共查询到18条相似文献,搜索用时 125 毫秒
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保持一个等价关系的部分变换半群 总被引:4,自引:0,他引:4
设X是一个集合,|X|≥3. Px为集合X上所有部分变换构成的半群.设E是集合X的一个等价关系.定义 PE(X)={f∈Px:(A)x,y∈domf,(x,y)∈E(→)f(x),f(y)∈E} 则PE(X)作成PX的一个子半群.本文讨论半群PE(X)的格林关系和正则性,并研究当等价关系E满足什么条件时,半群PE(X)是富足半群. 相似文献
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一类广义变换半群的格林关系 总被引:1,自引:0,他引:1
设X是一个全序集,E是X上的一个凸等价关系.令
OE(X)={f∈TE(X):Ax,y∈X,x≤y→f(x)≤f(y)),
其中TE(X)是E-保持变换半群.对于取定的θ∈OE(X),在OE(X)上定义运算fog=fθg,使OE(X)成为广义半群OE(X;θ).对于有限全序集X上的凸等价关系E,本文刻画了广义半群OE(X;θ)的正则元,描述了这个半群的格林关系. 相似文献
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设P_n是X_n={1,…,n}上的部分变换半群.对任意1≤k≤n,令P_n(k)={α∈P_n:(x∈dom(α)x≤k■xα≤k},则易验证P_n(k)是P_n的子半群.刻画了半群P_n(k)的正则元的特征,并且描述了这个半群上的Green关系. 相似文献
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设OI_n是[n]上的保序严格部分一一变换半群.对任意1≤k≤n-1,研究半群OI_n(k)={α∈OI_n:(■x∈dom(α))x≤k■xα≤k}的秩,证明了半群OI_n(k)的秩为n+1. 相似文献
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设TX是非空集合X上全变换半群,E是X上非平凡的等价关系,则T?(X)是TX的子半群.在赋予半群T?(X)自然偏序关系的条件下,本文刻画了它的相容元. 相似文献
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§1.引言称P=(X,≤)是一个序集是指,X是一个集合,“≤”是X上的一个二元关系(叫做小于等于),它满足:(1)自反性,(x≤x,x∈X),(2)传递性(x≤y,y≤z■x≤z)和(3)反对称性x≤y,y≤x,■x=y)。本文只讨论有限序集。用|X|或|P|表示序集P=(X,≤)所含有的元素个数,用x∈P或x∈X表示x是P的元素。对任一序集Q,我们也用相同的字母Q表示它的基本集。在序集P中,如果x≤y,则我们也用x≤y(P),y≥x及y≥x(P)来表示这一关系。 相似文献
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分析了n元模糊逻辑函数集合中的偏序结构,论证了该集合M-={f|f:[0,1]n→[0,1],(A)x∈[0,1]n,f(x)∈[0,1]}是一个双格半群.并且M-关于其上定义的等值关系构成的商集W={Cf|(A)g∈Cf(∈)M-,f(x)=g(x),f,g∈M,x∈[0,1]n}也构成一个双格半群. 相似文献
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1.已知全集I={实数对(x,y)},集合A={(x,y)|(y-4)/(x-2)=3},B={(x,y)|y==3x-2},求A∩B。 2.设全集I={2,4,a~2-a+1}及集合A={a+1,2},A={7},求实数a。 3.设集合A={(x,y)|x∈Z,y∈N,x+y,<3},集合B={0,1,2},从A到B的对应法则f:(x,y)→x+y,试画出对应图,判断这个对应是不是映射? 4.已知集合A={x|x∈R},B={y|y∈R},从A到B的对应法则f:x→y=tg2x,(1)求A的元素arctg2的象;(2)求B里元素5的原象;(3)上述对应f是否一一映射?为什么? 5.已知函数y=2/3(9-x~2)~(1/2)(-3≤x≤0),求它 相似文献
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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
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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
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Let Y be a subset of X and T(X, Y) the set of all functions from X into Y. Then, under the operation of composition, T(X, Y) is a subsemigroup of the full transformation semigroup T(X). Let E be an equivalence on X. Define a subsemigroup $$T_E(X,Y)$$ of T(X, Y) by $$\begin{aligned} T_E(X,Y)=\{\alpha \in T(X,Y):\forall (x,y)\in E, (x\alpha ,y\alpha )\in E\}. \end{aligned}$$Then $$T_E(X,Y)$$ is the semigroup of all continuous self-maps of the topological space X for which all E-classes form a basis carrying X into a subspace Y. In this paper, we give a necessary and sufficient condition for $$T_E(X,Y)$$ to be regular and characterize Green’s relations on $$T_E(X,Y)$$. Our work extends previous results found in the literature. 相似文献
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Let
be the full transformation semigroup on a set X. For a non-trivial equivalence E on X, let
Then TE(X) is a subsemigroup of
. For a finite totally ordered set X and a convex equivalence E on X, the set of all orientation-preserving transformations
in TE(X) forms a subsemigroup of TE(X) which is denoted by OPE(X). In this paper, under the hypothesis that the set X is a totally ordered set with mn (m ≥ 2,n ≥ 2) points and the equivalence
E has m classes each of which contains n consecutive points, we discuss the regularity of elements and the Green's relations
for OPE(X). 相似文献
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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
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完全图全符号控制数的较小上界和下确界 总被引:2,自引:0,他引:2
设图G=G(V,E),令函数f∶V∪E→{-1,1},f的权w(f)=∑x∈V∪Ef[x],对V∪E中任一元素,定义f[x]=∑y∈NT[x]f(y),这里NT[x]表示V∪E中x及其关联边、邻点的集合.图G的全符号控制函数为f∶V∪E→{-1,1},满足对所有的x∈V∪E有f[x]1,图G的全符号控制数γT(G)就是图G上全符号控制数的最小权,称其f为图G的γT-函数.本文得到了完全图全符号控制数的一个较小上界和下确界. 相似文献
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Let (X,≤) be a totally ordered set, T
X
the full transformation semigroup on X and E an arbitrary equivalence on X. We consider a subsemigroup of T
X
defined by
= T_X: x,y X,(x,y) Eandx y(x,y) Eandx y\mathit{EOP}_X=\{\alpha\in T_X:\forall x,y\in X,(x,y)\in E~\hbox{and}~x\leq y\Rightarrow(x\alpha,y\alpha)\in E~\hbox{and}~x\alpha\leq y\alpha\} 相似文献
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设G=(X,Y,E(G))是一个二分图,分别用V(G)=XUY和E(G)表示G的顶点集和边集.设f是定义在V(G)上的整数值函数且对(A)x∈V(G)有f(x)≥k.设H_1,H_2,…,H_k是G的k个顶点不相交的子图,且|E(H_i)|=m,1≤i≤k.本文证明了每个二分(0,mf-m+1)-图G有一个(0,f)-因子分解正交于Hi(i=1,2,…,k). 相似文献
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