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1.
A colorful theorem on transversal lines to plane convex sets 总被引:1,自引:0,他引:1
We prove a colorful version of Hadwiger’s transversal line theorem: if a family of colored and numbered convex sets in the
plane has the property that any three differently colored members have a transversal line that meet the sets consistently
with the numbering, then there exists a color such that all the convex sets of that color have a transversal line.
All authors are partially supported by CONACYT research grant 5040017. 相似文献
2.
We characterize the duality of convex bodies in d-dimensional Euclidean vector space, viewed as a mapping from the space of convex bodies containing the origin in the interior
into the same space. The question for such a characterization was posed by Vitali Milman. The property that the duality interchanges
pairwise intersections and convex hulls of unions is sufficient for a characterization, up to a trivial exception and the
composition with a linear transformation.
Received: March 2007, Accepted: April 2007 相似文献
3.
The concept of antipodality relative to a closed convex cone has been explored in detail in a recent work of ours. The antipodality problem consists of finding a pair of unit vectors
in K achieving the maximal angle of the cone. Our attention now is focused not just in the maximal angle, but in the angular spectrum
of the cone. By definition, the angular spectrum of a cone is the set of angles satisfying the stationarity (or criticality)
condition associated to the maximization problem involved in the determination of the maximal angle. In the case of a polyhedral
cone, the angular spectrum turns out to be a finite set. Among other results, we obtain an upper bound for the cardinality
of this set. We also discuss the link between the critical angles of a cone K and the critical angles of its dual cone.
Dedicated to Boris Polyak on his 70th Birthday. 相似文献
4.
J. M. Aldaz 《Rendiconti del Circolo Matematico di Palermo》2001,50(1):213-216
We show that given any Borel measure onR, every Lipschitz function is μ-a.e. differentiable with respect to μ. 相似文献
5.
Outer Minkowski content for some classes of closed sets 总被引:1,自引:0,他引:1
We find conditions ensuring the existence of the outer Minkowski content for d-dimensional closed sets in , in connection with regularity properties of their boundaries. Moreover, we provide a class of sets (including all sufficiently
regular sets) stable under finite unions for which the outer Minkowski content exists. It follows, in particular, that finite
unions of sets with Lipschitz boundary and a type of sets with positive reach belong to this class. 相似文献
6.
Tai-Chia Lin Chi-Cheung Poon Dong-Ho Tsai 《Calculus of Variations and Partial Differential Equations》2009,34(2):153-178
We study the evolution driven by curvature of a given convex immersed closed plane curve. We show that it will converge to
a self-similar solution eventually. This self-similar solution may or may not contain singularities. In case it does, we also
have estimate on the curvature blow-up rate. 相似文献
7.
Let X and Y be Banach spaces. A set
(the space of all weakly compact operators from X into Y) is weakly equicompact if, for every bounded sequence (x
n) in X, there exists a subsequence (x
k(n)) so that (Txk(n)) is uniformly weakly convergent for T ∈ M. In this paper, the notion of weakly equicompact set is used to obtain characterizations of spaces X such that
X ↩̸ ℓ1, of spaces X such that B
X*
is weak* sequentially compact and also to obtain several results concerning to the weak operator and the strong operator
topologies. As another application of weak equicompactness, we conclude a characterization of relatively compact sets in
when this space is endowed with the topology of uniform convergence on the class of all weakly null sequences. Finally, we
show that similar arguments can be applied to the study of uniformly completely continuous sets.
Received: 5 July 2006 相似文献
8.
Joaquín Pérez 《Calculus of Variations and Partial Differential Equations》2007,29(2):267-279
We prove that if is a properly embedded oriented stable minimal surface whose boundary is a straight line and the area of M in extrinsic balls grows quadratically in the radius, then M is a half-plane or half of the classical Enneper minimal surface. This solves a conjecture posed by B. White in Geometric Analysis and the Calculus of Variations for Stefan Hildebrandt, International Press, Somerville, 1996. 相似文献
9.
Sever S. Dragomir 《Archiv der Mathematik》2008,90(5):450-460
Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation are given. Applications
for the trapezoid and mid-point inequalities are also provided.
Received: 19 May 2008 相似文献
10.
Bassam Shayya 《Mathematische Zeitschrift》2009,262(1):41-55
Suppose dμ is affine surface measure on a convex radial surface Γ(x) = (x, γ(|x|)), a ≤ |x| < b, in . Under appropriate smoothness and growth conditions on γ, we prove and Fourier restriction estimates for Γ. 相似文献
11.
Paula A. Kemp 《Rendiconti del Circolo Matematico di Palermo》1997,46(1):119-122
It is well known that any distributive poset (short for partially ordered set) has an isomorphic representation as a poset
(Q, ⊆) such that the supremum and the infimum of any finite setF ofP correspond, respectively to the union and intersection of the images of the elements ofF. Here necessary and sufficient conditions are given for similar isomophic representation of a poset where however the supremum
and infimum of also infinite subsetsI correspond to the union and intersection of images of elements ofI. 相似文献
12.
LiJingwen 《高校应用数学学报(英文版)》2000,15(4):391-398
Consider the discrete Lasota-Wazewska model Nn 1-Nn=-μNn pe^-rNn-k,n=0,1,2,……where μ∈(0,1),r,p∈(0,∞) and k∈N. A sufficient condition for all positive solutions of ( * )to be attracted to its equilibrium N^* is obtained. It improves correspondent result obtained by Chen and Yu in 1999. 相似文献
13.
Christian Richter 《Archiv der Mathematik》1997,68(4):331-339
Controllable partitions, which arise in approximation theory, are finite partitions of compact metric spaces into subsets
whose sizes fulfil a uniformity condition depending on the entropy numbers of the underlying space. We characterize a class
of partitions of the cube ([0,2]
m
, d
max) which possess a controllable refinement and, in the end, give an ascending chain of controllable partitions of [0,2]
m
. 相似文献
14.
Suppose that
is a 0-symmetric convex body
which denes the usual norm
on
. Let also
be a measurable set of positive upper density .
We show that if the body K is not a polytope, or if it is a polytope with
many faces (depending on ), then the distance set
contains all points t t0 for some positive number t0 . This was proved
by Furstenberg, Katznelson and Weiss, by Falconer and Marstrand and
by Bourgain in the case where K is the Euclidean ball in any dimension
greater than 1. As corollaries we obtain (a) an extension to any dimension
of a theorem of Iosevich and Laba regarding distance sets with respect to
convex bodies of well-distributed sets in the plane, and also (b) a new proof
of a theorem of Iosevich, Katz and Tao about the nonexistence of Fourier
spectra for smooth convex bodies with positive curvature. 相似文献
15.
First-order regularity of convex functions on Carnot Groups 总被引:1,自引:0,他引:1
Matthieu Rickly 《Journal of Geometric Analysis》2006,16(4):679-702
We prove that h-convex functions on Carnot groups of step two are locally Lipschitz continuous with respect to any intrinsic
metric. We show that an additional measurability condition implies the local Lipschitz continuity of h-convex functions on
arbitrary Carnot groups.
To the Memory of Q. G. 相似文献
16.
Josef Niederle 《Rendiconti del Circolo Matematico di Palermo》1998,47(3):463-464
A sufficient condition for each extensive mapping of an ordered set to have a fixpoint is presented.
Financial support of the Grant Agency of the Czech Republic under the grant no. 201/93/0950 is gratefully acknowledged. 相似文献
17.
Marilyn Breen 《Archiv der Mathematik》1997,68(1):60-64
Let S be a nonempty closed, simply connected set in the plane, and let α τ; 0. If every three points of 5 see a common point of
S via paths of length at most α, then for some point s0 of S, s0 sees each point of S via such a path. That is, S is starshaped via paths of length at most α.
Supported in part by NSF grant DMS-9207019 相似文献
18.
We find all finite unavoidable ordered sets, finite unavoidable semilattices and finite unavoidable lattices.
While working on this paper, the second and third authors were supported by US NSF grant DMS-0604065. The second author was
also supported by the Grant Agency of the Czech Republic, grant #201/05/0002 and by the institutional grant MSM0021620839
financed by MSMT. 相似文献
19.
Sylvie Monniaux 《Archiv der Mathematik》1997,68(5):407-417
We give a new proof of a perturbation result due to J. Prüss and H. Sohr [11]: if an operator A has bounded imaginary powers, then so does A+w (w ≧ 0). Instead of Mellin transform on which the proof in [11] is based, we use the functional calculus for sectorial operators
developed in particular by A. McIntosh ([8], [3] and [1]). It turns out that our method gives a more general result than the
one used in [11]. 相似文献
20.
Extensions of some inequalities 总被引:2,自引:0,他引:2
ChenDaoqi 《高校应用数学学报(英文版)》2001,16(3):241-243
Abstract. By using a simple analytic method the following inequalities are proved: 相似文献