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Mathematics, Volume 5, Issue 3 (September 2017)

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Research

Open AccessArticle Banach Subspaces of Continuous Functions Possessing Schauder Bases
Mathematics 2017, 5(3), 35; doi:10.3390/math5030035
Received: 12 February 2017 / Revised: 20 May 2017 / Accepted: 20 May 2017 / Published: 24 June 2017
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Abstract
In this article, Müntz spaces MΛ,C of continuous functions supplied with the absolute maximum norm are considered. An existence of Schauder bases in Müntz spaces MΛ,C is investigated. Moreover, Fourier series approximation of functions in Müntz spaces
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In this article, Müntz spaces M Λ , C of continuous functions supplied with the absolute maximum norm are considered. An existence of Schauder bases in Müntz spaces M Λ , C is investigated. Moreover, Fourier series approximation of functions in Müntz spaces M Λ , C is studied. Full article
Open AccessArticle Lattices and Rational Points
Mathematics 2017, 5(3), 36; doi:10.3390/math5030036
Received: 12 June 2017 / Revised: 4 July 2017 / Accepted: 4 July 2017 / Published: 9 July 2017
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Abstract
In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geometry to bound explicitly the height of the points of rank N-1 on transverse curves in EN, where E is an elliptic
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In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geometry to bound explicitly the height of the points of rank N - 1 on transverse curves in E N , where E is an elliptic curve without Complex Multiplication (CM). We then apply our result to give a method for finding the rational points on such curves, when E has Q -rank N - 1 . We also give some explicit examples. This result generalises from rank 1 to rank N - 1 previous results of S. Checcoli, F. Veneziano and the author. Full article
(This article belongs to the Special Issue Geometry of Numbers)
Open AccessArticle Elimination of Quotients in Various Localisations of Premodels into Models
Mathematics 2017, 5(3), 37; doi:10.3390/math5030037
Received: 27 March 2016 / Revised: 29 June 2017 / Accepted: 3 July 2017 / Published: 9 July 2017
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Abstract
The contribution of this article is quadruple. It (1) unifies various schemes of premodels/models including situations such as presheaves/sheaves, sheaves/flabby sheaves, prespectra/Ω-spectra, simplicial topological spaces/(complete) Segal spaces, pre-localised rings/localised rings, functors in categories/strong stacks and, to some extent, functors from a
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The contribution of this article is quadruple. It (1) unifies various schemes of premodels/models including situations such as presheaves/sheaves, sheaves/flabby sheaves, prespectra/ Ω -spectra, simplicial topological spaces/(complete) Segal spaces, pre-localised rings/localised rings, functors in categories/strong stacks and, to some extent, functors from a limit sketch to a model category versus the homotopical models for the limit sketch; (2) provides a general construction from the premodels to the models; (3) proposes technics that allow one to assess the nature of the universal properties associated with this construction; (4) shows that the obtained localisation admits a particular presentation, which organises the structural and relational information into bundles of data. This presentation is obtained via a process called an elimination of quotients and its aim is to facilitate the handling of the relational information appearing in the construction of higher dimensional objects such as weak ( ω , n ) -categories, weak ω -groupoids and higher moduli stacks. Full article
(This article belongs to the Special Issue Homological and Homotopical Algebra and Category Theory)
Open AccessArticle Variable Shape Parameter Strategy in Local Radial Basis Functions Collocation Method for Solving the 2D Nonlinear Coupled Burgers’ Equations
Mathematics 2017, 5(3), 38; doi:10.3390/math5030038
Received: 31 May 2017 / Revised: 10 July 2017 / Accepted: 12 July 2017 / Published: 21 July 2017
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Abstract
This study aimed at investigating a local radial basis function collocation method (LRBFCM) in the reproducing kernel Hilbert space. This method was, in fact, a meshless one which applied the local sub-clusters of domain nodes for the approximation of the arbitrary field. For
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This study aimed at investigating a local radial basis function collocation method (LRBFCM) in the reproducing kernel Hilbert space. This method was, in fact, a meshless one which applied the local sub-clusters of domain nodes for the approximation of the arbitrary field. For time-dependent partial differential equations (PDEs), it would be changed to a system of ordinary differential equations (ODEs). Here, we intended to decrease the error through utilizing variable shape parameter (VSP) strategies. This method was an appropriate way to solve the two-dimensional nonlinear coupled Burgers’ equations comprised of Dirichlet and mixed boundary conditions. Numerical examples indicated that the variable shape parameter strategies were more efficient than constant ones for various values of the Reynolds number. Full article
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