共查询到20条相似文献,搜索用时 62 毫秒
1.
Raphael Yuster 《Order》2003,20(2):121-133
Let TT
k
denote the transitive tournament on k vertices. Let TT(h,k) denote the graph obtained from TT
k
by replacing each vertex with an independent set of size h≥1. The following result is proved: Let c
2=1/2, c
3=5/6 and c
k
=1−2−k−log k
for k≥4. For every ∈>0 there exists N=N(∈,h,k) such that for every undirected graph G with n>N vertices and with δ(G)≥c
k
n, every orientation of G contains vertex disjoint copies of TT(h,k) that cover all but at most ∈n vertices. In the cases k=2 and k=3 the result is asymptotically tight. For k≥4, c
k
cannot be improved to less than 1−2−0.5k(1+o(1)).
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
2.
We obtain a new upper bound for the sum Σ
h≤H
Δ
k
(N, h) when 1 ≤ H ≤ N, k ∈ ℕ, k ≥ 3, where Δ
k
(N, h) is the (expected) error term in the asymptotic formula for Σ
N<n≤2N
d
k
(n)d
k
(n + h), and d
k
(n) is the divisor function generated by ζ(s)
k
. When k = 3, the result improves, for H ≥ N
1/2, the bound given in a recent work of Baier, Browning, Marasingha and Zhao, who dealt with the case k = 3. 相似文献
3.
Ismailescu 《Discrete and Computational Geometry》2002,28(4):571-575
Abstract. Given k≥ 3 , denote by t'
k
(N) the largest integer for which there is a set of N points in the plane, no k+1 of them on a line such that there are t'
k
(N) lines, each containing exactly k of the points. Erdos (1962) raised the problem of estimating the order of magnitude of t'
k
(N) . We prove that
improving a previous bound of Grunbaum for all k≥ 5 . The proof for k≥ 18 uses an argument of Brass with his permission. 相似文献
4.
C. Aistleitner I. Berkes R. Tichy 《Proceedings of the Steklov Institute of Mathematics》2012,276(1):3-20
It is known that for any smooth periodic function f the sequence (f(2
k
x))
k≥1 behaves like a sequence of i.i.d. random variables; for example, it satisfies the central limit theorem and the law of the
iterated logarithm. Recently Fukuyama showed that permuting (f(2
k
x))
k≥1 can ruin the validity of the law of the iterated logarithm, a very surprising result. In this paper we present an optimal
condition on (n
k
)
k≥1, formulated in terms of the number of solutions of certain Diophantine equations, which ensures the validity of the law of
the iterated logarithm for any permutation of the sequence (f(n
k
x))
k≥1. A similar result is proved for the discrepancy of the sequence ({n
k
x})
k≥1, where {·} denotes the fractional part. 相似文献
5.
Goran Mui? 《The Ramanujan Journal》2012,27(2):181-208
Let Γ⊂SL
2(ℝ) be a Fuchsian group of the first kind. For a character χ of Γ→ℂ× of finite order, we define the usual space S
m
(Γ,χ) of cuspidal modular forms of weight m≥0. For each ξ in the upper half–plane and m≥3, we construct cuspidal modular forms Δ
k,m,ξ,χ
∈S
m
(Γ,χ) (k≥0) which represent the linear functionals
f?\fracdkfdzk|z=xf\mapsto\frac{d^{k}f}{dz^{k}}|_{z=\xi} in terms of the Petersson inner product. We write their Fourier expansion and use it to write an expression for the Ramanujan
Δ-function. Also, with the aid of the geometry of the Riemann surface attached to Γ, for each non-elliptic point ξ and integer m≥3, we construct a basis of S
m
(Γ,χ) out of the modular forms Δ
k,m,ξ
,χ (k≥0). For Γ=Γ
0(N), we use this to write a matrix realization of the usual Hecke operators T
p
for S
m
(N,χ). 相似文献
6.
V. F. Gaposhkin 《Mathematical Notes》1998,64(3):316-321
The asymptotic behavior asn → ∞ of the normed sumsσn =n
−1 Σ
k
=0n−1
Xk for a stationary processX = (X
n
,n ∈ ℤ) is studied. For a fixedε > 0, upper estimates for P(sup
k≥n
|σ
k
| ≥ε) asn → ∞ are obtained.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 366–372, September, 1998. 相似文献
7.
By a well known result of Philipp (1975), the discrepancy D
N
(ω) of the sequence (n
k
ω)
k≥1 mod 1 satisfies the law of the iterated logarithm under the Hadamard gap condition n
k + 1/n
k
≥ q > 1 (k = 1, 2, …). Recently Berkes, Philipp and Tichy (2006) showed that this result remains valid, under Diophantine conditions
on (n
k
), for subexpenentially growing (n
k
), but in general the behavior of (n
k
ω) becomes very complicated in the subexponential case. Using a different norming factor depending on the density properties
of the sequence (n
k
), in this paper we prove a law of the iterated logarithm for the discrepancy D
N
(ω) for subexponentially growing (n
k
) without number theoretic assumptions.
C. Aistleitner, Research supported by FWF grant S9603-N13.
I. Berkes, Research supported by FWF grant S9603-N13 and OTKA grants K 61052 and K 67961.
Authors’ addresses: C. Aistleitner, Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010 Graz,
Austria; I. Berkes, Institute of Statistics, Graz University of Technology, Steyrergasse 17/IV, 8010 Graz, Austria 相似文献
8.
A characteristic property of spheres 总被引:1,自引:1,他引:0
A. D. Alexandrov 《Annali di Matematica Pura ed Applicata》1962,58(1):303-315
Summary We prove: Let S be a closed n-dimensional surface in an(n+1)-space of constant curvature (n ≥ 2); k1 ≥ ... ≥ kn denote its principle curvatures. Let φ(ξ1, ..., ξn) be such that
. Then if φ(k1, ..., kn)=const on S and S is subject to some additional general conditions (those(II
0) or(II) no 1), S is a sphere.
To Enrico Bompiani on his scientific Jubilee 相似文献
9.
Tatiana Shingel 《Constructive Approximation》2010,32(3):597-618
This paper extends previous work on approximation of loops to the case of special orthogonal groups SO(N), N≥3. We prove that the best approximation of an SO(N) loop Q(t) belonging to a Hölder class Lip α , α>1, by a polynomial SO(N) loop of degree ≤n is of order $\mathcal{O}(n^{-\alpha+\epsilon})This paper extends previous work on approximation of loops to the case of special orthogonal groups SO(N), N≥3. We prove that the best approximation of an SO(N) loop Q(t) belonging to a H?lder class Lip
α
, α>1, by a polynomial SO(N) loop of degree ≤n is of order O(n-a+e)\mathcal{O}(n^{-\alpha+\epsilon}) for n≥k, where k=k(Q) is determined by topological properties of the loop and ε>0 is arbitrarily small. The convergence rate is therefore ε-close to the optimal achievable rate of approximation. The construction of polynomial loops involves higher-order splitting
methods for the matrix exponential. A novelty in this work is the factorization technique for SO(N) loops which incorporates the loops’ topological aspects. 相似文献
10.
Let (B
δ (t))
t ≥ 0 be a Brownian motion starting at 0 with drift δ > 0. Define by induction S
1=− inf
t ≥ 0
B
δ (t), ρ1 the last time such that B
δ (ρ1)=−S
1, S
2=sup0≤ t ≤ρ 1
B
δ (t), ρ2 the last time such that B
δ (ρ2)=S
2 and so on. Setting A
k
=S
k
+S
k+1; k ≥ 1, we compute the law of (A
1,...,A
k
) and the distribution of (B
δ (t+ρ l) − B
δ (ρ
l
); 0 ≤ t ≤ ρ
l-1 − ρ
l
)2 ≤ l ≤ k
for any k ≥ 2, conditionally on (A
1,...,A
k
). We determine the law of the range R
δ (t) of (B
δ (s))
s≥ 0 at time t, and the first range time θδ (a) (i.e. θδ (a)=inf{t > 0; R
δ (t) > a}). We also investigate the asymptotic behaviour of θ δ (a) (resp. R
δ (t)) as a → ∞ (resp. t → ∞). 相似文献
11.
Large Vertex-Disjoint Cycles in a Bipartite Graph 总被引:4,自引:0,他引:4
Hong Wang 《Graphs and Combinatorics》2000,16(3):359-366
Let s≥2 and k be two positive integers. Let G=(V
1,V
2;E) be a bipartite graph with |V
1|=|V
2|=n≥s
k and the minimum degree at least (s−1)k+1. When s=2 and n >2k, it is proved in [5] that G contains k vertex-disjoint cycles. In this paper, we show that if s≥3, then G contains k vertex-disjoint cycles of length at least 2s.
Received: March 2, 1998 Revised: October 26, 1998 相似文献
12.
Matt DeVos Agelos Georgakopoulos Bojan Mohar Robert Šámal 《Discrete and Computational Geometry》2010,44(4):931-945
Eberhard proved that for every sequence (p
k
), 3≤k≤r, k≠6, of nonnegative integers satisfying Euler’s formula ∑
k≥3(6−k)p
k
=12, there are infinitely many values p
6 such that there exists a simple convex polyhedron having precisely p
k
faces of size k for every k≥3, where p
k
=0 if k>r. In this paper we prove a similar statement when nonnegative integers p
k
are given for 3≤k≤r, except for k=5 and k=7 (but including p
6). We prove that there are infinitely many values p
5,p
7 such that there exists a simple convex polyhedron having precisely p
k
faces of size k for every k≥3. We derive an extension to arbitrary closed surfaces, yielding maps of arbitrarily high face-width. Our proof suggests
a general method for obtaining results of this kind. 相似文献
13.
A. Borel 《Proceedings Mathematical Sciences》1987,97(1-3):45-52
In this noteG is a locally compact group which is the product of finitely many groups Gs(ks)(s∈S), where ks is a local field of characteristic zero and Gs an absolutely almost simplek
s-group, ofk
s-rank ≥1. We assume that the sum of the rs is ≥2 and fix a Haar measure onG. Then, given a constantc > 0, it is shown that, up to conjugacy,G contains only finitely many irreducible discrete subgroupsL of covolume ≥c (4.2). This generalizes a theorem of H C Wang for real groups. His argument extends to the present case, once it is shown
thatL is finitely presented (2.4) and locally rigid (3.2). 相似文献
14.
LiuYING LiuYANPEI 《高校应用数学学报(英文版)》1997,12(3):253-258
The purpose of this paper is to display a new kind of simple graphs which belong to B. inwhich any graph has its orientable genus n,n≥3. Furthermore, for any integer k,1≤k≤n,there exists a graph B^kn of B. such that the non-orientable genus of B^kn is k. 相似文献
15.
A tree is called a k-tree if the maximum degree is at most k. We prove the following theorem, by which a closure concept for spanning k-trees of n-connected graphs can be defined. Let k ≥ 2 and n ≥ 1 be integers, and let u and v be a pair of nonadjacent vertices of an n-connected graph G such that deg
G
(u) + deg
G
(v) ≥ |G| − 1 − (k − 2)n, where |G| denotes the order of G. Then G has a spanning k-tree if and only if G + uv has a spanning k-tree. 相似文献
16.
Matthew Bennett Vyjayanthi Chari R. J. Dolbin Nathan Manning 《Journal of Algebraic Combinatorics》2011,34(1):1-18
For each integer k≥1, we define an algorithm which associates to a partition whose maximal value is at most k a certain subset of all partitions. In the case when we begin with a partition λ which is square-bounded, i.e. λ=(λ
1≥⋅⋅⋅≥λ
k
) with λ
1=k and λ
k
=1, applying the algorithm ℓ times gives rise to a set whose cardinality is either the Catalan number c
ℓ−k+1 (the self dual case) or twice that Catalan number. The algorithm defines a tree and we study the propagation of the tree,
which is not in the isomorphism class of the usual Catalan tree. The algorithm can also be modified to produce a two-parameter
family of sets and the resulting cardinalities of the sets are the ballot numbers. Finally, we give a conjecture on the rank
of a particular module for the ring of symmetric functions in 2ℓ+m variables. 相似文献
17.
It is shown that the entropy function H(N
1,…,N
k
) on finite dimensional von Neumann subalgebras of a finite von Neumann algebra attains its maximal possible value H(⋁ℓ=1k
N
ℓ) if and only if there exists a maximal abelian subalgebra A of ⋁ℓ=1k
N
ℓ such that A=⋁ℓ=1k(A∩N
ℓ).
Oblatum 24-IV-1997 & 6-V-1997 相似文献
18.
Maryam Atapour Seyyed Mahmoud Sheikholeslami Rana Hajypory Lutz Volkmann 《Central European Journal of Mathematics》2010,8(6):1048-1057
Let k ≥ 1 be an integer, and let D = (V; A) be a finite simple digraph, for which d
D
− ≥ k − 1 for all v ɛ V. A function f: V → {−1; 1} is called a signed k-dominating function (SkDF) if f(N
−[v]) ≥ k for each vertex v ɛ V. The weight w(f) of f is defined by $
\sum\nolimits_{v \in V} {f(v)}
$
\sum\nolimits_{v \in V} {f(v)}
. The signed k-domination number for a digraph D is γ
kS
(D) = min {w(f|f) is an SkDF of D. In this paper, we initiate the study of signed k-domination in digraphs. In particular, we present some sharp lower bounds for γ
kS
(D) in terms of the order, the maximum and minimum outdegree and indegree, and the chromatic number. Some of our results are
extensions of well-known lower bounds of the classical signed domination numbers of graphs and digraphs. 相似文献
19.
For every fixedk≥3 there exists a constantc
k
with the following property. LetH be ak-uniform,D-regular hypergraph onN vertices, in which no two edges contain more than one common vertex. Ifk>3 thenH contains a matching covering all vertices but at mostc
k
ND
−1/(k−1). Ifk=3, thenH contains a matching covering all vertices but at mostc
3
ND
−1/2ln3/2
D. This improves previous estimates and implies, for example, that any Steiner Triple System onN vertices contains a matching covering all vertices but at mostO(N
1/2ln3/2
N), improving results by various authors.
Research supported in part by a USA-Israel BSF grant.
Research supported in part by a USA-Israel BSF Grant. 相似文献
20.
Thorsten Bernholt Friedrich Eisenbrand Thomas Hofmeister 《Discrete and Computational Geometry》2009,42(1):22-36
In this paper, we introduce the notion of a constrained Minkowski sum: for two (finite) point-sets P,Q⊆ℝ2 and a set of k inequalities Ax≥b, it is defined as the point-set (P
⊕
Q)
Ax≥b
={x=p+q∣p∈P,q∈Q,Ax≥b}. We show that typical interval problems from computational biology can be solved by computing a set containing the vertices
of the convex hull of an appropriately constrained Minkowski sum. We provide an algorithm for computing such a set with running
time O(Nlog N), where N=|P|+|Q| if k is fixed. For the special case
where P and Q consist of points with integer x
1-coordinates whose absolute values are bounded by O(N), we even achieve a linear running time O(N). We thereby obtain a linear running time for many interval problems from the literature and improve upon the best known
running times for some of them. The main advantage of the presented approach is that it provides a general framework within
which a broad variety of interval problems can be modeled and solved.
T. Bernholt gratefully acknowledges the Deutsche Forschungsgemeinschaft for the financial support (SFB 475, “Reduction of
complexity in multivariate data structures”). 相似文献