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A contemporary linear representation theory for ordinary differential equations: multilinear algebra in folded arrays (folarrs) perspective and its use in multidimensional case

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Abstract

In this paper, we extend the framework describing the probabilistic evolution of explicit unidimensional ODEs, which is described in the companion of this paper, to multidimensional cases. We show that an infinite set of linear ODEs accompanied by an initial condition (represented with an infinite vector) can also be constructed for the multidimensional cases. The principles that underly the construction of the equations and the truncated approximants of the solutions are the same. The crucial addition of this paper is the use of multiindex, folded and unfolded vectors and matrices. Unlike our earlier work on folded arrays, which relied on probabilistic principles of construction, in this work, we use a purely mathematical approach for the construction of the multidimensional structures. We provide a procedural description of how such constructions can be made.

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Authors and Affiliations

  1. İstanbul Teknik Üniversitesi Bilişim Enstitüsü, 34469, Maslak, Istanbul, Turkey

    Metin Demiralp

  2. Department of Psychology, University of Michigan, 1012 East Hall, 530 Church Street, Ann Arbor, MI, 41809-1043, USA

    Emre Demiralp

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  1. Metin Demiralp
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  2. Emre Demiralp
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Demiralp, M., Demiralp, E. A contemporary linear representation theory for ordinary differential equations: multilinear algebra in folded arrays (folarrs) perspective and its use in multidimensional case. J Math Chem 51, 38–57 (2013). https://doi.org/10.1007/s10910-012-0064-0

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  • DOI: https://doi.org/10.1007/s10910-012-0064-0

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