共查询到20条相似文献,搜索用时 93 毫秒
1.
Let G = (V, E) be a graph without isolated vertices. A set S lohtain in V is a domination set of G if every vertex in V - S is adjacent to a vertex in S, that is N[S] = V. The domination number of G, denoted by γ(G), is the minimum cardinality of a domination set of G. A set S lohtain in V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S] has a perfect matching. The paired-domination number, denoted by γpr(G), is defined to be the minimum cardinality of a paired-domination set S in G. A subset S lohtain in V is a power domination set of G if all vertices of V can be observed recursively by the following rules: (i) all vertices in N[S] are observed initially, and (ii) if an observed vertex u has all neighbors observed except one neighbor v, then v is observed (by u). The power domination number, denoted by γp(G), is the minimum cardinality of a power domination set of G. In this paper, the constructive characterizations for trees with γp=γ and γpr = γp are provided respectively. 相似文献
2.
Let Gn(C) be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc(Jr~) the set of all primitive matrices in Gn(C). In this paper, some necessary and sufficient conditions for A in the semigroup Gn(C) to be primitive are given. We also show that Gc(Jn) is a subsemigroup of Gn(C). 相似文献
3.
蒋继光 《数学物理学报(B辑英文版)》1988,(3)
Let A be a fuzzy set in a fuzzy topological space (X,τ) and β∈(0, 1]. We denote by ζ_x~a the fuzzy point defined by ζ_x~a(x)=a and ζ_x~a(y)=0 for eaoh y≠x, where a is called the height of ζ_x~a. A subfamily u of τ is called an open β-cover of A if each fuzzy point in A with height β is quasi-coincident with ([1]) some member of u. By a β-subcover of the open β-cover u of A is meant any subfamily of u that is also an open β-cover of A. A is called β-compact in (X, τ) if every open β-cover 相似文献
4.
Let I be an interval of positive rational numbers. Then the set S (I) = T ∩ N, where T is the submonoid of (Q0+, +) generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S (I) has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals. 相似文献
5.
Let X be a compact metric space and C(X) be the space of all continuous functions on X. In this article, the authors consider the Markov operator T : C(X)N C(X)N defined by
for any f = (f1,f2,… ,fN), where (pij) is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T*-invariant measures where T* is the adjoint operator of T. 相似文献
for any f = (f1,f2,… ,fN), where (pij) is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T*-invariant measures where T* is the adjoint operator of T. 相似文献
6.
L. M. EZQUERRO X. SOLER-ESCRIVA 《数学学报(英文版)》2007,23(11):2069-2078
In this paper, we prove the following result. Let ξ be a saturated formation and ∑ a Hall system of a soluble group G. Let X be a w-solid set of maximal subgroups of G such that ∑ reduces into each element of X. Consider in G the following three subgroups: the ξ-normalizer D of G associated with ∑; the X-prefrattini subgroup W = W(G, X) of G; and a hypercentrally embedded subgroup T of G. Then the lattice ζ(T, W, D) generated by T, D and W is a distributive lattice of pairwise permutable subgroups of G with the cover and avoidance property.
This result remains true for the lattice ,ζ(V, W, D), where V is a subgroup of G whose Sylow subgroups are also Sylow subgroups of hypercentrally embedded subgroups of G such that ∑ reduces into V. 相似文献
7.
Rong Bao GU Tai Xiang SUN Ting Ting ZHENG 《数学学报(英文版)》2005,21(4):873-880
Let G be a graph (i.e., a finite one-dimensional polyhedron) and f : G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non-wandering point; every accumulation point of the set of non-wandering points of f with infinite orbit is a two-order accumulation point of the set of recurrent points of f; the derived set of an ω-limit set of f is equal to the derived set of an the set of recurrent points of f; and the two-order derived set of non-wandering set of f is equal to the two-order derived set of the set of recurrent points of f. 相似文献
8.
Let G = (V,E) be a graph without isolated vertices.A set S V is a domination set of G if every vertex in V - S is adjacent to a vertex in S,that is N[S] = V.The domination number of G,denoted by γ(G),is the minimum cardinality of a domination set of G.A set S C V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S] has a perfect matching.The paired-domination number,denoted by γpr(G),is defined to be the minimum cardinality of a paired-domination set S in G.A subset S V is a power domination set of G if all vertices of V can be observed recursively by the following rules: (i) all vertices in N[S] are observed initially,and (ii) if an observed vertex u has all neighbors observed except one neighbor v,then v is observed (by u).The power domination number,denoted by γp(G),is the minimum cardinality of a power domination set of G.In this paper,the constructive characterizations for trees with γp = γ and γpr = γp are provided respectively. 相似文献
9.
Zhen-long Chen San-yang Liu 《应用数学学报(英文版)》2005,21(4):623-636
Let φ be a Hausdorff measure function and A be an infinite increasing sequence of positive integers. The Hausdorff-type measure φ - mA associated to φ and A is studied. Let X(t)(t ∈ R^N) be certain Gaussian random fields in R^d. We give the exact Hausdorff measure of the graph set GrX([0, 1]N), and evaluate the exact φ - mA measure of the image and graph set of X(t). A necessary and sufficient condition on the sequence A is given so that the usual Hausdorff measure function for X([0, 1] ^N) and GrX([0, 1]^N) are still the correct measure functions. If the sequence A increases faster, then some smaller measure functions will give positive and finite ( φ A)-Hausdorff measure for X([0, 1]^N) and GrX([0, 1]N). 相似文献
10.
Let N denote the set of positive integers. The sum graph G^+(S) of a finite subset S belong to N is the graph (S, E) with uv ∈ E if and only if u + v ∈ S. A graph G is said to be a sum graph if it is isomorphic to the sum graph of some S belong to N. By using the set Z of all integers instead of N, we obtain the definition of the integral sum graph. A graph G = (V, E) is a mod sum graph if there exists a positive integer z and a labelling, λ, of the vertices of G with distinct elements from {0, 1, 2,..., z - 1} so that uv ∈ E if and only if the sum, modulo z, of the labels assigned to u and v is the label of a vertex of G. In this paper, we prove that flower tree is integral sum graph. We prove that Dutch m-wind-mill (Dm) is integral sum graph and mod sum graph, and give the sum number of Dm. 相似文献
11.
Let N denote the set of all nonnegative integers and A be a subset of N.Let W be a nonempty subset of N.Denote by F~*(W) the set of all finite,nonempty subsets of W.Fix integer g≥2,let A_g(W) be the set of all numbers of the form sum f∈Fa_fg~f where F∈F~*(W)and 1≤a_f≤g-1.For i=0,1,2,3,let W_i = {n∈N|n≡ i(mod 4)}.In this paper,we show that the set A = U_i~3=0 A_g(W_i) is a minimal asymptotic basis of order four. 相似文献
12.
Let G be a group. We consider the set cd(G)/{m}, where m ∈ cd(G). We define the graph △(G - m) whose vertex set is p(G - m), the set of primes dividing degrees in cd(G)/{m}. There is an edge between p and q in p(G - m) ifpq divides a degree a ∈ cd(G)/{m}. We show that if G is solvable, then △(G - m) has at most two connected components. 相似文献
13.
Mo Guoduan 《数学年刊B辑(英文版)》1982,3(2):189-194
Let E be a bounded closed set, d(E) be the logarithmic capacity of E. If A is any bounded set, then
$[d(A) = \mathop {\sup }\limits_{E \in A} d(E)\]$
For each $Z_0 \in E$, and $\delta >0$, let
$[\Delta = \Delta _{{Z_0}}^\delta = CE \cap (|Z - {Z_0}| < \delta )\]$
where CE is complement of E, then \Delta is an open set. By [{\bar \Delta ^0}\] we denote the interior of the closure A of A. Clearly,$\Delta \subset [{\bar \Delta ^0}\]$ and $d(\Delta) \leq d([{\bar \Delta ^0}\])$,
and there exists an open set D such that d(D) 0, the equation
$d(\Delta)=d([{\bar \Delta ^0}\])$ holds. 相似文献
14.
《复变函数与椭圆型方程》2012,57(5):409-415
Let $ \cal W $ be the set of entire functions equal to a Weierstrass product of the form $ {f(x)= Ax^q\lim_{r \to \infty} \prod_{|a_j|\leq r}{(1- \fraca {x} {a_j})}} $ where the convergence is uniform in all bounded subsets of $ {\shadC} $ , let $ \cal V $ be the set of $ f\in {\cal W} $ such that $ {\shadC} [\,f]\subset {\cal W} $ , and let $ {\cal H} $ be the $ {\shadC} $ -algebra of entire functions satisfying $ { {\lim_{r\to \infty } } ({\ln M(r,f) / r})=0} $ . Then $ \cal H $ is included in $ {\cal V} $ and strictly contains the set of entire functions of genus zero, (which, itself, strictly contains the $ {\shadC} $ -algebra of entire functions of order 𝜌 < 1). Let $ n, m\in {\shadN} ^* $ satisfy n > m S 3. Let $ a\in {\shadC}^* $ satisfies $ {a^n\not = \fraca{n^n}{(m^m(n-m)^{n-m}})} $ and assume that for every ( n m m )-th root ξ of 1 different from m 1, a satisfies further $ {a^{n}\neq (1+\xi )^{n-m} (\fraca{n^n}{((n-m)^{n-m}m^m}))} $ . Let P ( X ) = X n m aX m + 1 and let T n,m ( a ) be the set of its zeros. Then T n,m ( a ) has n distinct points and is a urs for $ {\cal V} $ . In particular this applies to functions such as sin x and cos x . 相似文献
15.
Let G be a group and $\pi$ be a set of primes. We consider the set ${\rm cd}^{\pi}(G)$ of
character degrees of G that are divisible only by primes in $\pi$. In particular, we define
$\Gamma^{\pi}(G)$ to be the graph whose vertex set is the set of primes dividing degrees in ${\rm cd}^{\pi}(G)$. There is an edge between
p and q if pq divides a degree
$a \in {\rm cd}^{\pi}(G)$. We show that if G is $\pi$-solvable, then
$\Gamma^{\pi}(G)$ has at most two connected components. 相似文献
16.
Let $I$ be an open interval of $\mathbb{R}$ and $f: I\to \mathbb{R}$. It is well-known that $f$ is convex in $I$ if and only if, for all $x,y\in I$ with $x相似文献
17.
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
18.
Let S be a nonempty, proper subset of all possible refined inertias of real matrices of order n. The set S is a critical set of refined inertias for irreducible sign patterns of order n,if for each n × n irreducible sign pattern A, the condition S ? ri(A) is sufficient for A to be refined inertially arbitrary. If no proper subset of S is a critical set of refined inertias, then S is a minimal critical set of refined inertias for irreducible sign patterns of order n.All minimal critical sets of refined inertias for full sign patterns of order 3 have been identified in [Wei GAO, Zhongshan LI, Lihua ZHANG, The minimal critical sets of refined inertias for 3×3 full sign patterns, Linear Algebra Appl. 458(2014), 183–196]. In this paper, the minimal critical sets of refined inertias for irreducible sign patterns of order 3 are identified. 相似文献
19.
Let $J$ be an infinite set and let $I={\cal P}_{f}( J)$, i.e., $I$ is the collection of all non empty finite subsets of $J$. Let $\beta I$ denote the collection of all ultrafilters on the set $I$. In this paper, we consider $( \beta I,\uplus ),$ the compact (Hausdorff) right topological semigroup that is the {\it Stone-$\check{C}\!\!$ech} $Compactification$ of the semigroup $\left( I,\cup \right)$ equipped with the discrete topology. It is shown that there is an injective map $A\rightarrow \beta _{A}( I) $ of ${\cal P}( J) $ into ${\cal P}( \beta I) $ such that each $\beta _{A}( I) $ is a closed subsemigroup of $ ( \beta I,\uplus ) $, the set $\beta _{J}( I) $ is a closed ideal of $( \beta I,\uplus ) $and the collection $\{ \beta _{A}( I) \mid A\in {\cal P} ( J) \} $ is a partition of $\beta I$. The algebraic structure of $\beta I$ is explored. In particular, it is shown that {\bf (1)} $\beta _{J}\left( I\right) =\overline{K( \beta I) }$, i.e., $\beta _{J}( I) $is the closure of the smallest ideal of $\beta I$, and {\bf (2)} for each non empty $A\subset J$, the set ${\cal V}_{A}=\tbigcup \{ \beta_{B}( I) \mid B\subset A\} $is a closed subsemigroup of $( \beta I,\uplus ) ,$ $\beta _{A}( I) $ is a proper ideal of ${\cal V}_{A},$ and ${\cal V}_{A}$ is the largest subsemigroup of $( \beta I,\uplus ) $ that has $ \beta _{A}( I) $ as an ideal. 相似文献
20.
设X(t)(t∈R )是一个d维非退化扩散过程.本文得到了比原有结果更一般的非退化扩散过程极性的充分条件,证明了对任意u∈Rd,紧集E(0, ∞),有若d=1,则对任意紧集F(?)R, 若d≥2,则对任意紧集E ∈(0, ∞), 其中B(Rd)为Rd上的Borel σ-代数,dim和Dim分别表示Hausdorff维数和Packing 维数. 相似文献