| 1. |
- Menden-Deuer, S., et al.
(författare)
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Biodiversity of marine microbes is safeguarded by phenotypic heterogeneity in ecological traits
- 2021
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Ingår i: Plos One. - : Public Library of Science (PLoS). - 1932-6203. ; 16:8
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Tidskriftsartikel (refereegranskat)abstract
- Why, contrary to theoretical predictions, do marine microbe communities harbor tremendous phenotypic heterogeneity? How can so many marine microbe species competing in the same niche coexist? We discovered a unifying explanation for both phenomena by investigating a non-cooperative game that interpolates between individual-level competitions and species-level outcomes. We identified all equilibrium strategies of the game. These strategies represent the probability distribution of competitive abilities (e.g. traits) and are characterized by maximal phenotypic heterogeneity. They are also neutral towards each other in the sense that an unlimited number of species can co-exist while competing according to the equilibrium strategies. Whereas prior theory predicts that natural selection would minimize trait variation around an optimum value, here we obtained a mathematical proof that species with maximally variable traits are those that endure. This discrepancy may reflect a disparity between predictions from models developed for larger organisms in contrast to our microbe-centric model. Rigorous mathematics proves that phenotypic heterogeneity is itself a mechanistic underpinning of microbial diversity. This discovery has fundamental ramifications for microbial ecology and may represent an adaptive reservoir sheltering biodiversity in changing environmental conditions.
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| 2. |
- Nursultanov, Medet, 1990, et al.
(författare)
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Evolution of Time-Harmonic Electromagnetic and Acoustic Waves Along Waveguides
- 2018
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Ingår i: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 90:5
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Tidskriftsartikel (refereegranskat)abstract
- We study time-harmonic electromagnetic and acoustic waveguides, modeled by an infinite cylinder with a non-smooth cross section. We introduce an infinitesimal generator for the wave evolution along the cylinder and prove estimates of the functional calculi of these first order non-self adjoint differential operators with non-smooth coefficients. Applying our new functional calculus, we obtain a one-to-one correspondence between polynomially bounded time-harmonic waves and functions in appropriate spectral subspaces.
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| 3. |
- Nursultanov, Medet, 1990
(författare)
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Spectral properties of the Schrodinger operator with delta-distribution
- 2016
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Ingår i: Mathematical Notes of the Academy of Sciences of the USSR. - : Pleiades Publishing Ltd. - 0001-4346 .- 1573-8876. ; 100:1-2, s. 263-275
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Tidskriftsartikel (refereegranskat)abstract
- For the one-dimensional Schrodinger operator with delta-interactions, two-sided estimates of the distribution function of the eigenvalues and a criterion for the discreteness of the spectrum in terms of the Otelbaev function are obtained. A criterion for the resolvent of the Schrodinger operator to belong to the class S (p) is established.
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| 4. |
- Rowlett, Julie, 1978, et al.
(författare)
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How to hear the corners of a drum
- 2019
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Ingår i: Matrix Annals. - Cham : Springer International Publishing. ; 2017, s. 243-278, s. 243-278
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Konferensbidrag (refereegranskat)abstract
- We prove that the existence of corners in a class of planar domain, which includes all simply connected polygonal domains and all smoothly bounded domains, is a spectral invariant of the Laplacian with both Neumann and Robin boundary conditions. The main ingredient in the proof is a locality principle in the spirit of Kac’s “principle of not feeling the boundary,” but which holds uniformly up to the boundary. Albeit previously known for Dirichlet boundary condition, this appears to be new for Robin and Neumann boundary conditions, in the geometric generality presented here. For the case of curvilinear polygons, we describe how the same arguments using the locality principle are insufficient to obtain the analogous result. However, we describe how one may be able to harness powerful microlocal methods and combine these with the locality principles demonstrated here to show that corners are a spectral invariant; this is current work-in-progress (Nursultanov et al., Preprint).
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