具有正则Gδ对角线空间的注记(英)

这篇简短的注记使用Mysior的例子说明具有正则Gδ对角线的空间不被有限到一的开映射保持．     

关于具有与某集合有关的正则Gδ对角线的空间的注记

本文研究了空间X中具有一定性质的子集可度量化的问题.利用一般拓扑学证明一个空间可度量的方法,得到如下结论:若正则空间具有与其有界子集有关的正则Gδ对角线,那么该子集的闭包是可度量化的;若正则空间具有与其有界强零集A有关的Gδ对角线,那么该子集A是X的紧可度量的子空间,推广了文献[1,2]的结果.     

论可裂 G2的缠结算子(I)

设G为线性连通单李群可裂G     

关于复射影空间中具有平行平均曲率向量的全实叶的注记(英文)

We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type.     

时标上δ±移位概周期解的存在唯一性定理(英文)

本文运用时标上微积分理论,δ_±移位概周期函数的性质,及压缩映射原理,研究了时标上非线性和线性动力学方程的δ_±移位概周期解的存在唯一性,分别给出了方程在有限区间和无穷区间上解的具体表达式.最后,将上述研究结果应用于一类具有小参数扰动动力学方程δ_±移位概周期解的存在性研究.     

退化弱(L1,L2)-BLD映射的正则性

本文给出空间退化的弱(L1,L2)-BLD映射的定义.利用Hodge分解,弱逆Holder不等式等工具,证明了其正则性结果对任意满足0＜L2lnl/2l2n+l×100n2[23l/2.(24l+n+1)](l-q1)＜1的q1,都存在可积指数p1=p1(n,l,q1,L1,L2)＞l,使得对任意退化的弱(L1,L2)-BLD映射f∈W1,q1 loc(Ω,Rn),都有f∈W1,p1 loc (Ω,Rn),即f为通常意义下的退化的(L1,L2)-BLD映射.     

空间l∞(Xn)中的弱紧性

本文首先得到了以l_∞(X_n)为值域的有界线性算子为弱紧算子的一个充要条件和一个充分条件，讨论了l_∞(X_n)中的弱收敛，然后给出了l_∞(X_n)中弱紧性的几种等价刻画．     

空间l1(Xn)中的弱紧性

本文首先讨论空间l₁(X_n)中的弱收敛性，然后给出了l₁(X_n)中弱紧性的几种等价刻画，同时对l_p(X_n)（１＜ｐ＜∞）中的弱紧性也得到了类似的结果．     

具有广义可行性余弦序列的E1?Ed型距离正则图

给出了具有广义可行性余弦序列的E₁?E_d型距离正则图的特征,并计算了这类图的交叉数.     

(δ,)-等距的稳定性

本文讨论了Banach空间之间非满射、非线性的弱等距逼近问题.在某些条件假设下,对(δ,(?))-等距算子的稳定性给出了一些肯定的结果,从而修正并推广了文[1—4]中的一些结果.     

$c$-半层空间与几乎完全正则空间一点注记

In this paper, we give some characterizations of almost completely regular spaces and c-semistratifiable spaces(CSS) by semi-continuous functions. We mainly show that:(1)Let X be a space. Then the following statements are equivalent:(i) X is almost completely regular.(ii) Every two disjoint subsets of X, one of which is compact and the other is regular closed, are completely separated.(iii) If g, h : X → I, g is compact-like, h is normal lower semicontinuous, and g ≤ h, then there exists a continuous function f : X → I such that g ≤ f ≤ h;and(2) Let X be a space. Then the following statements are equivalent:(a) X is CSS;(b) There is an operator U assigning to a decreasing sequence of compact sets(Fj)j∈N,a decreasing sequence of open sets(U(n,(Fj)))n∈N such that(b1) Fn■U(n,(Fj)) for each n ∈ N;(b2)∩n∈NU(n,(Fj)) =∩n∈NFn;(b3) Given two decreasing sequences of compact sets(Fj)j∈N and(Ej)j∈N such that Fn■Enfor each n ∈ N, then U(n,(Fj))■U(n,(Ej)) for each n ∈ N;(c) There is an operator Φ : LCL(X, I) → USC(X, I) such that, for any h ∈ LCL(X, I),0 Φ(h) h, and 0 Φ(h)(x) h(x) whenever h(x) 0.     

关于sn度量空间的注记

The main purpose of this paper is to establish the mapping relation between metric spaces and sn-metric spaces.     

A Note on Sobolev Spaces

In the theory of averaging and other branches of mathematical physics, a crucial role is played by Sobolev spaces connected with a Borel measure defined in the Euclidean space ℝ^d. These spaces are defined as closures of the sets of smooth functions in an appropriate norm. In this paper, we propose another (dual) definition of Sobolev spaces and give an example of using this definition.__________Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 10, Suzdal Conference-4, 2003.     

A Note on Almost Regular Graphs

It can easily be seen that a conjecture of Runge does not hold for a class of graphs whose members will be called “almost regular”. This conjecture is replaced by a weaker one, and a classification of almost regular graphs is given.     

A Note on Regular Near Polygons

Let be a regular near polygon of order (s,t) with s>1 and t3. Let d be the diameter of , and let r:= max{i(c_i,a_i,b_i)=(c₁,a₁,b₁)}. In this note we prove several inequalities for . In particular, we show that s is bounded from above by function in t if We also consider regular near polygons of order (s,3).This work was partly supported by the Grant-in-Aid for Scientific Research (No 14740072), the Ministry of Education, Culture, Sports, Science and Technology, JapanThis work was partly done when the author was at the Com²MaC center at the Pohang University of Science and Technology. He would like to thank the Com²MaC-KOSEF for its support     

关于超一致空间的一个注记

最近,张德学引入了拓扑构造的co-tower扩张这一概念,并证明了不分明拓扑学中若干熟知的范畴构造可以表示为较为简单的范畴构造的co-tower扩张.本文证明了由J.GutiérrezGarcía和M.A.dePradaVicente[3]引入的超一致空间构造SUS具体同构与R.Lowen[9]意义下的不分明一致空间构造FUS的cco-tower扩张的一个满子构造,而已知FUS同构于一致空间构造的co-tower扩张.     

关于单调亚紧空间

In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fó-subspaces. For a generalized ordered (GO)-space X, we also show that X is monotonically metacompact if and only if its closed linearly ordered extension X* is monotonically metacompact. We also point out that every non-Archimedean space X is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact.     

A Note on Partial b-Metric Spaces

Mediterranean Journal of Mathematics - Let (X,b) be a partial b-metric space with coefficient $${s geq 1. ,,{rm For ,, each},, x in X ,,{rm and ,,each},, varepsilon > 0,...     

强正则自补图的一个注记

Kotzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongly-regular self- complementary graph whose order is 4k 1, where 4k 1=x2 y2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k 1 orders.     

A Note on Almost Regular Group Rings

It is proved that a group ring R = AG is almost regular if and only if (i) the ring A is almost regular; (ii) the group G is locally finite; (iii) the order |H| of every finite subgroup H of G is invertible in A. Bibliography: 7 titles.