Browsing Natural and Agricultural Sciences by Author "Van der Walt, Jan Harm"

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Browsing Natural and Agricultural Sciences by Author "Van der Walt, Jan Harm"

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  • Category measures, the dual of C(K)δ and hyper-stonean spaces 
    Van der Walt, Jan Harm (American Mathematical Society, 2021-11)
    Please read abstract in the article.
  • A closed graph theorem for order bounded operators 
    Van der Walt, Jan Harm (Routledge, 2016)
    The closed graph theorem is one of the cornerstones of linear functional analysis in Frechet spaces, and the extension of this result to more general topological vector spaces is a difficult problem comprising a great ...
  • Convergence of sequences of semi-continuous functions 
    Van der Walt, Jan Harm (Elsevier, 2012-04)
    In this paper we investigate how three well-known modes of convergence for (real-valued) functions are related to one another. In particular, we consider order convergence, pointwise convergence and continuous convergence ...
  • Differential chain of algebras of generalized functions 
    Agbebaku, Dennis Ferdinand; Van der Walt, Jan Harm (University of Novi Sad, Serbia, 2022)
    In this paper, it is shown how the spaces of generalized functions associated with the construction of the generalized solution for nonlinear partial differential equations through the order completion method using convergence ...
  • Generalized solutions of systems of nonlinear partial differential equations 
    Van der Walt, Jan Harm (University of Pretoria, 2009-06-02)
    In this thesis, we establish a general and type independent theory for the existence and regularity of generalized solutions of large classes of systems of nonlinear partial differential equations (PDEs). In this regard, ...
  • Limits of vector lattices 
    Van Amstel, Sarel Jakobus van der Walt; Van der Walt, Jan Harm (Elsevier, 2024-03)
    Please read abstract in the article.
  • Net convergence structures with applications to vector lattices 
    O’Brien, M.; Troitsky, V.G.; Van der Walt, Jan Harm (NISC (Pty) Ltd and Informa UK Limited (trading as Taylor & Francis Group), 2023)
    Convergence is a fundamental topic in analysis that is most commonly modeled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a ...
  • The order bidual of C(X) for a real compact space 
    De Jeu, Marcel; Van der Walt, Jan Harm (NISC (Pty) Ltd and Informa UK Limited (trading as the Taylor & Francis Group), 2024)
    Please read abstract in the article.
  • The order completion method : a differential-algebraic representation 
    Agbebaku, Dennis Ferdinand; Van der Walt, Jan Harm (University of Novi Sad, Serbia, 2017-04-18)
    This paper deals with an interpretation of the Order Completion Method for systems of nonlinear partial differential equations (PDEs) in terms of suitable differential algebras of generalized functions. In particular, ...
  • The order completion method for systems of nonlinear PDEs: solutions of initial value problems 
    Van der Walt, Jan Harm; Stanek, Svatoslav (Hindawi Publishing Corporation, 2013)
    We present an existence result for generalized solutions of initial value problems obtained through the order completion method. The solutions we obtain satisfy the initial condition in a suitable extended sense, and each ...
  • Order convergence on Archimedean vector lattices and applications 
    Van der Walt, Jan Harm (University of Pretoria, 2007-05-15)
    We study the order convergence of sequences on a vector lattice. It is shown that this mode of convergence is induced by a convergence structure. One such a convergence structure is defined and its properties are studied. ...
  • Solutions of smooth nonlinear partial differential equations 
    Van der Walt, Jan Harm; Clark, Stephen (Hindawi Publishing Corporation, 2011-04-15)
    The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations PDEs . Recently, ...