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1.
A hybrid triple system of order v and index λ,denoted by HTS(v,λ),is a pair(X,B) where X is a v-set and B is a collection of cyclic triples and transitive triples on X,such that every ordered pair of X belongs to λ triples of B. An overlarge set of disjoint HTS(v,λ),denoted by OLHTS(v,λ),is a collection {(Y \{y},Ai)}i,such that Y is a(v+1)-set,each(Y \{y},Ai) is an HTS(v,λ) and all Ais form a partition of all cyclic triples and transitive triples on Y.In this paper,we shall discuss the existence problem of OLHTS(v,λ) and give the following conclusion: there exists an OLHTS(v,λ) if and only if λ=1,2,4,v ≡ 0,1(mod 3) and v≥4. 相似文献
2.
Zi-hong TIAN~ 《中国科学A辑(英文版)》2007,50(10):1369-1381
A directed triple system of order v,denoted by DTS(v,λ),is a pair(X,B)where X is a v- set and B is a collection of transitive triples on X such that every ordered pair of X belongs toλtriples of B.An overlarge set of disjoint DTS(v,λ),denoted by OLDTS(v,λ),is a collection{(Y\{y},A_i)}_i, such that Y is a(v 1)-set,each(Y\{y},A_i)is a DTS(v,λ)and all A_i's form a partition of all transitive triples of Y.In this paper,we shall discuss the existence problem of OLDTS(v,λ)and give the following conclusion:there exists an OLDTS(v,λ)if and only if eitherλ=1 and v≡0,1(mod 3),orλ=3 and v≠2. 相似文献
3.
A directed triple system of order v,denoted by DTS(v),is a pair (X,B) where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs to exactly one triple of B.A DTS(v) (X,A) is called pure and denoted by PDTS(v) if (a,b,c) ∈ A implies (c,b,a) ∈/ A.An overlarge set of PDTS(v),denoted by OLPDTS(v),is a collection {(Y \{yi},Aij) : yi ∈ Y,j ∈ Z3},where Y is a (v+1)-set,each (Y \{yi},Aij) is a PDTS(v) and these Ais form a partition of all transitive triples on Y .In this paper,we shall discuss the existence problem of OLPDTS(v) and give the following conclusion: there exists an OLPDTS(v) if and only if v ≡ 0,1 (mod 3) and v 3. 相似文献
4.
§ 1 IntroductionLet X be a set of v points.A packing(directed packing) of X is a collection of subsets(ordered subsets) of X(called blocks) such that any pair(ordered pair) of distinct pointsfrom X occur together in atmostone block in the collection.A packing(directed packing)is called resolvable ifitsblock setadmitsa partition into parallel classes,each parallel classbeing a partition of the pointset X.A Kirkman triple system KTS(v) is a collection Tof3 -subsets of X(triples) suchthat … 相似文献
5.
Let G be a graph. An independent set Y in G is called an essential independent set (or essential set for simplicity) if there is {Y1, Y2} 包含于Y such that dist (y1,y2)=2. In this paper, we use the technique of the vertex insertion on l-connected (l=k or k 1, k≥2) graphs to provide a unified proof for G to be hamiltonian, or hamiltonian-connected. The sufficient conditions are expressed an inequality on ∑i=1 K|N(Yi)| b|N(y0)| and n(Y) for each essential set Y={y0,y1,…,yk}, where b (1≤b≤k)is an integer,Yi={yi,yi-1,…,yi-(b-1}包含于Y\{y0} for i属于V(G):dist(v,Y)≤2}|. 相似文献
6.
A directed triple system of order v with index λ, briefly by DTS(v,λ), is a pair (X, B) where X is a v-set and B is a collection of transitive triples (blocks) on X such that every ordered pair of X belongs to λ blocks of B. A simple DTS(v, λ) is a DTS(v, λ) without repeated blocks. A simple DTS(v, ),) is called pure and denoted by PDTS(v, λ) if (x, y, z) ∈ B implies (z, y, x), (z, x, y), (y, x, z), (y, z, x), (x, z, y) B. A large set of disjoint PDTS(v, λ), denoted by LPDTS(v, λ), is a collection of 3(v - 2)/λ disjoint pure directed triple systems on X. In this paper, some results about the existence for LPDTS(v, λ) are presented. Especially, we determine the spectrum of LPDTS(v, 2). 相似文献
7.
A λ-fold triple system TS(ν,λ)is an ordered pair(V,B)where V is a setof v elements and B is a collection of 3-subsets(called blocks or triples)of Vsuch that each 2-subset of V is contained in exactly λ triples.A triple system iscalled simple if it contains no repeated triples. 相似文献
8.
A Mendelsohn triple system of order v (MTS(v)) is a pair (X,B) where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS(v) (X,B) is called pure and denoted by PMTS(v) if (x, y, z) ∈ B implies (z, y, x) ∈B. A large set of MTS(v)s (LMTS(v)) is a collection of v - 2 pairwise disjoint MTS(v)s on a v-set. A self-converse large set of PMTS(v)s, denoted by LPMTS* (v), is an LMTS(v) containing [ v-2/2] converse pairs of PMTS(v)s. In this paper, some results about the existence and non-existence for LPMTS* (v) are obtained. 相似文献
9.
A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups. 相似文献
10.
LI Qing 《中国科学 数学(英文版)》2013,56(9):1773-1780
Let D be an integral domain and X an indeterminate over D . We show that if S is an almost splitting set of an integral domain D , then D is an APVMD if and only if both DS and DN(S) are APVMDs. We also prove that if {Dα}α∈I is a collection of quotient rings of D such that D=∩α∈IDα has finite character (that is, each nonzero d∈D is a unit in almost all Dα) and each of Dα is an APVMD, then D is an APVMD. Using these results, we give several Nagata-like theorems for APVMDs. 相似文献
11.
一个Mendelsohn (Directed, 或Hybrid)三元系 MTS$(v, \lambda)$~(DTS$(v, \lambda)$,或HTS$(v,\lambda))$, 是由$v$元集$X$ 上的一些循环(可迁,或循环和可迁)三元组(简称区组)构成的集合${\cal B}$, 使得$X$上每个由不同元素组成的有序对都恰在 ${\cal B}$的$\lambda$个区组中出现.本文主要讨论了这三类有向三元系之间的一种关联关系,给出猜想:任意MTS$(v,\lambda)$的区组关联图$G(\ 相似文献
12.
In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1. 相似文献
13.
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
14.
${\cal N}$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
15.
Let G(V, E) be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V(Cm). The G - E(Cm) are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui : i = 1, 2 , m}. Let κ = ec+1. Forj = 1,2,...,k- 1, let δij = max{dv : dist(v, ui) = j,v ∈ Ti}, δj = max{δij : i = 1, 2,..., m}, δ0 = max{dui : ui ∈ V(Cm)}. Then λ1(G)≤max{max 2≤j≤k-2 (√δj-1-1+√δj-1),2+√δ0-2,√δ0-2+√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 (G) is the largest eigenvalue of the adjacency matrix of G. 相似文献
16.
Assume X is a normed space,every x * ∈ S(X*) can reach its norm at some point in B(X),and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L(X,Y) contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L(X,Y) fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L(X,Y). 相似文献
17.
本文利用差方法对自反MD设计SCMD$(4mp, p,1)$的存在性给出了构造性证明, 这里$p$为奇素数, $m$为正整数. 相似文献
18.
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
19.
《复变函数与椭圆型方程》2012,57(2):95-110
Let $ k \in {\shadN} $ , $ w(x) = (1+x^2)^{1/2} $ , $ V^{\prime} _k = w^{k+1} {\cal D}^{\prime} _{L^1} = \{{ \,f \in {\cal S}^{\prime}{:}\; w^{-k-1}f \in {\cal D}^{\prime} _{L^1}}\} $ . For $ f \in V^{\prime} _k $ , let $ C_{\eta ,k\,}f = C_0(\xi \,f) + z^k C_0(\eta \,f/t^k)$ where $ \xi \in {\cal D} $ , $ 0 \leq \xi (x) \leq 1 $ $ \xi (x) = 1 $ in a neighborhood of the origin, $ \eta = 1 - \xi $ , and $ C_0g(z) = \langle g, \fraca {1}{(2i \pi (\cdot - z))} \rangle $ for $ g \in V^{\,\prime} _0 $ , z = x + iy , y p 0 . Using a decomposition of C 0 in terms of Poisson operators, we prove that $ C_{\eta ,k,y} {:}\; f \,\mapsto\, C_{\eta ,k\,}f(\cdot + iy) $ , y p 0 , is a continuous mapping from $ V^{\,\prime} _k $ into $ w^{k+2} {\cal D}_{L^1}$ , where $ {\cal D}_{L^1} = \{ \varphi \in C^\infty {:}\; D^\alpha \varphi \in L^1\ \forall \alpha \in {\shadN} \} $ . Also, it is shown that for $ f \in V^{\,\prime} _k $ , $ C_{\eta ,k\,}f $ admits the following boundary values in the topology of $ V^{\,\prime} _{k+1} : C^+_{\eta ,k\,}f = \lim _{y \to 0+} C_{\eta ,k\,}f(\cdot + iy) = (1/2) (\,f + i S_{\eta ,k\,}f\,); C^-_{\eta ,k\,}f = \lim _{y \to 0-} C_{\eta ,k\,} f(\cdot + iy)= (1/2) (-f + i S_{\eta ,k\,}f ) $ , where $ S_{\eta ,k} $ is the Hilbert transform of index k introduced in a previous article by the first named author. Additional results are established for distributions in subspaces $ G^{\,\prime} _{\eta ,k} = \{ \,f \in V^{\,\prime} _k {:}S_{\eta ,k\,}f \in V^{\,\prime} _k \} $ , $ k \in {\shadN} $ . Algebraic properties are given too, for products of operators C + , C m , S , for suitable indices and topologies. 相似文献