共查询到20条相似文献,搜索用时 485 毫秒
1.
Hanno Lefmann 《Discrete and Computational Geometry》2008,40(3):401-413
We consider a variant of Heilbronn’s triangle problem by investigating for a fixed dimension d≥2 and for integers k≥2 with k≤d distributions of n points in the d-dimensional unit cube [0,1]
d
, such that the minimum volume of the simplices, which are determined by (k+1) of these n points is as large as possible. Denoting by Δ
k,d
(n), the supremum of this minimum volume over all distributions of n points in [0,1]
d
, we show that c
k,d
⋅(log n)1/(d−k+1)/n
k/(d−k+1)≤Δ
k,d
(n)≤c
k,d
′/n
k/d
for fixed 2≤k≤d, and, moreover, for odd integers k≥1, we show the upper bound Δ
k,d
(n)≤c
k,d
″/n
k/d+(k−1)/(2d(d−1)), where c
k,d
,c
k,d
′,c
k,d
″>0 are constants.
A preliminary version of this paper appeared in COCOON ’05. 相似文献
2.
ZhangJianfeng 《高校应用数学学报(英文版)》2005,20(2):183-196
Let M^n be a closed spacelike submanifold isometrically immersed in de Sitter space Sp^(n p)(c), Denote by R,H and S the normalized scalar curvature,the mean curvature and the square of the length of the second fundamental form of M^n ,respectively. Suppose R is constant and R≤c. The pinching problem on S is studied and a rigidity theorem for M^n immersed in Sp^(n p)(c) with parallel normalized mean curvature vector field is proved. When n≥3, the pinching constant is the best. Thus, the mistake of the paper “Space-like hypersurfaces in de Sitter space with constant scalar curvature”(see Manus Math, 1998,95 :499-505) is corrected. Moreover,the reduction of the codimension when M^n is a complete submanifold in Sp^(n p)(c) with parallel normalized mean curvature vector field is investigated. 相似文献
3.
In this paper, we prove that
and round geodesic spheres are the only n-dimensional compact embedded rotation hypersurfaces with Hm = 0 (1 ≤ m ≤ n − 1) in a unit sphere Sn+1(1). When m = 1, our result reduces to the result of T. Otsuki [O1], [O2], Brito and Leite [BL].
The project is supported by the grant No. 10531090 of NSFC. 相似文献
4.
In this work we generalize the case of scalar curvature zero the results of Simmons (Ann. Math. 88 (1968), 62–105) for minimal cones in Rn+1. If Mn−1 is a compact hypersurface of the sphere Sn(1) we represent by C(M)ε the truncated cone based on M with center at the origin. It is easy to see that M has zero scalar curvature if and only if the cone base on M also has zero scalar curvature. Hounie and Leite (J. Differential Geom. 41 (1995), 247–258) recently gave the conditions for the ellipticity of the partial differential equation of the scalar curvature.
To show that, we have to assume n ⩾ 4 and the three-curvature of M to be different from zero. For such cones, we prove that, for n ≤slant 7 there is an ε for which the truncate cone C(M)ε is not stable. We also show that for n ⩾ 8 there exist compact, orientable hypersurfaces Mn−1 of the sphere with zero scalar curvature and S3 different from zero, for which all truncated cones based on M are stable.
Mathematics Subject Classifications (2000): 53C42, 53C40, 49F10, 57R70. 相似文献
5.
This paper considers some random processes of the form X
n+1=T
X
n
+B
n
(mod p) where B
n
and X
n
are random variables over (ℤ/pℤ)
d
and T is a fixed d×d integer matrix which is invertible over the complex numbers. For a particular distribution for B
n
, this paper improves results of Asci to show that if T has no complex eigenvalues of length 1, then for integers p relatively prime to det (T), order (log p)2 steps suffice to make X
n
close to uniformly distributed where X
0 is the zero vector. This paper also shows that if T has a complex eigenvalue which is a root of unity, then order p
b
steps are needed for X
n
to get close to uniformly distributed for some positive value b≤2 which may depend on T and X
0 is the zero vector. 相似文献
6.
J. C. Gómez-Larrañaga F. González-Acuña Wolfgang Heil 《Mathematische Zeitschrift》2008,259(2):419-432
A closed topological n-manifold M
n
is of S
1-category 2 if it can be covered by two open subsets W
1,W
2 such that the inclusions W
i
→ M
n
factor homotopically through maps W
i
→ S
1 → M
n
. We show that the fundamental group of such an n-manifold is a cyclic group or a free product of two cyclic groups with nontrivial amalgamation. In particular, if n = 3, the fundamental group is cyclic.
相似文献
7.
V. E. Maiorov 《Ukrainian Mathematical Journal》2010,62(3):452-466
We study the approximation of the classes of functions by the manifold R
n
formed by all possible linear combinations of n ridge functions of the form r(a · x)): It is proved that, for any 1 ≤ q ≤ p ≤ ∞, the deviation of the Sobolev class W
r
p
from the set R
n
of ridge functions in the space L
q
(B
d
) satisfies the sharp order n
-r/(d-1). 相似文献
8.
Yun Qing Xu 《数学学报(英文版)》2009,25(8):1325-1336
A Latin squares of order v with ni missing sub-Latin squares (holes) of order hi (1 〈= i 〈 k), which are disjoint and spanning (i.e. ∑k i=l1 nihi = v), is called a partitioned incomplete Latin squares and denoted by PILS. The type of PILS is defined by (h1n1 h2n2…hknk ). If any two PILS inaset of t PILS of type T are orthogonal, then we denote the set by t-HMOLS(T). It has been proved that 3-HMOLS(2n31) exist for n ≥6 with 11 possible exceptions. In this paper, we investigate the existence of 3-HMOLS(2nu1) with u ≥ 4, and prove that 3-HMOLS(2~u1) exist if n ≥ 54 and n ≥7/4u + 7. 相似文献
9.
T. S. Kopaliani 《Ukrainian Mathematical Journal》2008,60(12):2006-2014
We point out that if the Hardy–Littlewood maximal operator is bounded on the space L
p(t)(ℝ), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ, then the well-known characterization of the spaces L
p
(ℝ), 1 < p < ∞, by the Littlewood–Paley theory extends to the space L
p(t)(ℝ). We show that, for n > 1 , the Littlewood–Paley operator is bounded on L
p(t) (ℝ
n
), 1 < a ≤ p(t) ≤ b < ∞, t ∈ ℝ
n
, if and only if p(t) = const.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1709–1715, December, 2008. 相似文献
10.
Let M be a compact manifold of dimension n, P=P(h) a semiclassical pseudodifferential operator on M, and u=u(h) an L
2 normalized family of functions such that P(h)u(h) is O(h) in L
2(M) as h↓0. Let H⊂M be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L
p
norms, p≥2, of u restricted to H, under the assumption that the u are semiclassically localized and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch
−δ(n,k,p) where k=dim H (except for a logarithmic divergence in the case k=n−2, p=2). When H is a hypersurface, i.e., k=n−1, we have δ(n,n−1, 2)=1/4, which is sharp when M is the round n-sphere and H is an equator. 相似文献
11.
12.
13.
Let ( Y,d,dl )\left( {\mathcal{Y},d,d\lambda } \right) be (ℝ
n
, |·|, μ), where |·| is the Euclidean distance, μ is a nonnegative Radon measure on ℝ
n
satisfying the polynomial growth condition, or the Gauss measure metric space (ℝ
n
, |·|, d
λ
), or the space (S, d, ρ), where S ≡ ℝ
n
⋉ ℝ+ is the (ax + b)-group, d is the left-invariant Riemannian metric and ρ is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces
{ Xs ( Y ) }0 < s \leqslant ¥\left\{ {X_s \left( \mathcal{Y} \right)} \right\}_{0 < s \leqslant \infty } and the BMO-type spaces
{ BMO( Y, s ) }0 < s \leqslant ¥\left\{ {BMO\left( {\mathcal{Y}, s} \right)} \right\}_{0 < s \leqslant \infty }. Let H
1
( Y )\left( \mathcal{Y} \right) be the known atomic Hardy space and L
01
( Y )\left( \mathcal{Y} \right) the subspace of f ∈ L
1
( Y )\left( \mathcal{Y} \right) with integral 0. The authors prove that the dual space of X
s
( Y )\left( \mathcal{Y} \right) is BMO( Y,s )BMO\left( {\mathcal{Y},s} \right) when s ∈ (0,∞), X
s
( Y )\left( \mathcal{Y} \right) = H
1
( Y )\left( \mathcal{Y} \right) when s ∈ (0, 1], and X
∞
( Y )\left( \mathcal{Y} \right) = L
01
( Y )\left( \mathcal{Y} \right) (or L
1
( Y )\left( \mathcal{Y} \right)). As applications, the authors show that if T is a linear operator bounded from H
1
( Y )\left( \mathcal{Y} \right) to L
1
( Y )\left( \mathcal{Y} \right) and from L
1
( Y )\left( \mathcal{Y} \right) to L
1,∞
( Y )\left( \mathcal{Y} \right), then for all r ∈ (1,∞) and s ∈ (r,∞], T is bounded from X
r
( Y )\left( \mathcal{Y} \right) to the Lorentz space L
1,s
( Y )\left( \mathcal{Y} \right), which applies to the Calderón-Zygmund operator on (ℝ
n
, |·|, μ), the imaginary powers of the Ornstein-Uhlenbeck operator on (ℝ
n
, |·|, d
γ
) and the spectral operator associated with the spectral multiplier on (S, d, ρ). All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces. 相似文献
14.
Lower estimates for the maximal weight multiplicities in irreducible representations of the algebraic groups of type C
n
in characteristic p ≤ 7 are found. If n ≥ 8 and p ≠ 2 , then for an irreducible representation either such a multiplicity is at least n− 4 − [n]4,where [n]4 is the residue of n modulo 4, or all the weight multiplicities are equal to 1.For p = 2, the situation is more complicated, and for every n and l there exists a class of representations with the maximal weight multiplicity equal to 2
l
. For symplectic groups in characteristic p > 7 and spinor groups similar results were obtained earlier. Bibliography: 15 titles. 相似文献
15.
Romain Dujardin 《Mathematische Annalen》2003,325(4):745-765
In this paper we study laminar currents in ℙ2. Given a sequence of irreducible algebraic curves (C
n
) converging in the sense of currents to T, we find geometric conditions on the curves ensuring that the limit current T is laminar. This criterion is then applied to meromorphic dynamical systems in ℙ2, and laminarity of the dynamical ``Green' current is obtained for a wide class of meromorphic self maps of ℙ2, as well as for all bimeromorphic maps of projective surfaces.
Received: 24 September 2001 / Published online: 10 February 2003
Mathematics Subject Classification (2000): 32U40, 37Fxx, 32H50 相似文献
16.
P. Mironescu 《Journal of Mathematical Sciences》2010,170(3):340-355
We describe the structure of the space
Ws,p( \mathbbSn;\mathbbS1 ) {W^{s,p}}\left( {{\mathbb{S}^n};{\mathbb{S}^1}} \right) , where 0 < s < ∞ and 1 ≤ p < ∞. According to the values of s, p, and n, maps in
Ws,p( \mathbbSn;\mathbbS1 ) {W^{s,p}}\left( {{\mathbb{S}^n};{\mathbb{S}^1}} \right) can either be characterised by their phases or by a couple (singular set, phase). 相似文献
17.
Humio Ichimura 《Archiv der Mathematik》2011,96(6):555-563
Let p be an odd prime number, and pn0{p^{n_0}} the highest power of p dividing 2
p−1 − 1. Let Kn=Q(zpn+1){K_n={\bf Q}(\zeta_{p^{n+1}})} and Ln,j=Kn+(z2j+2){L_{n,j}=K_n^+(\zeta_{2^{j+2}})} for j ≥ 0. Let hn*{h_n^*} be the relative class number of K
n
, and h
n,j
the class number of L
n,j
, respectively. Let n be an integer with n ≥ n
0. We prove that if the ratio hn*/hn-1*{h_n^*/h_{n-1}^*} is odd, then h
n,j
/h
n−1,j
is odd for any j ≥ 0. 相似文献
18.
We present a heuristic for the Euclidean Steiner tree problem in ℜ
d
for d≥2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning
tree to identify the Steiner points to remove, and second-order cone programming to optimize the location of the remaining
Steiner points. Unlike other ESTP heuristics relying upon Delaunay triangulation, we insert Steiner points probabilistically
into Delaunay triangles to achieve different subtrees on subsets of terminal points. We govern this neighbor generation procedure
with a local search framework that extends effectively into higher dimensions. We present computational results on benchmark
test problems in ℜ
d
for 2≤d≤5. 相似文献
19.
We consider the superlinear elliptic equation on Sn
where ΔSn
is the Laplace-Beltrami operator on S
n. We prove that for any k = 1,..., n − 1, there exists p
k
> 1 such that for 1 < p < p
k
and ε sufficiently small, there exist at least n−k positive solutions concentrating on a k-dimensional subset of the equator. We also discuss the problem on geodesic balls of S
n and establish the existence of positive non-radial solutions. The method extends to Dirichlet problems with more general non-linearities. The proofs are based on the finite-dimensional
reduction procedure which was successfully used by the second author in singular perturbation problems. 相似文献
20.
Soltan 《Discrete and Computational Geometry》2003,29(4):561-573
Abstract. Generalizing the characteristic intersection property of Choquet simplices, it is proved that for line-free convex bodies
B
1
and B
2
in E
d
, the following conditions are equivalent: (i) there is a line-free convex body B ⊂ E
d
such that every nonempty intersection B
1
∩ (v + B
2
) , v ∈ E
d
, is a homothetic copy of B , (ii) both B
1
and B
2
are Choquet simplices and the nonempty intersections B
1
∩ (v + B
2
) , v ∈ E
d
, are homothetic copies of a Choquet simplex B . All such triplets B
1
,B
2
,B are described. 相似文献