共查询到20条相似文献,搜索用时 46 毫秒
1.
Oswald Gschnitzer 《manuscripta mathematica》1996,91(1):235-245
For each positive integerk≦∞ we construct a family {M
k
n
} of generators of the unoriented bordims ring. The manifoldsM
k
n
are total spaces of fiber bundles whose base spaces are high-dimensional products of projective spaces
wherer
i≦k. The fibers are themselves iterated projective bundles with maximal fiber dimension two. In the special casek=3 we obtain generatorsM
3
n
which admit approximately 7/8·n pointwise linearly independent vector fields.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag 相似文献
2.
Strashimir G. Popvassilev 《Discrete and Computational Geometry》2008,40(2):279-288
We call a metric space X (m,n)-equidistant if, when A⊆X has exactly m points, there are exactly n points in X each of which is equidistant from (the points of) A. We prove that, for k≥2, the Euclidean space ℝ
k
contains an (m,1)-equidistant set if and only if k≥m. Although the sphere
is (3,2)-equidistant,
and ℝ4 contain no (4,2)-equidistant sets. We discuss related results about projective spaces, and state a conjecture about
analogous to the Double Midset Conjecture. 相似文献
3.
Let G=(I
n
,E) be the graph of the n-dimensional cube. Namely, I
n
={0,1}
n
and [x,y]∈E whenever ||x−y||1=1. For A⊆I
n
and x∈A define h
A
(x) =#{y∈I
n
A|[x,y]∈E}, i.e., the number of vertices adjacent to x outside of A. Talagrand, following Margulis, proves that for every set A⊆I
n
of size 2
n−1
we have for a universal constant K independent of n. We prove a related lower bound for graphs: Let G=(V,E) be a graph with . Then , where d(x) is the degree of x. Equality occurs for the clique on k vertices.
Received: January 7, 2000
RID="*"
ID="*" Supported in part by BSF and by the Israeli academy of sciences 相似文献
4.
Ricardo Abreu-Blaya Juan Bory-Reyes Richard Delanghe Frank Sommen 《Advances in Applied Clifford Algebras》2007,17(4):589-610
The space HF
k
(Ω) of harmonic multi-vector fields in a domain
as introduced in [1] is closely connected to the space of harmonic forms. The main aim of this paper is to characterize the
dual space of HF
k
(E) being
a compact set. It is proved that HF
k
(E)* is isomorphic to a certain quotient space of so-called harmonic pairs outside E vanishing at infinity.
Research of the third author was supported by the FWO Research Network WO. 003. 01N, research of the fourth author was supported
by the FWO “Krediet aan Navorsers: 1.5.106.02” 相似文献
5.
Assume that no cardinal κ < 2
ω
is quasi-measurable (κ is quasi-measurable if there exists a κ-additive ideal
$
\mathbb{I}
$
\mathbb{I}
of X contains uncountably many pairwise disjoint subfamilies
$
\mathbb{I}
$
\mathbb{I}
-Bernstein unions ∪
$
\mathbb{I}
$
\mathbb{I}
-Bernstein if A and X \ A meet each Borel $
\mathbb{I}
$
\mathbb{I}
-positive subset B ⊆ X). This result is a generalization of the Four Poles Theorem (see [1]) and results from [2] and [4]. 相似文献
6.
Piotr Niemiec 《Rendiconti del Circolo Matematico di Palermo》2008,57(3):391-399
The aim of the paper is to prove that every f ∈ L
1([0,1]) is of the form f = , where j
n,k
is the characteristic function of the interval [k- 1 / 2
n
, k / 2
n
) and Σ
n=0∞Σ
k=12n
|a
n,k
| is arbitrarily close to ||f|| (Theorem 2). It is also shown that if μ is any probabilistic Borel measure on [0,1], then for any ɛ > 0 there exists a sequence (b
n,k
)
n≧0
k=1,...,2n
of real numbers such that and for each Lipschitz function g: [0,1] → ℝ (Theorem 3).
相似文献
7.
Jorge Galindo 《Mathematische Zeitschrift》2009,263(1):211-220
We prove that the additive group (E*, τ
k
(E)) of an -Banach space E, with the topology τ
k
(E) of uniform convergence on compact subsets of E, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is unitarily representable). This is the same as proving that the topological group (E*, τ
k
(E)) is uniformly homeomorphic to a subset of for some κ. As an immediate consequence, preduals of commutative von Neumann algebras or duals of commutative C*-algebras are unitarily representable in the topology of uniform convergence on compact subsets. The unitary representability
of free locally convex spaces (and thus of free Abelian topological groups) on compact spaces, follows as well. The above
facts cannot be extended to noncommutative von Neumann algebras or general Schwartz spaces.
Research partially supported by Spanish Ministry of Science, grant MTM2008-04599/MTM. The foundations of this paper were laid
during the author’s stay at the University of Ottawa supported by a Generalitat Valenciana grant CTESPP/2004/086. 相似文献
8.
9.
Given an elliptic curve Σ, flat E
k
-bundles over Σ are in one-to-one correspondence with smooth del Pezzo surfaces of degree 9 − k containing Σ as an anti-canonical curve. This correspondence was generalized to Lie groups of any type. In this article,
we show that there is a similar correspondence between del Pezzo surfaces of degree 0 with an A
d
-singularity containing Σ as an anti-canonical curve and Kac–Moody [(E)\tilde]k{\widetilde{E}_{k}}-bundles over Σ with k = 8 − d. In the degenerate case where surfaces are rational elliptic surfaces, the corresponding [(E)\tilde]k{\widetilde{E}_k}-bundles over Σ can be reduced to E
k
-bundles. 相似文献
10.
We prove inequalities about the quermassintegralsV
k
(K) of a convex bodyK in ℝ
n
(here,V
k
(K) is the mixed volumeV((K, k), (B
n
,n − k)) whereB
n
is the Euclidean unit ball). (i) The inequality
holds for every pair of convex bodiesK andL in ℝ
n
if and only ifk=2 ork=1. (ii) Let 0≤k≤p≤n. Then, for everyp-dimensional subspaceE of ℝ
n
,
whereP
E
K denotes the orthogonal projection ofK ontoE. The proof is based on a sharp upper estimate for the volume ratio |K|/|L| in terms ofV
n−k
(K)/V
n−k
(L), wheneverL andK are two convex bodies in ℝ
n
such thatK ⊆L. 相似文献
11.
Precise Rates in the Law of Iterated Logarithm for the Moment of I.I.D. Random Variables 总被引:1,自引:0,他引:1
Ye JIANG Li Xin ZHANG 《数学学报(英文版)》2006,22(3):781-792
Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1+X2+…+Xn,Mn=max k≤n│Sk│,n≥1.Let an=O(1/loglogn).In this paper,we prove that,for b〉-1,lim ε→0 →^2(b+1)∑n=1^∞ (loglogn)^b/nlogn n^1/2 E{Mn-σ(ε+an)√2nloglogn}+σ2^-b/(b+1)(2b+3)E│N│^2b+3∑k=0^∞ (-1)k/(2k+1)^2b+3 holds if and only if EX=0 and EX^2=σ^2〈∞. 相似文献
12.
Ian M. Wanless 《Combinatorica》2006,26(6):743-745
Let
denote the set of n×n binary matrices which have each row and column sum equal to k. For 2≤k≤n→∞ we show that
is asymptotically equal to (k−1)k−1k2−k. This confirms Conjecture 23 in Minc's catalogue of open problems.
* Written while the author was employed by the Department of Computer Science at the Australian National University. 相似文献
13.
Abstract
Let Λ = {λ
k
} be an infinite increasing sequence of positive integers with λ
k
→∞. Let X = {X(t), t ∈? R
N
} be a multi-parameter fractional Brownian motion of index α(0 < α < 1) in R
d
. Subject to certain hypotheses, we prove that if N < αd, then there exist positive finite constants K
1 and K
2 such that, with unit probability,
if and only if there exists γ > 0 such that
where ϕ(s) = s
N/α
(log log 1/s)
N/(2α), ϕ-p
Λ(E) is the Packing-type measure of E,X([0, 1])
N
is the image and GrX([0, 1]
N
) = {(t,X(t)); ∈? [0, 1]
N
} is the graph of X, respectively. We also establish liminf type laws of the iterated logarithm for the sojourn measure of X.
Supported by the National Natural Science Foundation of China (No.10471148), Sci-tech Innovation Item for Excellent Young
and Middle-Aged University Teachers and Major Item of Educational Department of Hubei (No.2003A005) 相似文献
14.
Roy Meshulam 《Order》2008,25(2):153-155
Let L be a finite lattice and let . It is shown that if the order complex satisfies then |L| ≥ 2
k
. Equality |L| = 2
k
holds iff L is isomorphic to the Boolean lattice {0,1}
k
.
Research supported by the Israel Science Foundation. 相似文献
15.
Melvin Hausner 《Combinatorica》1985,5(3):215-225
Ifμ is a positive measure, andA
2, ...,A
n
are measurable sets, the sequencesS
0, ...,S
n
andP
[0], ...,P
[n] are related by the inclusion-exclusion equalities. Inequalities among theS
i
are based on the obviousP
[k]≧0. Letting
=the average average measure of the intersection ofk of the setsA
i
, it is shown that (−1)
k
Δ
k
M
i
≧0 fori+k≦n. The casek=1 yields Fréchet’s inequalities, andk=2 yields Gumbel’s and K. L. Chung’s inequalities. Generalizations are given involvingk-th order divided differences. Using convexity arguments, it is shown that forS
0=1,
whenS
1≧N−1, and
for 1≦k<N≦n andv=0, 1, .... Asymptotic results asn → ∞ are obtained. In particular it is shown that for fixedN,
for all sequencesM
0, ...,M
n
of sufficiently large length if and only if
for 0<t<1. 相似文献
16.
S. P. Eveson 《Integral Equations and Operator Theory》2005,53(3):331-341
Given k ∈ L1 (0,1) satisfying certain smoothness and growth conditions at 0, we consider the Volterra convolution operator Vk defined on Lp (0,1) by
and its iterates
We construct some much simpler sequences which, as n → ∞, are asymptotically equal in the operator norm to Vkn. This leads to a simple asymptotic formula for ||Vkn|| and to a simple ‘asymptotically extremal sequence’; that is, a sequence (un) in Lp (0, 1) with ||un||p=1 and
as n → ∞. As an application, we derive a limit theorem for large deviations, which appears to be beyond the established theory. 相似文献
17.
ZhiXiangWU 《数学学报(英文版)》2004,20(1):125-134
In this paper.we study the ring #(D.B)and obtain two very interesting results. First we prove in Theorem 3 that the category of rational left BU-modules is equivalent to both the category of #-rational left modules and the category of all(B.D)-Hopf modules BM^D.Cai and Chen have proved this result in the case B=D=A.Secondly they have proved that if A has a nonzero left integral then A#A^*rat is a dense subring of Endk(A).We prove that #(A,A) is a dense subring of Endk(Q),where Q is a certain subspace of #(A.A)under the condition that the antipode is bijective(see Theorem18).This condition is weaker than the condition that A has a nonzero integral.It is well known the antipode is bijective in case A has a nonzero integral.Furthermore if A has nonzero left integral,Q can be chosen to be A(see Corollary 19)and #(A,A)is both left and right primitive.Thus A#A^*rat #(A,A)-Endk(A).Moreover we prove that the left singular ideal of the ring #(A,A)is zero.A corollary of this is a criterion for A with nonzero left integral to be finite-dimensional,namely the ring #(A,A)has a finite uniform dimension. 相似文献
18.
Alvaro Liendo 《Transformation Groups》2010,15(2):389-425
Let X = Spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus
\mathbbT \mathbb{T} of dimension n. Let also ∂ be a homogeneous locally nilpotent derivation on the normal affine
\mathbbZn {\mathbb{Z}^n} -graded domain A, so that ∂ generates a k
+-action on X that is normalized by the
\mathbbT \mathbb{T} -action. 相似文献
19.
For κ ⩾ 0 and r0 > 0 let ℳ(n, κ, r0) be the set of all connected, compact n-dimensional Riemannian manifolds (Mn, g) with Ricci (M, g) ⩾ −(n−1) κ g and Inj (M) ⩾ r0. We study the relation between the kth eigenvalue λk(M) of the Laplacian associated to (Mn,g), Δ = −div(grad), and the kth eigenvalue λk(X) of a combinatorial Laplacian associated to a discretization X of M. We show that there exist constants c, C > 0 (depending only on n, κ and r0) such that for all M ∈ ℳ(n, κ, r0) and X a discretization of
for all k < |X|. Then, we obtain the same kind of result for two compact manifolds M and N ∈ ℳ(n, κ, r0) such that the Gromov–Hausdorff distance between M and N is smaller than some η > 0. We show that there exist constants c, C > 0 depending on η, n, κ and r0 such that
for all
.
Mathematics Subject Classification (2000): 58J50, 53C20
Supported by Swiss National Science Foundation, grant No. 20-101 469 相似文献
20.
We consider solutions ψ to equations of the form
in a sector Ω ofR
2. The basic assumptions are that the limitsa
ij(x)→δij,b
i(x)→0,c
i→E at infinity are achieved at certain rates and thatg decays faster than ψ. We then discuss the possible patterns of exponential decay for ψ in Ω.
NSERC University Research Fellow.
Research partially supported by USNEF grant MCS-83-01159. 相似文献