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• 1.
Danderyds Gymnasium, Danderyd, Sweden.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Umeå University, Umeå, Sweden. Uppsala University, Uppsala, Sweden.
Semi-Bloch Functions in Several Complex Variables2016In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 26, no 1, p. 463-473Article in journal (Refereed)

Let M be an n-dimensional complex manifold. A holomorphic function f:M→C is said to be semi-Bloch if for every λ∈C the function (Formula presented.) is normal on M. We characterize semi-Bloch functions on infinitesimally Kobayashi non-degenerate M in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.

• 2.
Danderyd gymnasium.
Mälardalen University, School of Education, Culture and Communication. Umeå University. Uppsala University.
Semi-Bloch functions in several complex variables2013Report (Other academic)

Let $M$ be an $n$-dimensional complex manifold. A holomorphic function $f:M\to \mathbb C$ is said to be semi-Bloch if for every $\lambda\in \mathbb C$ the function $g_\lambda=\exp(\lambda f(z))$ is normal on $M$. We characterise Semi-Bloch functions on infinitesimally Kobayashi non-degenerate $M$ in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.

• 3. Brännström, Åke
Umeå universitet.
Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces2011In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, no 3, p. 575-592Article in journal (Refereed)
• 4.
Umeå University.
Umeå University. Umeå University.
On the convergence of the Escalator Boxcar Train2013In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 51, no 6, p. 3213-3231Article in journal (Refereed)

The Escalator Boxcar Train (EBT) is a numerical method that is widely used in theoretical biology to investigate the dynamics of physiologically structured population models, i.e., models in which individuals differ by size or other physiological characteristics. The method was developed more than two decades ago, but has so far resisted attempts to give a formal proof of convergence. Using a modern framework of measure-valued solutions, we investigate the EBT method and show that the sequence of approximating solution measures generated by the EBT method converges weakly to the true solution measure under weak conditions on the growth rate, birth rate, and mortality rate. In rigorously establishing the convergence of the EBT method, our results pave the way for wider acceptance of the EBT method beyond theoretical biology and constitutes an important step towards integration with established numerical schemes.

• 5.
Umeå University.
An equivalence to the Gleason problem2010In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 370, no 2, p. 373-378Article in journal (Refereed)

In this article we study the Gleason problem locally. A new method for solving the Gleason A problem is presented. This is done by showing an equivalent statement to the Gleason A problem. In order to prove this statement, necessary and a sufficient conditions for a bounded domain to have the Gleason A property are found. Also an example of a bounded but not smoothly-bounded domain in Cn is given, which satisfies the sufficient condition at the origin, and hence has the Gleason A property there.

• 6.
Umeå universitet.
Analytic properties in the spectrum of certain Banach algebras2009In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 261, no 1, p. 189-200Article in journal (Refereed)
• 7.
Mälardalen University, School of Education, Culture and Communication.
Ideals and boundaries in Algebras of Holomorphic functions2006Doctoral thesis, monograph (Other academic)
• 8.
Umeå universistet.
Nebenhülle and the Gleason problem2010In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 138, no 1, p. 267-273Article in journal (Refereed)

This article concerns the Gleason property as a local phenomenon. We prove that there always exists an open set where the domain D (sic) C(2) has the Gleason beta property whenever the boundary of the Nebenhulle of D coincides with a C(2) smooth part of the boundary bD; here beta is either one of the Banach algebras, H(infinity) or A. As an easy consequence of this, we see that if the extremal boundary points are C(2)-smooth, then D has the Gleason beta property close to those points. Also a partial derivative-problem for locally supported forms is solved.

• 9.
Umeå universitet.
Trivial generators for nontrivial fibres2008In: MATHEMATICA BOHEMICA, ISSN 0862-7959, Vol. 133, no 2, p. 121-131Article in journal (Refereed)
• 10.
Umeå University.
Umeå University. Umeå University.
Spectrum of certain Banach algebras and DBAR-problems2007In: Annales Polonici Mathematici, ISSN 0066-2216, Vol. 90, no 1, p. 51-58Article in journal (Refereed)

We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂−-problems with certain estimates can be solved. We show that the projection of the spectrum onto Cn equals Ω−− and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.

• 11.
Umeå university.
Umeå university.
A note on B-envelope of holomorphy and B-extendable domains2008In: Complex Variables and Elliptic Equations, ISSN 1747-6933, Vol. 53, no 4, p. 307-309Article in journal (Refereed)
• 12.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Umea Univ, Dept Math & Math Stat, SE-90187 Umeå, Sweden.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Umea Univ, Dept Math & Math Stat, SE-90187 Umea, Sweden. Univ New South Wales, Evolut & Ecol Res Ctr, Sydney, NSW 2052, Australia.;Univ New South Wales, Sch Biol Earth & Environm Sci, Sydney, NSW 2052, Australia.;Macquarie Univ, Dept Biol Sci, Sydney, NSW 2109, Australia.. Macquarie Univ, Dept Biol Sci, Sydney, NSW 2109, Australia.. Umea Univ, Dept Math & Math Stat, SE-90187 Umea, Sweden.;Int Inst Appl Syst Anal, Evolut & Ecol Program, A-2361 Laxenburg, Austria..
Branch Thinning and the Large-Scale, Self-Similar Structure of Trees2018In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 192, no 1, p. E37-E47Article in journal (Refereed)

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.

• 13.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Innovation, Design and Engineering, Embedded Systems. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Solution of Two-Dimensional Electromagnetic Scattering Problem by FDTD with Optimal Step Size, Based on a Semi-Norm Analysis2014In: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2014, p. 683-690Conference paper (Refereed)

To solve the electromagnetic scattering problem in two dimensions, the Finite Difference Time Domain (FDTD)method is used. The order of convergence of the FDTD algorithm, solving the two-dimensional Maxwell’s curl equations,is estimated in two different computer implementations: with and without an obstacle in the numerical domain of the FDTDscheme. This constitutes an electromagnetic scattering problem where a lumped sinusoidal current source, as a source ofelectromagnetic radiation, is included inside the boundary. Confined within the boundary, a specific kind of AbsorbingBoundary Condition (ABC) is chosen and the outside of the boundary is in form of a Perfect Electric Conducting (PEC)surface. Inserted in the computer implementation, a semi-norm has been applied to compare different step sizes in the FDTDscheme. First, the domain of the problem is chosen to be the free-space without any obstacles. In the second part of thecomputer implementations, a PEC surface is included as the obstacle. The numerical instability of the algorithms can berather easily avoided with respect to the Courant stability condition, which is frequently used in applying the general FDTDalgorithm.

• 14.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Innovation, Design and Engineering, Embedded Systems. Mälardalen University, School of Innovation, Design and Engineering, Embedded Systems. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
GPU Implementation of a Biological Electromagnetic Scattering Problem by FDTD2015In: 16th ASMDA 2015 Conference and Demographics 2015 Proceedings, 2015Conference paper (Refereed)
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