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How to Be Positive in Natural Sciences?

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Positivity and its Applications

Part of the book series: Trends in Mathematics ((TM))

Abstract

In many fields of science there is the chicken or the egg dispute—whether applications drive theory, or the theory makes applications possible. Actually, in mathematics, there is another option, when certain concepts existed both in applications and in pure theory, happily oblivious of each other. An example of such concepts are order and positivity which, together with compactness, created an important bridge between the finite and infinite dimensional spaces, allowing for a number of concepts from the undergraduate calculus, like the Bolzano–Weierstrass theorem, or the Lyapunov stability theorems, to be applied in probability theory and partial differential equations, before finding their place in the abstract Banach space theory.

In this paper we will illustrate how positivity methods can create such a bridge between finite and infinite dimensional population models, and what are potential pitfalls, within the framework of the theory of semigroups of operators. This paper is based on the lecture given at the conference Positivity X, Pretoria, 8–12 July 2019.

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Authors and Affiliations

  1. University of Pretoria, Hatfield, Pretoria, South Africa

    Jacek Banasiak

  2. Technical University of Łódź, Łódź, Poland

    Jacek Banasiak

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  1. Jacek Banasiak
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Correspondence to Jacek Banasiak .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Eder Kikianty

  2. Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Mokhwetha Mabula

  3. Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Miek Messerschmidt

  4. Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Jan Harm van der Walt

  5. Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Marten Wortel

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Banasiak, J. (2021). How to Be Positive in Natural Sciences?. In: Kikianty, E., Mabula, M., Messerschmidt, M., van der Walt, J.H., Wortel, M. (eds) Positivity and its Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-70974-7_4

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