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even mapping
相关语句
  相似匹配句对
     THE EVEN-MAPPING THEOREM
     偶映射定理
短句来源
     FUZZY MAPPING
     模糊映射
短句来源
     Application of Mapping
     映射的应用
短句来源
     The background is even.
     背景基本均匀。
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     Even if M ?
     一般地,即使M (?)
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Motivated by the odd mapping theorem, we show in this paper that Brouwer's degree of the even continuous mappings is an even number,i.e. the even mapping theorem.(H) Let D be a symmetric bounded open set in 1Rn containg the origin and f:D→1Rn an even continuous mapping(f(x)=f(-x), for all x∈D)with o f(D).The main results are as follows:1° If the condition (H) is satisfied, then deg(f,D,0) is an even number.2° Suppose the condition (H) is satisfied and the dimension of 1Rn is an odd number,...

Motivated by the odd mapping theorem, we show in this paper that Brouwer's degree of the even continuous mappings is an even number,i.e. the even mapping theorem.(H) Let D be a symmetric bounded open set in 1Rn containg the origin and f:D→1Rn an even continuous mapping(f(x)=f(-x), for all x∈D)with o f(D).The main results are as follows:1° If the condition (H) is satisfied, then deg(f,D,0) is an even number.2° Suppose the condition (H) is satisfied and the dimension of 1Rn is an odd number, and f(x)+(λ-1)x o for all x D and λ>1. Then f has zero point at some point of δD.3° There is y∈D and λ>0(orλ <0) such that f(y)= y. if the condition (H) is satisfied and the dimension of 1Rn is an odd number.Moreprer, we discuss the totally even mapping in the above way. A mapping f:D→ 1Rn is called totally even, iffor all (a1,… ,an) ∈ δn(0,1) , where δn (0,1)= { (a1 ,… ,an)|ai = o or 1 for i∈ { 1,2,…,n} .

受奇映射定理的启发,本文证明了连续偶映射的Brouwer度为偶数,即偶映射定理.(H)设D(?)R~n是有界对称含0的开集,f:D→R~n是连续偶映射(f(x)=f(-X),(?)X∈D)使O(?)f((?)D)有如下主要结果:1~0如假设(H)满足,则deg(f,D,0)是偶数.2~0如假设(H)满足,R~n的维数n为奇数且f(x)+(λ-1)x≠0,(?)x∈D和λ>1,则f在(?)D上必有零点.3~0如假设(H)满足但R~n的维数n为奇数,则存在y∈(?)D和λ>0(或λ<0)使f(y)=λy.我们进一步按上述内容对全偶连续映时进行了讨论.映射f:D→R~n是全偶的,只要f((-1)~(a1)x_1,…(-1)~(an)x_n)=f(x_1,…x_n),(?)(a_1,…a_n)∈δ_n(0,1),这里δ_n(0,1)={(a_1,…,a_n)|a_i=0或1,(?)i∈{1,2,…,n}}.

 
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