Cantor集并的自相似性(英文)

本文研究了Cantor集和其并的自相似性.利用Cantor展式的方法,得到了关于Cantor集和迭代函数系的一个基本关系:T∪(T+α)为自相似的当且仅当存在一个非负整数n使得α=±(k2-k1)dn.进一步,若T∪(T+α)是自相似的,则它满足开集条件.     

沿齐次曲线的强奇异积分算子在调幅空间上的有界性

设Γ_θ(t)为R~n(n≥2)中的齐次曲线,定义沿齐次曲线的强奇异积分算子T_(n,α,β)f(x)=p.v.∫_(-1)~1f(x-Γ_θ(t))(e~((-2πi|t|)~(-β))/(t|t|~α))dt,α,β>0.本文讨论了上述奇异积分算子在广义调幅空间上的有界性.     

广义树映射的吸引中心和ω-极限集空间

设D是广义树(即具有有限个分支点的树突(dendrite)),f是D上的连续自映射.用P(f)、R(f)、SA(f)、Γ(f)、UΓ(f)、ω(x,f)和?(f)分别表示f的周期点集、回归点集、特殊α-极限点集、γ-极限点集、单侧γ-极限点集、x的ω-极限集和非游荡集.对任意A?D,记ω(A)=∪_(x∈A)ω(x,f).对任意的自然数n≥2,记ω~n(f)=ω(ω~(n-1)(f)),其中ω(f)=∪_(x∈D)ω(x,f).本文证明:对任意的正整数n,有ω~(n+2)(f)=ω~2(f)=ω(?(f))=ω(SA(f))=ω(Γ(f))=ω(P(f)∪(∪_(n=0)~∞f~n(UΓ(f))))=ω(P(f))=ω(R(f)∪UΓ(f))=P(f)∪(∪_(n=0)~∞f~n(UΓ(f)))?P(f).此外,本文还构造了一个只有一个分支点的广义树D和D上的一个连续自映射f,使得{ω(x,f):x∈D}在Hausdorff度量下不是闭的.     

齐次Fourier-Besov-Morrrey空间上广义磁流体力学方程组的存在性和渐近稳定性

考虑了R~n上n维广义磁流体力学方程组,当初值("_0,d_0)∈FN_(r,λ,∞)~(-β)×FN_(r,λ,∞)~(-β)时,广义磁流体力学方程组对应的Cauchy问题的存在性和渐近稳定性,其中1≤r≤∞,0≤λ≤n或者1≤r≤∞,λ=0以及n≥3,1/2≤σ=α≤(n+2)/4-(n-λ)/(4r),β=2σ-1+(n-λ)/r-n.最后,得到了广义磁流体力学方程组一类自相似解的渐近稳定性.     

带有对合的流形的协边类Ⅱ

本文考虑如下问题:对于给定的 n 维协边类 α,n-1维协边类β_(n-1)和 n-k_i维协边类β_(n-k_i)(1相似文献   

在对称群中一类正则图所确定的极大子群

对称群的极大子群之确定,在多值逻辑理论和有限自动机理论中都有着重要而广泛的应用,同时也是置换群理论中的一个基本问题.本文提出了 k 次对称群中一类新的极大子群,k=h~m,m≥3,h≥7.设Γ=(Ω,E)是一个无向正则图,其中顶点集Ω={(α_1,…,α_m)|β_i∈Ω_h={10,1,…,h-1},i=1,…,m},边集 E={α,β〉|α=(α_1,…,α_m),β=(β_1,…,β_m)∈Ω,α_i≠β_i,i=1,….m}:G 是Γ的所自同构作成之群.于是,(1)G 是本原群,且G={g|g(x)=g(x_1,…,x_m)=(g_1(x_σ(1)),…,g_m(x_σ(m))),σ∈S_m(集合{1,…,m}上的对称群),g,∈S_h(Ω_h 上的对称群),i=1,…,m};(2)若 h 为奇数 h=2_n+1且 n 为偶数或 h-1>m,则 G 是 k 次对称群 S_k 中的极大子群;(3)若 k 为偶数且2(k-1)>m,则 G 是 k 次交代群 A_k 中的极大子群.     

关于带重力项一维渗流方程解的自由边界的C^k正则性的一点注记

本文研究带重力项的一维渗流方程 u_t=(u~m)_(xx)+(u~n)_x,m>1,n>1Cauchy问题解的自由边界的正则性.正如我们所知,此退化方程解的显著特征是满足有限传播速度:当初值u_0(x)具有紧支集时,自由边界x=ζ_i(t),(i=1,2)是两条Lipschitz连续曲线.本文进一步研究指出:当n≥m对压力v=m/(m-1)u~(m-1)有ζ'_1(t)=-limv_x(x,t),t∈(0,∞),且对ζ_1(t)的任何移动部份Γ是C~1正则的;当n-1/m-1≥k,k为正整数,则微商(1≤2l+j≤k)在Γ的每一侧附近是有界的;特别当n-1/m-1=k,则任意阶微商(l≥0,j≥0)在Γ的每一侧附近有界,从而v在Γ的每一侧是C~∞的。 本文只考虑i=1的情形,至于i=2可类似地加以考虑。     

含参变量Cantor集的Hausdorff测度

本文研究了菱形为基本集所构成的的广义Cantor集的Hausdorff测度问题.利用菱形几何结构的相关证明方法,获得了此类广义Cantor集的Hausdorff测度准确值,推广了曾超益和许绍元等人的已有结果.     

一类不等式

<正> 本文首先将(2)换为下面的(4),然后将(3)推广,导出一类不等式. §.2 本文采用记号如下: S_n为n元集{1,2,…,n}上的全体置换所组成的置换群,G为S_n的一个子群. x=(x_1,x_2,…,x_n),α=(α_1,α_2,…,α_n),β=(β_1,β_2,…,β_n)等均为n维欧氏空间中的点,并且不作特别申明时约定各个分量为正.     

一类齐次Moran集的维数

本文研究了一类特殊的齐次Moran集的维数.将齐次均匀Cantor集通过一系列平移,获得了一类特殊的齐次Moran集并得到了它们维数的精确值,推广了齐次均匀Cantor集维数的计算公式.     

Cantor尘的Hausdorff测度的初等证明

本文从自相似集的几何性质出发 ,用初等的方法得到了 Cantor尘的 Hausdorff测度 .     

GENERALIZED HILBERT OPERATOR AND FEJR-RIESZ TYPE INEQUALITIES ON THE POLYDISC

Let f be a holomorphic function on the unit polydisc Dn,with Taylor expansion f(z) = ∞ |k|=0 akzk ≡∞ (k1+···+kn=0) (ak1,···,kn zk1 1znkn)where k = (k1, , kn) ∈ Z+n. The authors define generalized Hilbert operator on Dn by Hγ,n(f)(z) = ∞ |k|=0 i1,···,in≥0 ai1,···,in n j=1 Γ(γj + kj + 1)Γ(kj + ij + 1) Γ(kj + 1)Γ(kj + ij + γj + 2) zk,where γ∈ Cn, such that R γj > -1, j = 1, 2, , n. An upper bound for the norm of the operator on Hardy spaces Hp(Dn) is found. The authors also present a Fejér-Riesz type inequalit...     

齐次Moran集的Bouligand维数

设m({nk}k≥1,{Ck}k≥1是由{nk}k≥1,{Ck}k≥1所确定的齐次Moran集类，其中{nk}k≥1是正整数序列，{Ck}k≥1是正实数列。本文确定了m中元素的上（下）Bouligand维数的最大、小值之间的数s，存在m中的元素使其上（下）Bouligand维数值为s。还讨论了齐次Cantor集与偏齐次Cantor集的Bouligand维数存在性之间的关系。     

A new evaluation method based on D–S generalized fuzzy soft sets and its application in medical diagnosis problem

Soft set theory, initiated by Molodtsov, is a general mathematical tool for dealing with uncertain problems. In this paper, we first point out that the similarity measure in a previous paper by Majumdar and Samanta [P. Majumdar, S.K. Samanta, Generalized fuzzy soft sets, Comput. Math. Appl. 59 (2010) 1425–1432] is limited by two counterexamples. To deal with the problems of subjective evaluation and uncertain knowledge, this paper proposes the concept of D–S generalized fuzzy soft sets by combining Dempster–Shafer theory of evidence and generalized fuzzy soft sets. We study some of its operations and basic properties, and the relationship between generalized fuzzy soft sets and D–S generalized fuzzy soft sets are introduced. Then we propose the concept of the similarity between two D–S generalized fuzzy soft sets. At last, we present a new method of evaluation based on D–S generalized fuzzy soft sets and apply it into a medical diagnosis problem.     

集合概念的扩张与完善

从集合概念的内涵出发,剖析了单值集——Cantor集合、Fuzzy集合、Rough集合、可拓集合概念的内涵;剖析了复值集——Grey集合、未确知集合、Vague集合、泛灰(UG)集合和广义泛灰(GUG)集合的内涵;从而得出广义泛灰集合是内涵最深的集合概念;它具有极强的描述能力,可以描述客观存在的一切现象,故又是外延最广的集合概念.     

Stable intersection of affine Cantor sets defined by two expanding maps

It is shown that in the context of affine Cantor sets with two increasing maps, the arithmetic sum of both of its elements is a Cantor set otherwise, it is a closure of countable union of nontrivial intervals. Also, a new family of pairs of affine Cantor sets is introduced such that each element of it has stable intersection. At the end, pairs of affine Cantor sets are characterized such that the sum of elements of each pair is a closed interval.     

The smallest degree sum that yields potentially Kr,r-graphic sequences

We consider a variation of a classical Turán-type extremal problem as follows: Determine the smallest even integer σ(Kr,r, n) such that every n-term graphic sequence π = (d1, d2,..., dn) with term sum σ(π) = d1 + d2 +…+ dn ≥σ(Kr,r, n) is potentially Kr,r-graphic, where Kr,r is an r × r complete bipartite graph, i.e. πr has a realization G containing Kr,r as its subgraph. In this paper, the values σ(Kr,r,n) for even r and n ≥ 4r2 - r - 6 and for odd r and n ≥ 4r2 + 3r - 8 are determined.     

Regular interval Cantor sets of <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript> and minimality

It is known that not every Cantor set of S ¹ is C ¹-minimal. In this work we prove that every member of a subfamily of what we here call regular interval Cantor set is not C ¹-minimal. We also prove that no member of a class of Cantor sets that includes this subfamily is C ^1+∈-minimal, for any ∈ > 0. Partially supported by CNPq-Brasil and PEDECIBA-Uruguay.