| 1. |
- Källström, Rolf, et al.
(författare)
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Hilbert series of modules over Lie algebroids
- 2015
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Ingår i: Journal of Algebra. - : Elsevier. - 0021-8693 .- 1090-266X. ; 432, s. 129-184
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Tidskriftsartikel (refereegranskat)abstract
- We consider modules M over Lie algebroids gA which are of finite type over a local noetherian ring A. Using ideals J ⊂ A such that gA ·J ⊂ J and the length ℓgA (M/JM) < ∞ we can define in a natural way the Hilbert series of M with respect to the defining ideal J. This notion is in particular studied for modules over the Lie algebroid of k-linear derivations gA = TA(I) that preserve an ideal I ⊂ A, for example when A = On, the ring of convergent power series. Hilbert series over Stanley-Reisner rings are also considered.
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| 2. |
- Barrera, Tony, et al.
(författare)
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Vectorized table driven algorithms for double precision elementary functions using Taylor expansions
- 2009
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Ingår i: APLIMAT 8th international conference. ; 2, s. 171-178
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Konferensbidrag (refereegranskat)abstract
- This paper presents fast implementations of the inverse square root and arcsine, both in double precision. In single precision it is often possible to use a small table and one ordinary Newton-Raphson iteration to compute elementary functions such as the square root. In double precision a substantially larger table is necessary to obtain the desired precision, or, if a smaller table is used, the additional Newton-Raphson iterations required to obtain the precision often requires the evaluation of other expensive elementary functions. Furthermore, large tables use a lot of the cash memory that should have been used for the application code.Obtaining the desired precision using a small table can instead be realised by using a higher order method than the second order Newton-Raphson method. A generalization of Newton's method to higher order is Householder's method, which unfortunately often results in very complicated expressions requiring many multiplications, additions, and even divisions.We show how a high-order method can be used, which only requires a few extra additions and multiplications for each degree of higher order. The method starts from the Taylor expansion of the difference of the value of the elementary function and a starting guess value for each iteration. If the Taylor series is truncated after the second term, ordinary Newton iterations are obtained. In several cases it is possible to algebraically simplify the difference between the true value and the starting guess value. In those cases we show that it is advantageous to use the Taylor series to higher order to obtain the fast convergent method. Moreover, we will show how the coefficients of a Chebyshev polynomial can be fitted to give as little error as possible for the functions close to zero and in the same time reduce the terms in the Taylor expansion.In the paper we benchmark two example implementations of the method on the x86_64 architecture. The first is the inverse square root, where the actual table (to 12 bit precision) is provided by the processor hardware. The inverse square root is important in many application programs, including computer graphics, and explicit particle simulation codes, for instance the Monte Carlo and Molecular Dynamics methods of statistical mechanics. The other example is the arcsine function, which has a slow converging Taylor expansion and where no tables are provided by the hardware. The vectorized versions of the implementations of the inverse square root are 3.5 times faster than compiled code on the Athlon64 and about 5 times faster on the Core 2. The scalar version of the arcsine function is, depending on order and table size, between 2 and 3 times faster than the compiled code, and the vectorized version is between 3 and 4 times faster on the Athlon64, while it is between 4 and 5 times faster than the compiled version on the Core 2.
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| 3. |
- Podlipenko, Yury, et al.
(författare)
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Guaranteed Estimates of Functionals from Solutions and Data of Interior Maxwell Problems Under Uncertainties
- 2013
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Ingår i: Springer Proceedings in Mathematics & statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. ; 52, s. 135-167
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Tidskriftsartikel (refereegranskat)abstract
- We are looking for linear with respect to observations optimal estimates of solutions and right-hand sides of Maxwell equations called minimax or guaranteed estimates. We develop constructive methods for finding these estimates and estimation errors which are expressed in terms of solutions to special variational equations and prove that Galerkin approximations of the obtained variational equations converge to their exact solutions. © Springer International Publishing Switzerland 2013.
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| 4. |
- Smirnov, Alexander, et al.
(författare)
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Modeling of Electromagnetic Wave Propagation in Guides with Inhomogeneous Dielectric Inclusions
- 2013
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Ingår i: Inverse Problems and Large-Scale Computations. - Cham : Springer. - 9783319006604 ; 52, s. 113-118
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Konferensbidrag (refereegranskat)abstract
- We consider scattering in the time domain of electromagnetic waves from inhomogeneous dielectric inclusions in a 3D waveguide of rectangular cross section. All electromagnetic field components are calculated, and transport of energy in the guide is investigated using finite difference time domain (FDTD) method in different frequency ranges. An efficient 3D FDTD EMWSolver3D solver for the nonstationary Maxwell equation system is used. The model computations are performed for the H10-mode scattering from parallelepiped-shaped dielectric inclusions. Attenuation and propagation factors are calculated for the transmitted modes and field distributions are visualized. The present method can be used for a wide class of waveguide problems that meet substantial difficulties as far as numerical solution by conventional FDTD methods is concerned due to complex geometries or computational requirements. The solver employs algorithms of parallel computations and is implemented on supercomputers of last generation for solving large-scale problems with characteristic matrix dimensions achieving 1012.
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| 5. |
- Kellner, Eva, et al.
(författare)
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The school–university intersection as a professional learning arena: evaluation of a two-year action research project
- 2020
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Ingår i: Teacher Development. - : Taylor & Francis. - 1366-4530 .- 1747-5120. ; 24:3, s. 366-383
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Tidskriftsartikel (refereegranskat)abstract
- This article presents the evaluation of a two-year action research project in biology and mathematics teaching involving a primary school and a university in Sweden. The aim of the study was to contribute knowledge about a school–university intersection as a professional learning arena. The teachers’ conceptions about the project implementation, the impact on their learning, teaching practices and pupil learning were made explicit by focus group interview. The evaluation revealed that several motivating factors in this specific learning community – the relevance of the project and connection to the continuing education course, mentors from university, planning tools and time for collaboration – were critical for project implementation and for professional learning to occur. Furthermore, it indicated how teacher learning and teaching practices were related to pupil learning in the professional learning community. The results are also discussed in the light of new research on teachers’ work identity and self-reported health.
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| 6. |
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| 7. |
- Cretois, Remi, et al.
(författare)
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The vanishing cycles of curves in toric surfaces I
- 2018
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Ingår i: Compositio Mathematica. - : Cambridge University Press. - 0010-437X .- 1570-5846. ; 154:8, s. 1659-1697
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Tidskriftsartikel (refereegranskat)abstract
- This article is the first in a series of two in which we study the vanishing cycles of curves in toric surfaces. We give a list of possible obstructions to contract vanishing cycles within a given complete linear system. Using tropical means, we show that any non-separating simple closed curve is a vanishing cycle whenever none of the listed obstructions appears.
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| 8. |
- Kellner, Eva, 1961-, et al.
(författare)
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Kollegialt lärande om progression i biologi- och matematikundervisning
- 2014
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Ingår i: Nämnaren. - Göteborg : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; 41:4, s. 3-8
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Tidskriftsartikel (populärvet., debatt m.m.)abstract
- Kan man utveckla undervisningen i biologi och matematik samtidigt? Ett lärarlag samarbetade med två forskare för att undersöka och svara på frågan. De undervisningsområden som valdes ut handlar om ekosystem och övergången mellan aritmetik och algebra.
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| 9. |
- Lang, Lionel, et al.
(författare)
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On the Number of Intersection Points of the Contour of an Amoeba with a Line
- 2021
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Ingår i: Indiana University Mathematics Journal. - : Indiana University Mathematics Journal. - 0022-2518 .- 1943-5258. ; 70:4, s. 1335-1353
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Tidskriftsartikel (refereegranskat)abstract
- In this note, we investigate the maximal number of intersection points of a line with the contour of a hypersurface amoeba in R-n. We define the latter number to be the R-degree of the contour. We also investigate the R-degree of related sets such as the boundary of an amoeba and the amoeba of the real part of a hypersurface defined over R. For all these objects, we provide bounds for the respective R-degrees.
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| 10. |
- Johansson, Anders, et al.
(författare)
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Countable state shifts and uniqueness of g-measures
- 2007
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Ingår i: American Journal of Mathematics. - : Project Muse. - 0002-9327 .- 1080-6377. ; 129:6, s. 1501-1511
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a new approach to studying g-measures which is based upon local absolute continuity. We extend an earlier result that square summability of variations of g ensures uniqueness of g-measures. The first extension is to the case of countably many symbols. The second extension is to some cases where g >= 0, relaxing the earlier requirement that inf g > 0.
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