| 1. |
- Bona, J L, et al.
(författare)
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Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
- 2005
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Ingår i: Annales de L'Institut Henri Poincaré. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449. ; 22:6, s. 783-797
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Tidskriftsartikel (refereegranskat)abstract
- The generalized Korteweg-de Vries equation has the property that solutions with initial data that are analytic in a strip in the complex plane continue to be analytic in a strip as time progresses. Established here are algebraic lower bounds on the possible rate of decrease in time of the uniform radius of spatial analyticity for these equations. Previously known results featured exponentially decreasing bounds.
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| 2. |
- Ehrnström, Mats, et al.
(författare)
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On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation
- 2019
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Ingår i: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 36:6, s. 1603-1637
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Tidskriftsartikel (refereegranskat)abstract
- We consider the Whitham equation u t +2uu x +Lu x =0, where L is the nonlocal Fourier multiplier operator given by the symbol m(ξ)=tanhξ/ξ. G. B. Whitham conjectured that for this equation there would be a highest, cusped, travelling-wave solution. We find this wave as a limiting case at the end of the main bifurcation curve of P-periodic solutions, and give several qualitative properties of it, including its optimal C 1/2 -regularity. An essential part of the proof consists in an analysis of the integral kernel corresponding to the symbol m(ξ), and a following study of the highest wave. In particular, we show that the integral kernel corresponding to the symbol m(ξ) is completely monotone, and provide an explicit representation formula for it. Our methods may be generalised.
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| 3. |
- Helsing, Johan, et al.
(författare)
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Classification of spectra of the Neumann–Poincaré operator on planar domains with corners by resonance
- 2017
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Ingår i: Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 34:4, s. 991-1011
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Tidskriftsartikel (refereegranskat)abstract
- We study spectral properties of the Neumann–Poincaré operator on planar domains with corners with particular emphasis on existence of continuous spectrum and pure point spectrum. We show that the rate of resonance at continuous spectrum is different from that at eigenvalues, and then derive a method to distinguish continuous spectrum from eigenvalues. We perform computational experiments using the method to see whether continuous spectrum and pure point spectrum appear on domains with corners. For the computations we use a modification of the Nyström method which makes it possible to construct high-order convergent discretizations of the Neumann–Poincaré operator on domains with corners. The results of experiments show that all three possible spectra, absolutely continuous spectrum, singularly continuous spectrum, and pure point spectrum, may appear depending on domains. We also prove rigorously two properties of spectrum which are suggested by numerical experiments: symmetry of spectrum (including continuous spectrum), and existence of eigenvalues on rectangles of high aspect ratio.
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| 4. |
- Wahlberg, Karin, et al.
(författare)
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Maternal polymorphisms in glutathione-related genes are associated with maternal mercury concentrations and early child neurodevelopment in a population with a fish-rich diet
- 2018
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Ingår i: Environment International. - : Elsevier BV. - 0160-4120 .- 1873-6750. ; 115, s. 142-149
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Tidskriftsartikel (refereegranskat)abstract
- Introduction: Glutathione (GSH) pathways play a key role the metabolism and elimination of the neurotoxicant methylmercury (MeHg). We hypothesized that maternal genetic variation linked to GSH pathways could influence MeHg concentrations in pregnant mothers and children and thereby also affect early life development. Methods: The GCLM (rs41303970, C/T), GCLC (rs761142, T/G) and GSTP1 (rs1695, A/G) polymorphisms were genotyped in 1449 mothers in a prospective study of the Seychellois population with a diet rich in fish. Genotypes were analyzed in association with maternal hair and blood Hg, fetal blood Hg (cord blood Hg), as well as children's mental (MDI) and motor development (PDI; MDI and PDI assessed by Bayley Scales of Infant Development at 20 months). We also examined whether genotypes modified the association between Hg exposure and developmental outcomes. Results: GCLC rs761142 TT homozygotes showed statistically higher mean maternal hair Hg (4.12 ppm) than G carriers (AG 3.73 and GG 3.52 ppm) (p = 0.037). For the combination of GCLC rs761142 and GCLM rs41303970, double homozygotes TT + CC showed higher hair Hg (4.40 ppm) than G + T carriers (3.44 ppm; p = 0.018). No associations were observed between GSTP1 rs1695 and maternal hair Hg or between any genotypes and maternal blood Hg or cord blood Hg. The maternal GSTP1 rs1695 rare allele (G) was associated with a lower MDI among children (β = −1.48, p = 0.048). We also observed some interactions: increasing Hg in maternal and cord blood was associated with lower PDI among GCLC rs761142 TT carriers; and increasing Hg in hair was associated with lower MDI among GSTP1 rs1695 GG carriers. Conclusions: Maternal genetic variation in genes involved in GSH synthesis is statistically associated with Hg concentrations in maternal hair, but not in maternal or fetal blood. We observed interactions that suggest maternal GSH genetics may modify associations between MeHg exposure and neurodevelopmental outcomes.
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