共查询到20条相似文献,搜索用时 15 毫秒
1.
Aequationes mathematicae - In this paper, some integral inequalities for uniformly convex functions are studied by using unordered submajorization for cumulative functions. Strongly convex... 相似文献
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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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In this paper, the authors prove the Liouville’s theorem for harmonic function on Alexandrov spaces by heat kernel approach, which extends the Liouville’s theorem of harmonic function from Riemannian manifolds to Alexandrov spaces. 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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We give an improvement for the second main theorem of algebraically non-degenerate holomorphic curves into a complex projective variety V intersecting hypersurfaces in subgeneral position, obtained by Chen et al.(2012). An explicit estimate for the truncation level is also obtained in the projective normal case. 相似文献
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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9.
Scott N. Armstrong Charles K. Smart 《Calculus of Variations and Partial Differential Equations》2010,37(3-4):381-384
We present a new, easy, and elementary proof of Jensen’s Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls. 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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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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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
相似文献
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We prove that in general it is not possible to extend a Lipschitz multiple valued function without increasing the Lipschitz constant, i.e. we show that there is no analog of Kirszbraun’s extension theorem for Almgren’s multiple valued functions. 相似文献
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Archiv der Mathematik - In this note we prove a semialgebraic counterpart of Whitney’s extension theorem. 相似文献
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In this paper, using the generalized Wronskian, we obtain a new sharp
bound for the generalized Masons theorem [1] for functions of several variables.
We also show that the Diophantine equation (The generalized Fermat-Catalan equation)
where
, such that k out of the
n-polynomials
are constant, and
under certain conditions for
has no non-constant solution.
Received: 20 March 2003 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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Sandro Bettin Jonathan W. Bober Andrew R. Booker Brian Conrey Min Lee Giuseppe Molteni Thomas Oliver David J. Platt Raphael S. Steiner 《The Ramanujan Journal》2018,45(3):659-681
By using specific subsequences of two different types of generalized Stern polynomials, we obtain several related classes of finite and infinite continued fractions involving a single term \(z^{t^j}\) in their partial numerators, where z is a complex variable and t is a positive integer. This approach is extended to other, sparser, subsequences of Stern polynomials, based on certain Lucas functions; this then leads to further infinite classes of continued fractions. 相似文献
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Positivity - In this paper, we study the local ordered $$*$$ -vector spaces and their representations. We prove that each Archimedean local ordered $$*$$ -vector space, can be represented as a... 相似文献
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