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  • 1.
    Hellström, Lars
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Matematiska institutionen. Mittag Leffler Inst, Djursholm, Sweden; Lund Univ, Ctr Math Sci, S-22100 Lund, Sweden .
    Rewriting in operads and PROPs2006Inngår i: Journal of nonlinear mathematical physics, Luleå: Norbert Euler , 2006, Vol. 13 S, s. 66-75Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper is an informal collection of observations on how established rewriting techniques can be applied to or need to be adapted for use in non-associative algebras, operads, and PROPs.

  • 2.
    Hellström, Lars
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Matematiska institutionen.
    The Diamond Lemma for Power Series Algebras2002Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to power series rings. This generalisation makes it possible to treat problems in which there arise infinite descending chains. Several results in the literature are shown to be special cases of this diamond lemma and examples are given of interesting problems which could not previously be treated. One of these examples provides a general construction of a normed skew field in which a custom commutation relation holds.

    There is also a general result on the structure of totally ordered semigroups, demonstrating that all semigroups with an archimedean element has a (up to a scaling factor) unique order-preserving homomorphism to the real numbers. This helps analyse the concept of filtered structure. It is shown that whereas filtered structures can be used to induce pretty much any zero-dimensional linear topology, a real-valued norm suffices for the definition of those topologies that have a reasonable relation to the multiplication operation.

    The thesis also contains elementary results on degree (as of polynomials) functions, norms on algebras (in particular ultranorms), (Birkhoff) orthogonality in modules, and construction of semigroup partial orders from ditto quasiorders.

    Fulltekst (pdf)
    FULLTEXT01
  • 3.
    Hellström, Lars
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden.
    Carlsson, Linus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden.
    Falster, Daniel S.
    Westoby, Mark
    Brännström, Åke
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Branch Thinning and the Large-Scale, Self-Similar Structure of Trees2018Inngår i: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 192, nr 1, s. E37-E47Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Branch formation in trees has an inherent tendency toward exponential growth, but exponential growth in the number of branches cannot continue indefinitely. It has been suggested that trees balance this tendency toward expansion by also losing branches grown in previous growth cycles. Here, we present a model for branch formation and branch loss during ontogeny that builds on the phenomenological assumption of a branch carrying capacity. The model allows us to derive approximate analytical expressions for the number of tips on a branch, the distribution of growth modules within a branch, and the rate and size distribution of tree wood litter produced. Although limited availability of data makes empirical corroboration challenging, we show that our model can fit field observations of red maple (Acer rubrum) and note that the age distribution of discarded branches predicted by our model is qualitatively similar to an empirically observed distribution of dead and abscised branches of balsam poplar (Populus balsamifera). By showing how a simple phenomenological assumptionthat the number of branches a tree can maintain is limitedleads directly to predictions on branching structure and the rate and size distribution of branch loss, these results potentially enable more explicit modeling of woody tissues in ecosystems worldwide, with implications for the buildup of flammable fuel, nutrient cycling, and understanding of plant growth.

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