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Abstract  

We study the hyperbolicity of metric spaces in the Gromov sense. We deduce the hyperbolicity of a space from the hyperbolicity of its “building block components”. These results are valuable since they simplify notably the topology of the space and allow to obtain global results from local information. We also study how the punctures and the decomposition of a Riemann surface in Y-pieces and funnels affect the hyperbolicity of the surface.

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Abstract  

The main purpose of this paper is to introduce the concepts of
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*-sets,
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*-continuous functions and to obtain new decompositions of continuous and ηζ-continuous functions. Moreover, properties of
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*-sets and some properties of
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-sets are discussed.
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, W. , Direct methods for primary decomposition, Invent. Math. , 110(2) (1992), 207–235. MR 1185582 93j :13032 Vasconcelos W. Direct methods for primary decomposition

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and Fractals 42 238 – 246 10.1016/j.chaos.2008.11.009 . [6] Keskin , A. , Yuksel , S. , Noiri , T. 2004 Decompositions of -continuity and continuity Commun. Fac. Sci. Univ. Ank

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Abstract

The Hodge–de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study some related results concerning a class of partial differential equation in a novel way.

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ZEMPLÉNI, A., In the max-semigroup of probability distributions over the plane there is no Khinchine-type decomposition theorem, Studia Sci. Math. Hungar. 30 (1995), 303-311. MR 96j :60020

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343 Gonska, H. , On the composition and decomposition of positive linear operators, in: Approximation Theory and its Applications (Ukrainian) (Kiev, 1999), 161–180, Pr. Inst. Mat. Nats

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, C. W. , The Decomposition Theorem for Ideals in Polynomial Rings over a Domain, Journal of Algebra , 76 (1982), 99–110. Ayoub C. W. The Decomposition Theorem for Ideals in

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Summary  

The main purpose of this paper is to introduce the concepts of η-sets, ηζ-sets,η-continuity and ηζ-continuity and to obtain a decomposition of continuity.

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