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In this work, we introduce a Representation of continuous real-valued functions defined over a real Hilbert space. As a consequence, we can introduce a Sandwich Theorem for semi-continuous functions, a Separation Theorem for close...
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In this work, we introduce a Representation of continuous real-valued functions defined over a real Hilbert space. As a consequence, we can introduce a Sandwich Theorem for semi-continuous functions, a Separation Theorem for closed sets and a representation Theorem of lower semi-continuous functions.
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We derive from Motzkin's Theorem that a point can be strongly separated by a hyperplane from a convex polytope and a finitely-generated convex cone. We state a similar result for Tucker's Theorem of the alternative. A generalisati...
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We derive from Motzkin's Theorem that a point can be strongly separated by a hyperplane from a convex polytope and a finitely-generated convex cone. We state a similar result for Tucker's Theorem of the alternative. A generalisation of the residual existence theorem for linear equations which has recently been proved by Rohn [8] is a corollary. We state all the results in the setting of a general vector space over a linearly ordered (possibly skew) field.
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We prove a Freiman–Ruzsa-type theorem valid in an arbitrary nilpotent group. Specifically, we show that a K-approximate group A in an s-step nilpotent group G is contained in a coset nilprogression of rank at most K~(O_s(1)) and ...
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We prove a Freiman–Ruzsa-type theorem valid in an arbitrary nilpotent group. Specifically, we show that a K-approximate group A in an s-step nilpotent group G is contained in a coset nilprogression of rank at most K~(O_s(1)) and cardinality at most exp(K~(O_s(1)))|A|. To motivate this, we give a direct proof of Breuillard and Green’s analogous result for torsion-free nilpotent groups, avoiding the use of Mal’cev’s embedding theorem.
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The purpose of this paper is to establishNadel type vanishing theoremswith multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu's metrics). F...
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The purpose of this paper is to establishNadel type vanishing theoremswith multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu's metrics). For this purpose, we generalize Kollár's injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics, by making use of the theory of harmonic integrals. Moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles.
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The aim of this paper is to prove a common fixed point theorem for six mappings on fuzzy metric space using notion of semicompatibility and reciprocal continuity of maps satisfying an implicit relation. We proposed to reanalysis t...
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The aim of this paper is to prove a common fixed point theorem for six mappings on fuzzy metric space using notion of semicompatibility and reciprocal continuity of maps satisfying an implicit relation. We proposed to reanalysis the theorems of Imdad et al. (2002), Popa (2001), Popa (2002) and Singh and Jain (2005).
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In tins paper we mainly survey results obtained in [MM3]. Forexample, we give an elementary proof of two versions of Koebe 1/4 theorem foranalytic functions (see Theorem 1.2 and Theorem 1.4 below). We also showa version of the Koe...
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In tins paper we mainly survey results obtained in [MM3]. Forexample, we give an elementary proof of two versions of Koebe 1/4 theorem foranalytic functions (see Theorem 1.2 and Theorem 1.4 below). We also showa version of the Koebe theorem for quasiregular harmonic functions. As anapplication, we show that holomorphic functions (more generally quasiregularharmonic functions) and their modulus have similar behavior in a certain sense.
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Let ν be a cosmos. In order to see that Theorem 3.1.1 is a consequence of Theorem 4.1.1, we first have to describe a 2-category M which is biequivalent to Mod(ν). In a second step, we have to show that M has Tannaka-Krein object...
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Let ν be a cosmos. In order to see that Theorem 3.1.1 is a consequence of Theorem 4.1.1, we first have to describe a 2-category M which is biequivalent to Mod(ν). In a second step, we have to show that M has Tannaka-Krein objects. Lastly, we have to show that the pseudofunctor Rep(-) from Proposition 4.7.1 is equivalent to the 2-functor R described in §3.6. In order to do all this we need the notions of weighted colimits and cocontinuous ν-functors. This is a place where the theory of enriched categories differs considerably from the unenriched theory. We will mention all the technical details about weighted colimits that are used later in the proof of our recognition result.
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If a Jacobi matrix J is reflectionless on (-2, 2) and has a single a_(n0) equal to 1, then J is the free Jacobi matrix an ≡ 1, b_n ≡0. The paper discusses this result and its generalization to arbitrary sets and presents several...
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If a Jacobi matrix J is reflectionless on (-2, 2) and has a single a_(n0) equal to 1, then J is the free Jacobi matrix an ≡ 1, b_n ≡0. The paper discusses this result and its generalization to arbitrary sets and presents several applications, including the following: if a Jacobi matrix has some portion of its an's close to 1, then one assumption in the Denisov-Rakhmanov Theorem can be dropped.
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In this paper we give sufficient conditions for a compactum in ? n to have Carathéodory number less than n+1, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carathéodory theorem a...
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In this paper we give sufficient conditions for a compactum in ? n to have Carathéodory number less than n+1, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carathéodory theorem and give a Tverberg-type theorem for families of convex compacta.
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In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the central point theorem, and Tverberg's theorem on partitions of a point set.
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