共查询到20条相似文献,搜索用时 15 毫秒
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Zsolt Páles 《Archiv der Mathematik》1989,52(3):265-268
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A central limit theorem for convex sets 总被引:4,自引:1,他引:3
B. Klartag 《Inventiones Mathematicae》2007,168(1):91-131
We show that there exists a sequence for which the following holds: Let K⊂ℝn be a compact, convex set with a non-empty interior. Let X be a random vector that is distributed uniformly in K. Then there exist a unit vector θ in ℝn, t0∈ℝ and σ>0 such that
where the supremum runs over all measurable sets A⊂ℝ, and where 〈·,·〉 denotes the usual scalar product in ℝn. Furthermore, under the additional assumptions that the expectation of X is zero and that the covariance matrix of X is the
identity matrix, we may assert that most unit vectors θ satisfy (*), with t0=0 and σ=1. Corresponding principles also hold for multi-dimensional marginal distributions of convex sets. 相似文献
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It is wellknown that the technique of character sums together with the tools of algebraic number theory is the adequate method for the study of difference sets in abelian groups, compare for instance Ott [5] or Turyn [6]. In this paper we use this method to prove a new non-existence theorem for certain difference sets in abelian groups of order rpa rp^a , where r 1 2 r \neq 2 and p are distinct primes. 相似文献
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《Advances in Mathematics》2003,174(2):227-235
A set of the form , where is convex and denotes the integer lattice, is called a convex lattice set. It is known that the Helly number of d-dimensional convex lattice sets is 2d. We prove that the fractional Helly number is only d+1: For every d and every α∈(0,1] there exists β>0 such that whenever F1,…,Fn are convex lattice sets in such that for at least index sets I⊆{1,2,…,n} of size d+1, then there exists a (lattice) point common to at least βn of the Fi. This implies a (p,d+1)-theorem for every p?d+1; that is, if is a finite family of convex lattice sets in such that among every p sets of , some d+1 intersect, then has a transversal of size bounded by a function of d and p. 相似文献
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A. R. Mirotin 《Functional Analysis and Its Applications》2012,46(3):210-217
In the context of the multidimensional functional calculus of semigroup generators, which is based on the class of Bernstein functions in several variables (and is also known as Bochner-Phillips multidimensional functional calculus), a spectral mapping theorem for the Taylor spectrum of a set of commuting generators is proved. 相似文献
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Applications of a theorem concerning sets with convex sections 总被引:7,自引:0,他引:7
Ky Fan 《Mathematische Annalen》1966,163(3):189-203
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V. Klee extended a well-known theorem of Minkowski to non-compact convex sets. We generalize Minkowski’s theorem to convex sets which are not necessarily closed. 相似文献
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B. Klartag 《Journal of Functional Analysis》2007,245(1):284-310
We investigate the rate of convergence in the central limit theorem for convex sets established in [B. Klartag, A central limit theorem for convex sets, Invent. Math., in press. [8]]. We obtain bounds with a power-law dependence on the dimension. These bounds are asymptotically better than the logarithmic estimates which follow from the original proof of the central limit theorem for convex sets. 相似文献
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This paper offers first- and higher-order necessary conditions for the local disjointness of a finite system of sets that are nonlinear inverse images of convex sets. The proof is based on the characterizations of α-admissible and α-tangent variations to nonlinear inverse images of convex sets and a necessary condition for the local disjointness in terms of these variations. As an application, the results are used to obtain first- and higher-order necessary conditions of optimality in constrained optimization problems. 相似文献
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J Vangeldère 《Journal of Mathematical Analysis and Applications》1977,60(1):36-46
First we give some elementary properties of the core of a subset relative to a linear subspace. Then we prove a theorem on the frank separation of two convex sets. This theorem admits as particular cases the known theorems on the frank separation and introduces new cases. Finally, we provide a very general version of the Hahn-Banach theorem in an analytic form. 相似文献
14.
Huidobro Pedro Alonso Pedro Janiš Vladimír Montes Susana 《Fuzzy Optimization and Decision Making》2022,21(4):553-580
Fuzzy Optimization and Decision Making - Convexity is a deeply studied concept since it is very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity... 相似文献
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G. Faltings 《Inventiones Mathematicae》1983,73(3):337-347
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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
20.
Gerd Rodé 《Semigroup Forum》1983,26(1):317-321
It is proved that each continuous semigroup {P(t)}t≥0 of convex operators P(t):Rn→Rn is continuously differentiable with respect to t.
This note represents a first step towards a better understanding of semigroups formed by convex operators. We establish the
differentiability of a convex semigroup in the finite dimensional case, generalizing a basic result from linear semigroup
theory.
Our motivation for the study of semigroups of convex operators comes from the theory of Markov decision processes. In [1]
and in [2] it was shown that the maximum reward of these processes can be described by a certain nonlinear semigroup. The
nonlinear operators are defined as suprema of linear operators (plus a constant), hence they are convex operators.
It seems that the convexity assumption keeps its smoothing influence even in the infinite dimensional situation. We hope to
discuss this in a future paper. 相似文献