共查询到20条相似文献,搜索用时 15 毫秒
1.
Pankaj K. Agarwal Boris Aronov Vladlen Koltun Micha Sharir 《Discrete and Computational Geometry》2005,34(2):231-250
Let B be a set of n unit balls
in ℝ3. We show that the combinatorial complexity of the
space of lines in ℝ3 that avoid all the balls of B is O(n3+ε), for any ε > 0. This result has connections to
problems in visibility, ray shooting, motion planning, and
geometric optimization. 相似文献
2.
K. Hosono 《European Journal of Combinatorics》2001,22(8):1083
Let F be a family of mutually nonoverlapping unit balls in the n -dimensional Euclidean space Rn. The distance between the centres of A,B F is denoted by d(A, B). We prove, among others, that if d(A, B) < 4 and n ≥ 5, then A andB are always visible from each other, that is, a light ray emanating from the surface of A reaches B without being blocked by other unit balls. Furthermore, if d(A, B) < 2n / 2, then any small “shake’ of F can make A, B visible from each other. 相似文献
3.
4.
5.
证明了赋范空间单位球之间任意保一的1-Lipshcitz算子在假设像空间是严格凸的,或者算子是满的条件下是定义在全空间上的线性等距算子在单位球上的限制.同时,也给出了这个结果的一些应用,以及当两个赋范空间是严格凸时推广了的结果. 相似文献
6.
We answer a question of David Larman, by proving the following result. Any four unit balls in three-dimensional space, whose centers are not collinear, have at most twelve common tangent lines. This bound is tight. Received October 25, 1999, and in final form May 24, 2000. Online publication January 17, 2001. 相似文献
7.
The bounded symmetric spaces naturally associated with the Poincaré and Beltrami-Klein models of hyperbolic geometry on the open unit ball B in ${\mathbb{R}^n}$ and with the automorphism group of biholomorphic maps on the open ball in ${\mathbb{C}^n}$ give rise by a standard construction to specialized loop structures (nonassociative groups), which we use to define canonical metrics, called rapidity metrics. We show that this rapidity metric agrees with the classical Poincaré metric resp. the Cayley-Klein metric resp. the Bergman metric. We introduce the Lorentz boost of vectors in B, which turns out to be a loop isomorphism. It induces a similarity of metrics between the rapidity metric of the Einstein or Möbius loop and the trace metric on positive definite matrices restricted to the Lorentz boosts. 相似文献
8.
Otfried Cheong Xavier Goaoc Andreas Holmsen Sylvain Petitjean 《Discrete and Computational Geometry》2008,39(1-3):194-212
We prove Helly-type theorems for line transversals to disjoint unit balls in ℝ
d
. In particular, we show that a family of n≥2d disjoint unit balls in ℝ
d
has a line transversal if, for some ordering ≺ of the balls, any subfamily of 2d balls admits a line transversal consistent with ≺. We also prove that a family of n≥4d−1 disjoint unit balls in ℝ
d
admits a line transversal if any subfamily of size 4d−1 admits a transversal.
Andreas Holmsen was supported by the Research Council of Norway, prosjektnummer 166618/V30. Otfried Cheong and Xavier Goaoc
acknowledge support from the French-Korean Science and Technology Amicable Relationships program (STAR). 相似文献
9.
The Bernstein space B
p () (1
$$
" align="middle" border="0">
0) is the set of functions from L
p(
) having Fourier transforms (in the sense of generalized functions) with supports in the compact segment [- , ]. Every function f
has an analytic continuation onto the complex plane, which is an entire function of exponential type . The spaces B
p ()\, are conjugate Banach spaces. Therefore, the closed unit ball
in B
p () has a rich set of extreme (boundary) points:
coincides with the weakly * closed convex hull of its extreme points. Since, for 1< p< , B
p () is a uniformly convex space, only the balls
and
have nontrivially arranged sets of extreme points. In this paper, in terms of zeros of entire functions, we obtain necessary and sufficient conditions of extremeness for functions from
. 相似文献
10.
Abstract. We prove that a set of n disjoint unit balls in R
d
admits at most four distinct geometric permutations, or line transversals, thus settling a long-standing conjecture in combinatorial geometry.
The constant bound significantly improves upon the Θ (n
d-1
) bound for disjoint balls of unrestricted radii. 相似文献
11.
Abstract. We prove that a set of n disjoint unit balls in R
d
admits at most four distinct geometric permutations, or line transversals, thus settling a long-standing conjecture in combinatorial geometry.
The constant bound significantly improves upon the Θ (n
d-1
) bound for disjoint balls of unrestricted radii. 相似文献
12.
Abstract. Let F be a family of disjoint unit balls in R
3
. We prove that there is a Helly-number n
0
≤ 46 , such that if every n
0
members of F ( | F | ≥ n
0
) have a line transversal, then F has a line transversal. In order to prove this we prove that if the members of F can be ordered in a way such that every 12 members of F are met by a line consistent with the ordering, then F has a line transversal. The proof also uses the recent result on geometric permutations for disjoint unit balls by Katchalski,
Suri, and Zhou. 相似文献
13.
Abstract. Let F be a family of disjoint unit balls in R
3
. We prove that there is a Helly-number n
0
≤ 46 , such that if every n
0
members of F ( | F | ≥ n
0
) have a line transversal, then F has a line transversal. In order to prove this we prove that if the members of F can be ordered in a way such that every 12 members of F are met by a line consistent with the ordering, then F has a line transversal. The proof also uses the recent result on geometric permutations for disjoint unit balls by Katchalski,
Suri, and Zhou. 相似文献
14.
Cai Tianxin 《东北数学》1994,(4)
On Selecting k Balls from an N-circle Without Unit SeparationCaiTianxin(蔡天新)(DepartmentofMathcmatics,HangzhonUniversity,Hangz... 相似文献
15.
On the Helly Number for Hyperplane Transversals to Unit Balls 总被引:5,自引:0,他引:5
B. Aronov J. E. Goodman R. Pollack R. Wenger 《Discrete and Computational Geometry》2000,24(2-3):171-176
We prove two results about the Hadwiger problem of finding the Helly number for line transversals of disjoint unit disks
in the plane, and about its higher-dimensional generalization to hyperplane transversals of unit balls in d -dimensional Euclidean space. These consist of (a) a proof of the fact that the Helly number remains 5 even for arbitrarily
large sets of disjoint unit disks—thus correcting a 40-year-old error; and (b) a lower bound of d+3 on the Helly number for hyperplane transversals to suitably separated families of unit balls in R
d
.
Received January 25, 1999, and in revised form July 7, 1999. 相似文献
16.
针对GAHP中群体偏好信息个体判断矩阵集结、个体排序向量集结两种方式之间的关系或优劣问题,从最终决策结果或综合排序向量角度考虑,运用线性代数方法,分析证明在统一使用加权几何平均模型前提下二者的等价性,并通过实际数值算例对其进行了直观显示. 相似文献
17.
Several authors have studied the Taylor expansion for the volume of geodesic balls under the exponential mapping of an analytic Riemannian manifold $ (M, {\cal G}) $ . A more general structure $ (M, D{\cal G}) $ , where D is a torsion-free and Ricci-symmetric connection, appears in several geometric situations. We study the Taylor expansion in this case, where all metric notions are Riemannian, while now the exponential mapping is induced from the connection D. We give many applications, in particular in different hypersurface theories. 相似文献
18.
19.
20.
DongshengLiu 《工科数学》1999,15(1):70-75
In this paper, we characterize BMOA and VMOA on the unit ball in terms of normsNp(f)=sup/x∈B{1/σ(Q(z))∫Q(z)│f(ξ)-f(z)│pdσ(ξ)}^1/p,1≤p&;lt;∞ and more general Garcia norms.Where Q(z)=Q(n(z),δz)={ξ∈S,│^1/2&;lt;δZ}.n(z)={e1,z=0,/z/│z│,z=0,δz=[2(1-│z│)]^1/2. 相似文献