up to

需要指出的是以上研究均没有考虑分歧参数的对称性，Futer，Sitta和Stewart的工作虽然考虑了分歧参数的对称性，但仅限于分歧参数与状态变量具有相同的对称性，他们得到了状态变量与分歧参数均关于二面体群D_4对称，拓扑余维数不大于1的分歧问题的分类。高守平和李养成则讨论状态变量和分歧参数均具有对称性且对称性可以不同的分歧问题，并给出了状态(来源：A770707BC论文网www.abclunwen.com)变量关于二面体群D_4对称，分歧参数关于S~1对称，拓扑余维不超过1的分歧问题的分类。本文第一章讨论两个状态变量关于二面体群D_3对称，两个分歧参数关于O(2)对称的分歧问题，给出了该类分歧问题在非退化条件q(0)≠0下所有情形的分类与相应的识别条来源：AdadaBC论文网www.abclunwen.com

The fixed point set F of the action of(Z_2)~k on M~n is a disjoint union of closed submanifolds of M~n,which are finite in number.

若F的每个分支具有常维数n-r，则称F具有常余维数r。

In this paper,we determine J_~(2~k+2v)by constructing ingeniously indecomposable manifolds M,which can be generators in MO_*,and defining appropriate(Z_2)~k-action on M.

在本文中，我们通过巧妙地构造流形M，使其所在的上协边类不可分解，从而可以作为上协边环MO_*的生成元，并在M上定义适当的(Z_2)~k作用使其不动点集F具有常余维数r，决定了未定向上协边环MO_*的理想J_~(2~k+2v)。

For compact hypersurfaces and highcodimension compact submanifolds initial data respectively, we prove that the flow hasa smooth solution for all time under almost optimal conditions. Those conditions arethat the second fundamental form on the initial submanifolds is not too large, the exter-nal force field, with its any order derivatives, is bounded, and the field is convex with itseigenvalues satisfying a pinch inequality.

我们分别对紧超曲面初值和高余维紧子流形初值证明了当初始曲率比较小，并且外力场除了要各阶导数一致有界外，还要满足凸性条件以及特征值的一个pinch条件时，这种热流的光滑解长时间存在。

与余维数相关的网络解释 [注：此内容来源于网络，仅供参考]

codifferential：上微分

codiagonal morphism 余对角射 | codifferential 上微分 | codimension 余维数

codify：编成法典, 使法律成文化

codification | 法典编纂, 法律成文化 | codify | 编成法典, 使法律成文化 | codimension | 余维数

codimension：余维数

codifferential 上微分 | codimension 余维数 | coding 编码

Kodimension codimension：余维数

Knotenueberdeckung vertex cover 顶点覆盖 | Kodimension codimension 余维数 | Koeffizient coefficient 系数

coherent sheaf：连贯层

集合的(凝)聚部{注:现已罕用} coherence of a set | 连贯层 coherent sheaf | 余调维数 cohomological dimension

cohomological dimension：余调维数

连贯层 coherent sheaf | 余调维数 cohomological dimension | 余调类 cohomology class

cohomology class：余调类

余调维数 cohomological dimension | 余调类 cohomology class | 余调群 cohomology group

pitchfork bifurcation：叉式分岔

余维[数]co-dimension | 叉式分岔pitchfork bifurcation | 鞍结分岔saddle-node bifurcation