Some capacities and applications - the lemma on mixed derivatives revisited
J. Korevaar (1986)
Matematički Vesnik
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J. Korevaar (1986)
Matematički Vesnik
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Bogdan Rzepecki (1975)
Annales Polonici Mathematici
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Jerzy August Gawinecki
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CONTENTS1. Introduction..................................................................................................................................... 5 1.1. Main Theorem 1.1................................................................................................................. 8 1.2. Main Theorem 1.2................................................................................................................. 92. Radon transform.......................................................................................................................................
W. Mlak (1963)
Annales Polonici Mathematici
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Antoni Sadowski (2003)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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B. Rzepecki in [5] examined the Darboux problem for the hyperbolic equation on the quarter-plane x ≥ 0, y ≥ 0 via a fixed point theorem of B.N. Sadovskii [6]. The aim of this paper is to study the Picard problem for the hyperbolic equation using a method developed by A. Ambrosetti [1], K. Goebel and W. Rzymowski [2] and B. Rzepecki [5].
François Delgove, Nicolas Retailleau (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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The aim of this paper is to give a classification of the right-angled hyperbolic hexagons in the real hyperbolic space , by using a quaternionic distance between geodesics in .
Arkadiusz Szymaniec (2010)
Applicationes Mathematicae
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We consider the initial-value problem for a linear hyperbolic parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove time decay estimates for the solution of the associated linear Cauchy problem.
Mao-Ting Chien, Hiroshi Nakazato (2016)
Czechoslovak Mathematical Journal
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The numerical range of an matrix is determined by an degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus . We reformulate the Fiedler-Helton-Vinnikov formulae for the genus , and present an elementary...
Zofia Szmydt, Bogdan Ziemian (1985)
Annales Polonici Mathematici
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Zofia Szmydt, Bogdan Ziemian (1979)
Annales Polonici Mathematici
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Denny H. Leung, Wee-Kee Tang (2006)
Studia Mathematica
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We investigate the existence of higher order ℓ¹-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space : (1) Every block subspace of X contains an -spreading model, (2) The Bourgain ℓ¹-index for any block subspace Y of X, (3) and every block subspace Y of X contains a block sequence equivalent to a subsequence of the unit vector basis of X. Moreover, if one (and hence all) of these...
Christopher J. Leininger, Saul Schleimer (2014)
Journal of the European Mathematical Society
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We prove, for any , that there is a closed connected orientable surface so that the hyperbolic space almost-isometrically embeds into the Teichmüller space of , with quasi-convex image lying in the thick part. As a consequence, quasi-isometrically embeds in the curve complex of .
Adrian Karpowicz (2010)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We consider the following Darboux problem for the functional differential equation a.e. in [0,a]×[0,b], u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b]where the function is defined by for (s,t) ∈ [-a₀,0]×[-b₀,0]. We prove a theorem on existence of the Carathéodory solutions of the above problem.
Victor Gerasimov, Leonid Potyagailo (2013)
Journal of the European Mathematical Society
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We describe the kernel of the canonical map from the Floyd boundary of a relatively hyperbolic group to its Bowditch boundary. Using the Floyd completion we further prove that the property of relative hyperbolicity is invariant under quasi-isometric maps. If a finitely generated group admits a quasi-isometric map into a relatively hyperbolic group then is itself relatively hyperbolic with respect to a system of subgroups whose image under is situated within a uniformly bounded...
Denka Kutzarova, Denny H. Leung, Antonis Manoussakis, Wee-Kee Tang (2008)
Studia Mathematica
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We study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis is said to be subsequentially minimal if for every normalized block basis of , there is a further block basis of such that is equivalent to a subsequence of . Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal, and connections with Bourgain’s ℓ¹-index are established. It is also shown that a large class of...
Mordechay B. Levin (2013)
Colloquium Mathematicae
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We prove the central limit theorem for the multisequence where , are reals, are partially hyperbolic commuting s × s matrices, and x is a uniformly distributed random variable in . The main tool is the S-unit theorem.
Adrian Karpowicz (2008)
Annales Polonici Mathematici
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We consider the Darboux problem for a functional differential equation: a.e. in [0,a]×[0,b], u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b]∖(0,a]×(0,b], where the function is defined by for (s,t) ∈ [-a₀,0]×[-b₀,0]. We give a few theorems about weak and strong inequalities for this problem. We also discuss the case where the right-hand side of the differential equation is linear.
Xiliang Bao, Francis Bonahon (2002)
Bulletin de la Société Mathématique de France
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A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic -space which, in the projective model for , is just the intersection of with a projective polyhedron whose vertices are all outside and whose edges all meet . We classify hyperideal polyhedra, up to isometries of , in terms of their combinatorial type and of their dihedral angles.
Florent Balacheff, Eran Makover, Hugo Parlier (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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In this note, we observe that the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature is greater than a function that grows logarithmically in terms of the ratio .