共查询到20条相似文献,搜索用时 15 毫秒
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Jerzy Grzybowski Hubert Przybycień Ryszard Urbański 《Set-Valued and Variational Analysis》2013,21(2):201-216
Any abstract convex cone S with a uniformity satisfying the law of cancellation can be embedded in a topological vector space $\widetilde{S}$ (Urbański, Bull Acad Pol Sci, Sér Sci Math Astron Phys 24:709–715, 1976). We introduce a notion of a cone symmetry and decompose in Theorem 2.12 a quotient vector space $\widetilde{S}$ into a topological direct sum of its symmetric subspace $\widetilde{S}_s$ and asymmetric subspace $\widetilde{S}_a$ . In Theorem 2.19 we prove a similar decomposition for a normed space $\widetilde{S}$ . In section 3 we apply decomposition to Minkowski–Rådström–Hörmander (MRH) space with three best known norms and four symmetries. In section 4 we obtain a continuous selection from a MRH space over ?2 to the family of pairs of nonempty compact convex subsets of ?2. 相似文献
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LetK
p(u1, ..., up) be the completep-partite graph whoseith vertex class hasu
i vertices (lip). We show that the theorem of Erds and Stone can be extended as follows. There is an absolute constant >0 such that, for allr1, 0<1 and=">1>1/r, every graphG=G
n of sufficiently large order |G|=n with at least
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We give a complementary generalization of the extensions of Bonnet–Myers theorem obtained by Calabi and also Cheeger–Gromov–Taylor. 相似文献7.
B. V. Dekster 《Israel Journal of Mathematics》1985,50(3):169-180
Theorem. Let a set X?Rn have unit circumradius and let B be the unit ball containing X. Put C =conv \(\bar X\) D =diam C (=diam X), k =dim C,d i = √(2i + 2)/i. Then: (i) D∈[dn, 2]; (ii) k≧m where m∈{2,3,...,n} satisfies D∈[dm, dm?1) (di decreases by i); (iii) In case k=m (by (ii), this is always the case when m=n), C contains a k-simplex Δ such that: (α) its vertices are on δB; (β) the centre of B belongs toint Δ; (γ) the inequalitiesλ k (D) ≦l ≦D with $$\lambda _k (D) = D\sqrt {\frac{{4k - 2D^2 (k - 1)}}{{2 - (k - 2)(D^2 - 2)}}, D \in (d_k ,d_{k - 1} )} $$ are unimprovable estimates for length l of any edge of Δ. 相似文献
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Laurent Moret-Bailly 《manuscripta mathematica》2012,139(1-2):153-166
We extend Greenberg’s strong approximation theorem to schemes of finite presentation over valuation rings with arbitrary value group. As an application, we prove a closed image theorem (in the strong topology on rational points) for proper morphisms of varieties over valued fields. 相似文献
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A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence x over a finite alphabet is ultimately periodic if and only if, for some n, the number of different factors of length n appearing in x is less than n+1. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let d≥2. A legitimate extension to a multidimensional setting of the notion of periodicity is to consider sets of Zd definable by a first order formula in the Presburger arithmetic 〈Z;<,+〉. With this latter notion and using a powerful criterion due to Muchnik, we exhibit a complete extension of the Morse–Hedlund theorem to an arbitrary dimension d and characterize sets of Zd definable in 〈Z;<,+〉 in terms of some functions counting recurrent blocks, that is, blocks occurring infinitely often. 相似文献
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We extend a theorem of Jörgens, Calabi and Pogorelov on entire solutions of elliptic Monge–Ampère equation to parabolic Monge–Ampère equation, and obtain delicate asymptotic behavior of solutions at infinity. For the dimension \(n\ge 3\), the work of Gutiérrez and Huang in Indiana Univ. Math. J. 47, 1459–1480 (1998) is an easy consequence of our result. And along the line of approach in this paper, we can treat other parabolic Monge–Ampère equations. 相似文献
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In this paper we study smooth complex projective varieties X containing a Grassmannian of lines ${{\mathbb G}(1, r)}$ which appears as the zero locus of a section of a rank two nef vector bundle E. Among other things we prove that the bundle E cannot be ample. 相似文献
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Let ? be the genealogical tree of a supercritical multitype Galton–Watson process, and let Λ be the limit set of ?, i.e., the set of all infinite self-avoiding paths (called ends) through ? that begin at a vertex of the first generation. The limit set Λ is endowed with the metric d(ζ, ξ) = 2
−n
where n = n(ζ, ξ) is the index of the first generation where ζ and ξ differ. To each end ζ is associated the infinite sequence Φ(ζ) of
types of the vertices of ζ. Let Ω be the space of all such sequences. For any ergodic, shift-invariant probability measure
μ on Ω, define Ωμ to be the set of all μ-generic sequences, i.e., the set of all sequences ω such that each finite sequence v occurs in ω with limiting frequency μ(Ω(v)), where Ω(v) is the set of all ω′?Ω that begin with the word v. Then the Hausdorff dimension of Λ∩Φ−1 (Ωμ) in the metric d is
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Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials' space on compact Riemann surfaces.And we also construct a basis of theλ-differentials' space.As the main result,the Cauchy type of integral formula on compact Riemann surfaces is established. 相似文献
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Konrad Engel 《Combinatorica》1984,4(2-3):133-140
LetP be that partially ordered set whose elements are vectors x=(x 1, ...,x n ) withx i ε {0, ...,k} (i=1, ...,n) and in which the order is given byx≦y iffx i =y i orx i =0 for alli. LetN i (P)={x εP : |{j:x j ≠ 0}|=i}. A subsetF ofP is called an Erdös-Ko-Rado family, if for allx, y εF it holdsx ≮y, x ≯ y, and there exists az εN 1(P) such thatz≦x andz≦y. Let ? be the set of all vectorsf=(f 0, ...,f n ) for which there is an Erdös-Ko-Rado familyF inP such that |N i (P) ∩F|=f i (i=0, ...,n) and let 〈?〉 be its convex closure in the (n+1)-dimensional Euclidean space. It is proved that fork≧2 (0, ..., 0) and \(\left( {0,...,0,\overbrace {i - component}^{\left( {\begin{array}{*{20}c} {n - 1} \\ {i - 1} \\ \end{array} } \right)}k^{i - 1} ,0,...,0} \right)\) (i=1, ...,n) are the vertices of 〈?〉. 相似文献
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The aim of this paper is to prove the existence of extension operators for SBV functions from periodically perforated domains. This result will be the fundamental tool to prove the compactness in a noncoercive homogenization problem. 相似文献
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The aim of this note if to give an extension of a classical volume comparison theorem for Riemannian manifolds with sectional curvature bounded above (see Günther, P. Einige Sätze über das Volumenelement eines Riemannschen Raumes, Publ. Math. Debrecen 7, 78–93 (1960)). For the case of a n-dimensional simply connected complete Riemannian manifold with nonpositive sectional curvature our theorem states that the function tarea(S
t
(p))/t
n–2
is convex for every pM where S
t
(p) denotes the sphere of radius t with center p. In view of area(S
0
(p))=0, it is easy to see that our theorem implies the classical result. A similar result holds true for simply connected manifolds with sectional curvature bounded above by a negative constant.Research partially supported by Fondecyt Grant # 1000713 and by UTFSM Grant # 120023 相似文献
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