共查询到20条相似文献,搜索用时 15 毫秒
1.
Fuquan Fang 《Mathematische Zeitschrift》2008,259(3):643-656
Let M be an oriented compact Riemannian 4-manifold with positive sectional curvature. Let G be a finite subgroup of the isometry group of M. We prove that, if G is a finite group of order , then
Moreover, M is homeomorphic to if G is non-abelian of odd order.
Supported partially by NSF Grant 19925104 of China, 973 project of Foundation Science of China and the Max-Planck Institut
für Mathematik at Bonn. 相似文献
(i) | G is isomorphic to a subgroup of PU(3) if |G| is odd; |
(ii) | G contains an index at most 2 normal subgroup which is isomorphic to a subgroup of SO(5) or PU(3) if |G| is even, and M is not homeomorphic to S 4. |
2.
Let (G, τ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following:
As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid
topological groups is established. 相似文献
(1) | If (G, τ) has the A(iii)-property, then its completion is an order-complete locally solid lattice group. |
(2) | If G is order-complete and τ has the Fatou property, then the order intervals of G are τ-complete. |
(3) | If (G, τ) has the Fatou property, then G is order-dense in Ĝ and has the Fatou property. |
(4) | The order-bound topology on any commutative lattice group is the finest locally solid topology on it. |
3.
In this paper, we show the equivalence of somequasi-random properties for sparse graphs, that is, graphsG with edge densityp=|E(G)|/(
2
n
)=o(1), whereo(1)→0 asn=|V(G)|→∞. Our main result (Theorem 16) is the following embedding result. For a graphJ, writeN
J(x) for the neighborhood of the vertexx inJ, and letδ(J) andΔ(J) be the minimum and the maximum degree inJ. LetH be atriangle-free graph and setd
H=max{δ(J):J⊆H}. Moreover, putD
H=min{2d
H,Δ(H)}. LetC>1 be a fixed constant and supposep=p(n)≫n
−1
D
H. We show that ifG is such that
Moreover, we discuss a setting under which an arbitrary graphH (not necessarily triangle-free) can be embedded inG. We also present an embedding result for directed graphs.
Research supported by a CNPq/NSF cooperative grant.
Partially supported by MCT/CNPq through ProNEx Programme (Proc. CNPq 664107/1997-4) and by CNPq (Proc. 300334/93-1 and 468516/2000-0).
Partially supported by NSF Grant 0071261.
Supported by NSF grant CCR-9820931. 相似文献
(i) | deg G (x)≤C pn for allx∈V(G), | ||
(ii) |
for all 2≤r≤D
H and for all distinct verticesx
1, ...,x
r ∈V(G), |
||
(iii) |
for all but at mosto(n
2) pairs {x
1,x
2} ⊆V(G), |
4.
Let H
1, H
2 be Hilbert spaces and T be a closed linear operator defined on a dense subspace D(T) in H
1 and taking values in H
2. In this article we prove the following results:
We prove all the above results without using the spectral theorem. Also, we give examples to illustrate all the above results. 相似文献
(i) | Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T*T) of T*T, In addition, if H 1 = H 2 and T is self-adjoint, then |
(ii) | inf {‖T x‖: x ∈ D(T) ∩ N(T)⊥‖x‖ = 1} = inf {|λ|: 0 ≠ λ ∈ σ(T)} |
(iii) | Every isolated spectral value of T is an eigenvalue of T |
(iv) | Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T) of T |
(v) | σ(T) bounded implies T is bounded. |
5.
QIU ZhiJian School of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2008,51(1):131-142
Let G be a bounded open subset in the complex plane and let H~2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1-1 with respect to the Lebesgue measure on D and if the Riemann map belongs to the weak-star closure of the polynomials in H~∞(W). Our main theorem states: in order that for each M∈Lat (M_z), there exist u∈H~∞(G) such that M=∨{uH~2(G)}, it is necessary and sufficient that the following hold: (1) each component of G is a perfectly connected domain; (2) the harmonic measures of the components of G are mutually singular; (3) the set of polynomials is weak-star dense in H~∞(G). Moreover, if G satisfies these conditions, then every M∈Lat (M_z) is of the form uH~2(G), where u∈H~∞(G) and the restriction of u to each of the components of G is either an inner function or zero. 相似文献
6.
LetK be a class of spaces which are eigher a pseudo-opens-image of a metric space or ak-space having a compact-countable closedk-network. LetK′ be a class of spaces which are either a Fréchet space with a point-countablek-network or a point-G
δ
k-space having a compact-countablek-network. In this paper, we obtain some sufficient and necessary conditions that the products of finitely or countably many
spaces in the classK orK′ are ak-space. The main results are that
Project supported by the Mathematical Tianyuan Foundation of China 相似文献
Theorem A | If X, Y∈K. Then X x Y is a k-space if and only if (X, Y) has the Tanaka's condition. |
Theorem B | The following are equivalent: |
(a) | BF(ω 2)is false. |
(b) | For each X, Y ∈ K′, X x Y is a k-space if and only if (X,Y) has the Tanaka's condition. |
7.
We present results on total domination in a partitioned graph G = (V, E). Let γ
t
(G) denote the total dominating number of G. For a partition , k ≥ 2, of V, let γ
t
(G; V
i
) be the cardinality of a smallest subset of V such that every vertex of V
i
has a neighbour in it and define the following
We summarize known bounds on γ
t
(G) and for graphs with all degrees at least δ we derive the following bounds for f
t
(G; k) and g
t
(G; k).
相似文献
(i) | For δ ≥ 2 and k ≥ 3 we prove f t (G; k) ≤ 11|V|/7 and this inequality is best possible. |
(ii) | for δ ≥ 3 we prove that f t (G; 2) ≤ (5/4 − 1/372)|V|. That inequality may not be best possible, but we conjecture that f t (G; 2) ≤ 7|V|/6 is. |
(iii) | for δ ≥ 3 we prove f t (G; k) ≤ 3|V|/2 and this inequality is best possible. |
(iv) | for δ ≥ 3 the inequality g t (G; k) ≤ 3|V|/4 holds and is best possible. |
8.
Let G be a 2-edge-connected simple graph with girth g, independence number α(G), and if one of the following two conditions holds
then G is upper embeddable and the lower bound v − 3g + 7 is best possible. Similarly the result for 3-edge-connected simple graph with girth g and independence number α(G) is also obtained.
Huang Yuanqiu: Partially supported by National Science Foundation of China (No. 10771062) and Program for New Century Excellent
Talents in University (No. NCET-07-0276). 相似文献
(1) | α(G) ≤ 2; | |
(2) | α(G) ≥ 3, and for any three nonadjacent vertices v
i
(i = 1,2,3), it has
|
9.
A graph G is a {d, d+k}-graph, if one vertex has degree d+k and the remaining vertices of G have degree d. In the special case of k = 0, the graph G is d-regular. Let k, p ⩾ 0 and d, n ⩾ 1 be integers such that n and p are of the same parity. If G is a connected {d, d+k{-graph of order n without a matching M of size 2|M| = n − p, then we show in this paper the following: If d = 2, then k ⩾ 2(p + 2) and
If d ⩾ 3 is odd and t an integer with 1 ⩽ t ⩽ p + 2, then
If d ⩾ 4 is even, then
The special case k = p = 0 of this result was done by Wallis [6] in 1981, and the case p = 0 was proved by Caccetta and Mardiyono [2] in 1994. Examples show that the given bounds (i)–(viii) are best possible. 相似文献
(i) | n ⩾ k + p + 6. |
(ii) | n ⩾ d + k + 1 for k ⩾ d(p + 2) |
(iii) | n ⩾ d(p + 3) + 2t + 1 for d(p + 2 −t) + t ⩽ k ⩽ d(p + 3 −t) + t − 3 |
(iv) | n ⩾ d(p + 3) + 2p + 7 for k ⩽ p. |
(v) | n ⩾ d + k + 2 − η for k ⩾ d(p + 3) + p + 4 + η |
(vi) | n ⩾ d + k + p + 2 − 2t = d(p + 4) + p + 6 for k = d(p + 3) + 4 + 2t and p ⩾ 1 |
(vii) | n ⩾ d + k + p + 4 for d(p + 2) ⩽ k ⩽ d(p + 3) + 2 |
(viii) | n ⩾ d(p + 3) + p + 4 for k ⩽ d(p + 2) − 2, where 0 ⩽ t ⩽ 1/2p − 1 and η = 0 for even p and 0 ⩽ t ⩽ 1/2(p − 1) and η = 1 for odd p. |
10.
For any two 2-regular spanning subgraphs G and H of the complete multipartite graph K, necessary and sufficient conditions are found for the existence of a 2-factorization of K in which
in the case where K has an odd number of vertices. 相似文献
1. | the first and second 2-factors are isomorphic to G and H respectively, and |
2. | each other 2-factor is a hamilton cycle |
11.
Yuji Kobayashi 《Archiv der Mathematik》2005,85(3):227-232
Let k ≧ 3 be an integer or k = ∞ and let K be a field. There is a recursive family
of finitely presented groups Gn over a fixed finite alphabet with solvable word problem such that
Received: 22 July 2004 相似文献
(1) | the center of Gn is trivial for every |
(2) | the dimension d(n) of the center of the group algebra K · Gn over K is either 1 or k, and |
(3) | it is undecidable given n whether d(n) = 1 or d(n) = k. |
12.
Let G be an affine algebraic group and let X be an affine algebraic variety. An action G × X → X is called observable if for any G-invariant, proper, closed subset Y of X there is a nonzero invariant f ∈
\Bbbk\Bbbk [X]
G
such that f|
Y
= 0. We characterize this condition geometrically as follows. The action G × X → X is observable if and only if:
相似文献
(1) the action is stable, that is there exists a nonempty open subset U ⊆ X consisting of closed orbits; and | |
(2) the field \Bbbk\Bbbk(X) G of G-invariant rational functions on X is equal to the quotient field of \Bbbk\Bbbk[X] G . |
13.
The star unfolding of a convex polytope with respect to a pointx on its surface is obtained by cutting the surface along the shortest paths fromx to every vertex, and flattening the surface on the plane. We establish two main properties of the star unfolding:
These two properties permit conceptual simplification of several algorithms concerned with shortest paths on polytopes, and
sometimes a worst-case complexity improvement as well:
相似文献
1. | It does not self-overlap: it is a simple polygon. |
2. | The ridge tree in the unfolding, which is the locus of points with more than one shortest path fromx, is precisely the Voronoi diagram of the images ofx, restricted to the unfolding. |
• | The construction of the ridge tree (in preparation for shortest-path queries, for instance) can be achieved by an especially simpleO(n 2) algorithm. This is no worst-case complexity improvement, but a considerable simplification nonetheless. |
• | The exact set of all shortest-path “edge sequences” on a polytope can be found by an algorithm considerably simpler than was known previously, with a time improvement of roughly a factor ofn over the old bound ofO(n 7 logn). |
• | The geodesic diameter of a polygon can be found inO(n 9 logn) time, an improvement of the previous bestO(n 10) algorithm. |
14.
LeA be an automaton whose set of inputs equalsX (|X|≧2) and whose cardinality of the set of states equalsn (n≧2), and letQ be the set of all primitive words overX. ByT(A) we denote the language accepted byA. In this paper, we give the following results:
Moreover, we deal with the case |T(A)⋔Q|<∞ and obtain upper bounds on the cardinalities ofT(A)⋔Q and of some language related toT(A). 相似文献
(1) | T(A)⋔Q≠ ⊘ if and only ifA accepts a primitive wordy withlg(y)≦3n−3, wherelg(y) means the length ofy. |
(2) | |T(A)⋔Q|=∞ if and only ifA accepts a primitive wordy withn≦lg(y)≦3n−3, where |T(A)⋔Q| means the cardinality ofT(A)⋔Q. |
15.
Let G be a finite group and H a subgroup of G. Then H is said to be S-permutable in G if HP = PH for all Sylow subgroups P of G. Let HsG be the subgroup of H generated by all those subgroups of H which are S-permutable in G. Then we say that H is S-embedded in G if G has a normal subgroup T and an S-permutable subgroup C such that T ∩ H HsG and HT = C. Our main result is the following Theorem A. A group G is supersoluble if and only if for every non-cyclic Sylow subgroup P of the generalized Fitting subgrou... 相似文献
16.
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by
X
α,p
. We show
相似文献
(i) | The subspace [(e nk )] generated by a subsequence (e nk ) of (e n ) is complemented. |
(ii) | The identity operator from X α,p to X α,p when p > q is unbounded. |
(iii) | Every bounded linear operator on some subspace of X α,p is compact. It is known that if any X α,p is a dual space, then |
(iv) | duals of X α,1 spaces contain isometric copies of ℓ ∞ and their preduals contain asymptotically isometric copies of c 0. |
(v) | We investigate the properties of the operators from X α,p spaces to their predual. |
17.
Given a connected graph G, a vertex v of G is said to be a branch vertex if its degree is greater than 2. We consider two problems arising in the context of optical networks:
For these NP-hard problems, heuristics, that give good quality solutions, do not exist in the literature. In this paper we
analyze the relation between the problems, provide a single commodity flow formulation to solve the problems by means of a
solver and develop different heuristic strategies to compute feasible solutions that are compared with the exact ones. Our
extensive computational results show the algorithms to be very fast and effective. 相似文献
(i) | Finding a spanning tree of G with the minimum number of branch vertices and |
(ii) | Finding a spanning tree of G such that the degree sum of the branch vertices is minimized. |
18.
In this paper, we discuss the representation-finite selfinjective artin algebras of classB
n andC
n and obtain the following main results:
For any fieldk, let Λ be a representation-finite selfinjective artin algebras of classB
n orC
n overk.
相似文献
(a) | We give the configuration ofZB n andZC n. |
(b) | We show that Λ is standard. |
(c) | Under the condition ofk being a perfect field, we describe Λ by boundenk-species and show that Λ is a finite covering of the trivial extension of some tilted algebra of typeB n orC n. |
19.
José Rodríguez 《Archiv der Mathematik》2007,88(1):62-70
Let X be a weakly Lindel?f determined Banach space. We prove that the following two statements are equivalent:
Some applications and related examples are given.
Received: 11 January 2006; Revised: 24 May 2006 相似文献
(i) | Every Radon probability measure on (BX*, w*) has separable support. |
(ii) | Every countably additive X*-valued measure with σ-finite variation has norm separable range. |
20.
We consider smooth non-degenerate surfaces in ℙ4, and prove that there is a finite number of such surfaces which are:
A complete list is given in both cases. 相似文献
(a) | sectionally non-special, i.e.h1(O C(1))=0, where C is a general hyperplane section of S; or |
(b) | not of general type and non-special (i.e. h1(O C(1))=0. |