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临界集
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  critical set
     Thus reaching the conclusion that the Sierpinski gasket which was not Whitney′s critical set could contain Whitney′s critical set E.
     于是得到不是 Whitney临界集的 Sierpinski垫可以包含 Whitney临界集 E
短句来源
     A connected set is constructed on the special fractal set (generalized Sierpinski rug), and whose Hausdorff dimension is ln10/ln9; then a differential function is constructed on the connected set to prove that the connected set is a Whitney's critical set.
     在特殊的分形集(广义的Sierpinski地毯)上构造一个Hausdorff维数为ln10/ln9连通集合,然后在该连通集合上构造一个可微函数,利用该函数证明了该连通集合是一个Whitney临界集
短句来源
     Taking the Sierpinski gasket as an example,the paper studied the problem of Fractal set that is not Whitney′s critical set could contain Whitney′s critical set.
     以 Sierpinski垫为例 ,进一步研究了不是 Whitney临界集的分形集可以包含 Whitney临界集的问题 .
短句来源
     secondly,a differential function was constructed on the connected set E to prove that E was a Whitney′s critical set by dividing the differential function into three cases.
     其次 ,在连通集合 E上构造一个可微函数 ,利用该函数分 3种情形证明了 E是一个 Whitney临界集 .
短句来源
     According to characteristics of the model, we use branch and bound method to search the critical set in feasible region, and only compare the values of objective function on critical set, we can find the optimal solution.
     根据模型的特点 ,采用分枝定界的方法 ,在可行域中搜索临界集 ,通过临界集上模型目标函数的比较 ,从而得到问题的最优解。
短句来源
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  critical sets
     Whitney's Critical Sets on the Sierpinski Rug
     Sierpinski地毯上的一个Whitney临界集
短句来源
     Some Problems of FractalⅡ ——Whitney’s Critical Sets
     分形几何若干前沿问题Ⅱ——Whitney临界集
短句来源
     Whitney's critical sets on the generalized Sierpinski rug
     广义的Sierpinski地毯的Whitney临界集
短句来源
     This paper studies the maximal critical sets in Latin Squares. The two known inequalities lcs(4) > = 7 and lcs(n), where n is even,are improved to lcs(4) = 7 and lcs(n) ≥ respectively.
     本文通过详细论证对《CriticalSetinLatinSquare》一文中关于最大临界集的两个不等式lcs(4)≥7和n偶数时,lcs(n≥3)分别改进为lcs(4)=7和lcs(n)≥。
短句来源
     Introduced in the paperwere The Whitney’s critical sets,the Norton’s conjecture and the auther′s corresponding work were introduced.
     介绍Whitney型临界集 ,Norton猜想及作者的相关工作
短句来源
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  “临界集”译为未确定词的双语例句
     SOME PROBLEMS OF FRACTAL Ⅲ——Some Progresses in Whitney Set
     分形几何前沿问题Ⅲ——Whitney临界集的一些进展(英文)
短句来源
     Whitney sets on Sierpinski gasket
     Sierpinski垫的Whitney临界集
短句来源
     Self-Similar Curves and Whitney Sets
     自相似曲线与Whitney型临界集
短句来源
     This is the report of author’s work on Whitney set.
     本文是作者在中科院数学所报告的有关Whitney临界集方面的工作 .
短句来源
     A class of self-similar curves including Koch curve is defined, and the following result is obtained: If a curve of this class is a simple curve, then it is a Whitney set.
     本文讨论一类(包括Koch曲线在内的)自相似曲线,证明了其上的简单曲线是Whitney型临界集,并在微小扰动下仍是简单曲线.
短句来源
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  critical set
Finally, we show that microlocally away from a critical set the continuity estimate can be mproved:
      
We study conditions involving the critical set of a regular polynomial endomorphism f∶?2??2 under which all complete external rays from infinity for f have well defined endpoints.
      
It is known that each critical set is parameterised by a Bordiga surface in ?4.
      
In addition, it is shown that every Bordiga surface parameterises a critical set of lines.
      
We assume f to be locally Lipschitz continuous in and nonincreasing near zero but we do not require any hypothesis on the critical set of the solution.
      
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  critical sets
Critical sets and two-dimensional topologically mixing attractors of a pair of coupled "Tent maps"
      
Reconstruction fails to be unique for certain critical sets of lines.
      
On critical sets of distance functions to a taut submanifold
      
Other results include the geometry of fractal critical sets, nonuniform hyperbolic behavior, symbolic coding of orbits, and formulas for topological entropy.
      
With the introduction of an alternate definition for critical point, this paper studies critical sets, as defined byW.
      
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In this paper, the relations between the inner set spaces and the weighted inner set spaces are studied. A necessary and sufficient condition for an inner set space with three critical sets which can be weighted is also given.

本文研究了内集空间与赋权内集空间之间的关系。给出了具有三个临界集的内集空间可以赋权的一个充分和必要条件。

This paper studies the maximal critical sets in Latin Squares.The two known inequalities lcs(4) > = 7 and lcs(n), where n is even,are improved to lcs(4) = 7 and lcs(n) ≥ respectively.

本文通过详细论证对《CriticalSetinLatinSquare》一文中关于最大临界集的两个不等式lcs(4)≥7和n偶数时,lcs(n≥3)分别改进为lcs(4)=7和lcs(n)≥。

The new results,developments and problems of fractal,including the latest work of author’s,will be stated in a series of papers. The first one contains the basis of fractal.

我们将探讨分形几何的一些最前沿问题 ,包括Wnitney型临界集 ,拟弧与自相似曲线 ,分形的双Lipschitz等价等内容 ,将用尽可能少的篇幅 ,引导读者进入分形研究前沿 .本文先回顾一下分形的必要的基础知识

 
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