共查询到20条相似文献,搜索用时 31 毫秒
1.
Green's Equivalences on Semigroups of Transformations Preserving Order and an Equivalence Relation 总被引:4,自引:0,他引:4
Let ${\cal T}_X$ be the full transformation semigroup on the set $X$,
\[
T_{E}(X)=\{f\in {\cal T}_X\colon \ \forall(a,b)\in E,(f(a),f(b))\in E\}
\]
be the subsemigroup of ${\cal T}_X$ determined by an equivalence
$E$ on $X$. In this paper the set $X$ under consideration is a
totally ordered set with $mn$ points where $m\geq 2$ and $n\geq
3$. The equivalence $E$ has $m$ classes each of which contains $n$
consecutive points. The set of all order preserving
transformations in $T_{E}(X)$ forms a subsemigroup of $T_E(X)$
denoted by
\[
{\cal O}_{E}(X)=\{f\in T_{E}(X)\colon \ \forall\, x, y\in X, \ x\leq
y \mbox{ implies } f(x)\leq f(y)\}.
\]
The nature of regular elements in ${\cal O}_{E}(X)$ is described
and the Green's equivalences on ${\cal O}_{E}(X)$ are
characterized completely. 相似文献
2.
该文引入了 cut*空间的概念,所谓的 cut*空间是指去掉任意一点连通,去掉任意两点不连通的连通空间.通过对其性质的讨论,得到如下主要结论: 首先得到cut*空间中每个点非开即闭,并且cut*空间中有无限多个闭点;其次讨论了一类特殊的 cut*空间,即去掉一点是COTS的 cut* 空间.指出``$X$是 cut*空间,任意 $x\inX,X\setminus\{x\}$是不可约cut空间'这样的空间类是不存在的.在文章的最后,讨论了去掉一点是LOTS的 cut*空间的覆盖性质,得到这样的空间是紧空间或Lindel\"of空间的结论. 相似文献
3.
保持两个等价关系的变换半群的Green关系 总被引:2,自引:0,他引:2
Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, let
TF(X) = {f ∈ Tx : arbieary (x, y) ∈ F, (f(x),f(y)) ∈ F}.
Then TF(X) is a subsemigroup of Tx. Let E be another equivalence on X and TFE(X) = TF(X) ∩ TE(X). In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green's relations for the semigroup TFE(X). 相似文献
TF(X) = {f ∈ Tx : arbieary (x, y) ∈ F, (f(x),f(y)) ∈ F}.
Then TF(X) is a subsemigroup of Tx. Let E be another equivalence on X and TFE(X) = TF(X) ∩ TE(X). In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green's relations for the semigroup TFE(X). 相似文献
4.
5.
On the Rank of the Semigroup TE(X) 总被引:1,自引:0,他引:1
Pei Huisheng 《Semigroup Forum》2005,70(1):107-117
${\cal T}_X $ denotes the full transformation semigroup on a set $ X $. For a
nontrivial equivalence $E$ on $X$, let
\[
T_E (X) =\{ f\in {\cal T}_X : \forall \, (a,b)\in E,\, (af,bf)\in E \} .
\]
Then $T_E (X) $ is exactly the semigroup of continuous selfmaps of
the topological space $X$ for which the collection of all
$E$-classes is a basis. In this paper, we first discuss the rank
of the homeomorphism group $G$, and then consider the rank of $T_E
(X)$ for a special case that the set $X$ is finite and that each
class of the equivalence $E$ has the same cardinality. Finally,
the rank of the closed selfmap semigroup $\Gamma(X)$ of the space
$X$ is observed. We conclude that the rank of $G$ is no more than
4, the rank of $T_E (X)$ is no more than 6 and the rank of
$\Gamma(X)$ is no more than 5. 相似文献
6.
设X是齐型空间.设T_(j,1)和T_(j,2)是具有非光滑核的奇异积分算子,或者是±II(I是恒等算子).令Toeplitz型算子T_b=■T_(j,1)M_T_(j,2),其中M_bf(x)=b(x)f(x).研究了当b∈BMO(X)时,T_b(f)在加权情况下的有界性,以及当b∈BMO(X)时,与经典Carderon-Zygmund算子相联的T_b(f)在Morrey空间上的有界性. 相似文献
7.
Si Ligeng 《数学年刊B辑(英文版)》1982,3(2):203-208
In this paper, we have obtained the equivalence theorems of stability between the system of differential equations
$[{\dot x_i}(t) = \sum\limits_{j = 1}^n {{a_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{b_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{c_{ij}}{{\dot x}_j}(t)} (i = 1,2, \cdots ,n)\]$
and the system of differential-difference equations of neutral type
$[{\dot x_i}(t) = \sum\limits_{j = 1}^n {{a_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{b_{ij}}{x_j}(t - {\Delta _{ij}})} + \sum\limits_{j = 1}^n {{c_{ij}}{{\dot x}_j}(t - {\Delta _{ij}})} (i = 1,2, \cdots ,n)\]$
where a_ij, b_ij, c_ij are given constants, and \Delta_ij are non-negative real constants. 相似文献
8.
Yan Ziqian 《数学年刊B辑(英文版)》1982,3(1):67-78
In this paper initial value problems and nonlinear mixed boundary value problems for the quasilinear parabolic systems below
$\[\frac{{\partial {u_k}}}{{\partial t}} - \sum\limits_{i,j = 1}^n {a_{ij}^{(k)}} (x,t)\frac{{{\partial ^2}{u_k}}}{{\partial {x_i}\partial {x_j}}} = {f_k}(x,t,u,{u_x}),k = 1, \cdots ,N\]$
are discussed.The boundary value conditions are
$\[{u_k}{|_{\partial \Omega }} = {g_k}(x,t),k = 1, \cdots ,s,\]$
$\[\sum\limits_{i = 1}^n {b_i^{(k)}} (x,t)\frac{{\partial {u_k}}}{{\partial {x_i}}}{|_{\partial \Omega }} = {h_k}(x,t,u),k = s + 1, \cdots N.\]$
Under some "basically natural" assumptions it is shown by means of the Schauder type estimates of the linear parabolic equations and the embedding inequalities in Nikol'skii spaces,these problems have solutions in the spaces $\[{H^{2 + \alpha ,1 + \frac{\alpha }{2}}}(0 < \alpha < 1)\]$.For the boundary value problem with $\[b_i^{(k)}(x,t) = \sum\limits_{j = 1}^n {a_{ij}^{(k)}} (x,t)\cos (n,{x_j})\]$ uniqueness theorem is proved. 相似文献
9.
LUSTERNIK-SCHNIRELMANN CATEGORY AND EMBEDDING FINITE
COVERING MAPS, PRINCIPAL G-BUNDLES INTO BUNDLES
Liu Luofei 《数学年刊B辑(英文版)》1996,17(3):317-324
The author proves several embedding theorems for finite covering maps,principal G-bundies into bundles.The main results are 1. Let π:E→X be a finite covering map, and X a connected locally path-connected paracompact space. If cat X≤k, then the finite covering space π:E→X can be embedded into the trivial real k-plane bundle. 2. Let π:E→X be a principal G-bundle over a paracompact space. If there exists a linera action of Gon F(F=R or C)and cat X≤k ,then π:E→X can be embedded into ξ1 … ξn for any F-vector bundles ξi,i=1,…k. 相似文献
10.
${\cal N}$和${\cal M}$分别是实或复Banach空间$X$ ($\dim X >5$)和$Y$中的两个套且Alg${\cal N}$和Alg${\cal M}$分别是与套${\cal N}$和${\cal M}$相关的套代数.符号Alg加映射;秩一幂零算子;套代数 Additive map,Rank one nilpotent operator,Nest algebra 国家自然科学基金;清华大学校科研和教改项目;教育部高等学校博士点教育基金;国家自然科学基金;山西省自然科学基金 2005-02-08 2007年4月25日 ${\cal N}$和${\cal M}$分别是实或复Banach空间$X$ ($\dim X >5$)和$Y$中的两个套且Alg${\cal N}$和Alg${\cal M}$分别是与套${\cal N}$和${\cal M}$相关的套代数.符号Alg加映射;秩一幂零算子;套代数 Additive map,Rank one nilpotent operator,Nest algebra 国家自然科学基金;清华大学校科研和教改项目;教育部高等学校博士点教育基金;国家自然科学基金;山西省自然科学基金 2005-02-08 2007年4月25日 令N和M分别是实或复Banach空间X(dim X>5)和Y中的两个套且AlgN和AlgM分别是与套N和M相关的套代数.符号AlgFN表示AlgN中所有有限秩算子全体.设Φ:AlgFN→AlgFM是可加映射,且值域包含AlgFM中的所有秩一幂零元.如果Φ-双边保秩一幂零性,作者证明了存在一个域自同构τ及τ-线性算子A和C使得要么对所有的秩一幂零元x(?)f∈AlgFN,Φ(x(?)f)=Ax(?)Cf,要么对所有的秩一幂零元x(?)f∈AlgFN,Φ(x(?)f)=Af(?)Cx.特别地,当X和Y是Hilbert空间且Φ是连续映射时,作者得到这类可加映射Φ的完全刻画. 相似文献
11.
Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator Cφ: Cφf = f °φ, for all f ∈ X. In this paper, the boundedness and compactness of the composition operators from α-Bloch spaces into QK(p,q) and QK,0(p,q) spaces are discussed, where 0 〈 α 〈 ∞. 相似文献
12.
Let X be a Banach space and Ф be an Orlicz function. Denote by L^Ф(I,X) the space of X-valued (I)-integrable functions on the unit interval I equipped with the Luxemburg norm. For f1,f2,... ,fm ∈ L^Ф(I,X), a distance formula distv(f1,f2,... ,fm,L^Ф(I,G)) is presented, where G is a close subspace of X. Moreover, some existence and characterization results concerning the best simultaneous approximation of L^Ф (I, G) in L^Ф (I, X) axe given. 相似文献
13.
Youhua Qian & Shengmin Chen 《数学研究通讯:英文版》2009,25(2):97-103
Let Aut$_∗(X)$ denote the group of homotopy classes of self-homotopy
equivalences of $X$, which induce identity automorphisms of homology group. We
describe a decomposition of Aut$_∗(X_1∨· · ·∨X_n)$ as a product of its simpler subgroups.
We consider the subgroup Aut$_Σ(X)$ of all self homotopy classes α of $X$ such that $Σα = 1_{ΣX} : ΣX → ΣX$, and also give some properties of Aut$_Σ(X)$. 相似文献
14.
In this note we define a new topology on C(X),the set of all real-valued continuous functions on a Tychonoff space X.The new topology on C(X) is the topology having subbase open sets of both kinds:[f,C,ε[={g E C(X):|f(x)-g(x)| ε for every x∈C} and[U,r]~-={g∈C(X):g~(-1)(r)∩U≠φ},where f∈C(X),C∈KC(X)={nonempty compact subsets of X},ε 0,while U is an open subset of X and r∈R.The space C(X) equipped with the new topology T_(kh) which is stated above is denoted by C_(kh)(X).Denote X_0={x∈X:x is an isolated point of X} and X_c={x∈X:x has a compact neighborhood in X}.We show that if X is a Tychonoff space such that X_0=X_c,then the following statements are equivalent:(1) X_0 is G_δ-dense in X;(2) C_(kh)(X) is regular;(3) C_(kh)(X) is Tychonoff;(4) C_(kh)(X) is a topological group.We also show that if X is a Tychonoff space such that X_0=X_c and C_(kh)(X) is regular space with countable pseudocharacter,then X is σ-compact.If X is a metrizable hemicompact countable space,then C_(kh)(X) is first countable. 相似文献
15.
In this paper, we concern the divergence Kohn-Laplace equation$$\sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {\left( {X_j^*({a^{ij}}{X_i}u) + Y_j^*({b^{ij}}{Y_i}u)} \right)} } + Tu = f - \sum\limits_{i = 1}^n {\left( {X_i^*{f^i} + Y_i^*{g^i}} \right)}$$ with bounded coefficients on the Heisenberg group ${{\mathbb{H}}^n}$, where ${X_1}, \cdots, {X_n},{Y_1}, \cdots, {Y_n}$ and $T$ are real smooth vector fields defined in a bounded region $\Omega \subset {\mathbb{H}^n}$. The local maximum principle of weak solutions to the equation is established. The oscillation properties of the weak solutions are studied and then the Hölder regularity and weak Harnack inequality of the weak solutions are proved. 相似文献
16.
设$R$是环. 称右$R$-模$M$是PS-模,如果$M$具有投射的socle. 称$R$是PS-环,如果$R_R$是PS-模. 称$M$是CESS-模,如果$M$的任意具有基本socle的子模是$M$的某个直和因子的基本子模.本文给出了形式三角矩阵环 $T=\left( \begin{array}{cc} A & 0 \\ 相似文献
17.
On the real line, the Dunkl operators$$D_{\nu}(f)(x):=\frac{d f(x)}{dx} + (2\nu+1) \frac{f(x) - f(-x)}{2x}, ~~ \quad\forall \, x \in \mathbb{R}, ~ \forall \, \nu \ge -\tfrac{1}{2}$$are differential-difference operators associated with the reflection group $\mathbb{Z}_2$ on $\mathbb{R}$, and on the $\mathbb{R}^d$ the Dunkl operators $\big\{D_{k,j}\big\}_{j=1}^{d}$ are the differential-difference operators associated with the reflection group $\mathbb{Z}_2^d$ on $\mathbb{R}^{d}$.In this paper, in the setting $\mathbb{R}$ we show that $b \in BMO(\mathbb{R},dm_{\nu})$ if and only if the maximal commutator $M_{b,\nu}$ is bounded on Orlicz spaces $L_{\Phi}(\mathbb{R},dm_{\nu})$. Also in the setting $\mathbb{R}^{d}$ we show that $b \in BMO(\mathbb{R}^{d},h_{k}^{2}(x) dx)$ if and only if the maximal commutator $M_{b,k}$ is bounded on Orlicz spaces $L_{\Phi}(\mathbb{R}^{d},h_{k}^{2}(x) dx)$. 相似文献
18.
Gao Ruxi 《数学年刊B辑(英文版)》1983,4(3):293-298
This paper deals with the following mixed problem for Quasilinear hyperbolic equationsThe M order uniformly valid asymptotic solutions are obtained and there errors areestimated. 相似文献
19.
设$T:X\rightarrow X$是紧度量空间$X$上的连续映射, $\mathcal{F}=\{f_n\}_{n\geq
1}$是$X$上的一族连续函数. 如果 $\mathcal{F}$是渐近次可加的, 那么$\sup\limits_{x\in
\mathrm{Reg}(\mathcal{F},T)}\lim\limits_{n\rightarrow\infty}\frac
1 n f_n (x)=\sup\limits_{x\in X}
\limsup\limits_{n\rightarrow\infty}\frac 1 n f_n (x)
=\lim\limits_{n\rightarrow\infty}\frac 1 n \max\limits_{x\in X}f_n
(x)=\sup\{\mathcal{F}^*(\mu):\mu\in\mathcal{M}_T\}$, 其中$\mathcal{M}_T$表示$T$-\!\!不变的Borel概率测度空间, $\mathrm{Reg}(\mathcal{F},T)$
表示函数族$\mathcal{F}$的正规点集, $\mathcal{F}^*(\mu)=\lim\limits_{n\rightarrow\infty}\frac 1 n \int
f_n \mathrm{d}\mu$. 这把Jenkinson, Schreiber 和 Sturman 等人的一些结果推广到渐近次可加势函数, 并且给出了次可加势函数从属原理成立的充分条件, 最后给出了
一些相关的应用. 相似文献
20.
In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf(x) = p. v.RnΩ(x- y)|x- y|n+1 A(x)- A(y)- A(y)(x- y) f(y)dy,where Ω is homogeneous of degree zero, has vanishing moment of order one, and belongs to Lipγ(Sn-1) with γ∈(0, 1], A has derivatives of order one in BMO(Rn). 相似文献