2,033 research outputs found
Generalized solutions of ordinary linear differential equations in the Colombeau algebra
No full textsummary:In this paper first order systems of linear of ODEs are considered. It is shown that these systems admit unique solutions in the Colombeau algebra \Cal L(\bold R^1)
On introduction of two diffeomorphism invariant Colombeau algebras
No full textsummary:Equivalent definitions of two diffeomorphism invariant Colombeau algebras introduced in [7] and [5] (Grosser et al.) are listed and some new equivalent definitions are presented. The paper can be treated as tools for proving in [8] the equality of both algebras
An intrinsic definition of the Colombeau generalized functions
No full textsummary:A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a \text{\Cal C^\infty } manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented
On the product of distributions in Colombeau algebra
No full textAbstract: Results on singular products of Schwartz distributions on the Euclidean space R m are derived when the products are so 'balanced' that they exist in the distribution space. The results follow the idea of a known distributional product introduced by Jan Mikusiński and are obtained in the Colombeau algebra of generalized functions. This algebra contains the distributions and the notion of 'association' permits obtaining results on the level of distributions. AMS Subject Classification: 46F30, 46F10 Key Words: Schwartz distributions, multiplication, Colombeau generalized functions * The Schwartz distributions are widely employed in natural sciences and many other mathematical fields. Since products of distributions with coinciding singularities often appear in them, the problem of their multiplication has been objective of studies for a long time. On the other hand, the differential algebra G of generalized functions of J.F. Colombeau [1] has become popular since it has almost optimal properties for tackling non-linear problems of Schwartz distributions: they are linearly embedded in G and the multiplication is compatible with differentiation and products with smooth functions. The so-called 'association' in G, being a faithful generalization of the equality of distributions
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Whitney's Extension Theorem For Generalized Functions
No full textIf X is a subset of Rn we define generalized functions on X as a direct generalization of C∞ functions on X in Whitney's sense and of generalized functions on X when X is open. Then we prove that, if X is closed, any generalized function on X may be extended as a generalized function on Rn, which is a Whitney's extension theorem for generalized functions. This result generalizes Borel's theorem for generalized functions already proved by the same authors. The proof is an adaptation of a classical proof. © 1986.1142574583Biagioni, Colombeau, Borel's theorem for generalized functions (1985) Stud. Math., 81, pp. 179-183Colombeau, A Multiplication of distributions (1983) J. Math. Anal. Appl., 91, pp. 96-115Colombeau, New Generalized Functions and Multiplication of Distributions (1984) North-Holland Math. Studies, No. 84Colombeau, Elementary Introduction to New Generalized Functions (1985) North-Holland Math Studies, No. 113Hestenes, Extension of the range of a differentiable function (1941) Duke Mathematical Journal, 8, pp. 183-192Whitney, Analytic extensions of differentiable functions defined in closed sets (1934) Transactions of the American Mathematical Society, 36, pp. 63-89Seeley, Extension of C∞ functions defined in a half space (1964) Proc. Amer. Math. Soc., 15, pp. 625-62
Fabrieksschema betreffende de "Bereiding van Magnesium uit Zeewater": Deel I
No full textDocument(en) uit de collectie Chemische Procestechnologie Deel II zie: Deeg, J.F., Chemical Process Design 1101DelftChemTechApplied Science
Generalized Functions and Multiplication of Distributions on C∞ Manifolds
No full textAbstractAn improvement in definition permits us to make invariant under the action of C∞ diffeomorphisms a concept of generalized functions introduced by the first author to define arbitrary products of distributions
Holomorphic maps with a given asymptotic expansion at a boundary point
No full textAbstractThe following result has been known for a long time: let 0 < α < 2π and let S be the sector {z ≠ 0 and arg z ≠ α(+ 2kπ)} of the complex plane; let (un) be a given infinite sequence of complex numbers; then there exists a holomorphic function on S which admits the formal power series ∑+∞n = 0 unzn as asymptotic expansion at the origin. A first generalization of this result to the infinite dimensional case is given by the author (A result of existence of holomorphic maps which admit a given asymptotic expansion, in “Advances in Holomorphy” (J. A. Barroso, Ed.), in press). We give here an improvement of this last result, based upon a different proof. Then we give two counterexamples showing that our assumptions on the spaces are essential
Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data
No full textIn [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.CAPES-BrazilCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES
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