| 1. |
- Samuelsson Kalm, Håkan, 1976, et al.
(författare)
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Adjunction for the Grauert-Riemenschneider canonical sheaf and extension of L^2-cohomology classes
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In the present paper, we derive an adjunction formula for the Grauert-Riemenschneider canonical sheaf of a singular hypersurface V in a complex manifold M. This adjunction formula is used to study the problem of extending L2-cohomology classes of dbar-closed forms from the singular hypersurface V to the manifold M in the spirit of the Ohsawa-Takegoshi-Manivel extension theorem. We do that by showing that our formulation of the L2-extension problem is invariant under bimeromorphic modifications, so that we can reduce the problem to the smooth case by use of an embedded resolution of V in M. The smooth case has recently been studied by Berndtsson.
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| 2. |
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| 3. |
- Eriksson, T., et al.
(författare)
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Successive Encoding of Correlated Sources
- 1982
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The encoding of a discrete memoryless multiple source for reconstruction of a sequence with is considered. We require that the encoding should be such that is encoded first without any consideration of , while in a seeond part of the encoding this latter sequence is encoded based on knowledge of the outcome of the first encoding. The resulting scheme is called successive encoding. We find general outer and inner bounds for the corresponding set of achievable rates along with a complete single letter characterization for the special case . Comparisons with the Slepian-Wolf problem [3] and the Ahlswede-Körner-Wyner side information problem [2 ], [9) are carried out.
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| 4. |
- Nyström, Peter, 1959, et al.
(författare)
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Hur samstämmiga är svenska styrdokument och nationella prov med ramverk och uppgifter i TIMSS Advanced 2015?
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- TIMSS Advanced (Trends in Mathematics and Science Study ) är en internationell studie som undersöker gymnasieelevers kunskaper i avancerad matematik och fysik. TIMSS Advanced har genomförts tre gånger, 1995, 2008 och 2015, och Sverige har deltagit varje gång. I 2015 års studie deltog svenska elever i årskurs 3 på naturvetenskaps- och teknikprogrammet som slutfört eller håller på att slutföra kursen matematik 4 respektive fysik 2. Studien ger möjlighet att analysera förändringar i motsvarande elevgruppers kunskaper över tid inom dessa områden, men också möjlighet att jämföra svenska resultat med resultat från andra länder. TIMSS Advanced 2015 har genomförts av Skolverket i samarbete med Nationellt Centrum för Matematikutbildning (NCM) vid Göteborgs universitet. Skolverket har sammanställt en nationell huvudrapport med resultaten från TIMSS Advanced 2015. En viktig utgångspunkt för tolkning och analys av resultaten är att veta i vilken utsträckning svenska elever fått möjlighet att lära sig det som prövas i TIMSS Advanced. I denna rapport analyseras därför samstämmigheten mellan TIMSS Advanced 2015 och svenska ämnesplaner, nationella prov och bedömningsstöd. Mot bakgrund av ämnenas kopplingar mellan varandra genomförs också en analys som särskilt fokuserar på inslaget av matematik i fysikuppgifterna.
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| 5. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
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Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
- 2009
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This study provides an account of how it is possible to work with mathematical models and modelling at the Swedish upper secondary level. It shows how a researcher and two teachers, departing from what is written in the mathematics curriculum document about mathematical models and modelling and the teachers’ mathematics teaching practices, collaborate to design and develop two so called modelling modules. These two modules designed for, and integrated in, the Mathematics C and Mathematics D course respectively, were implemented in the teachers’ classes and the whole process was evaluated. The students’ experiences of working with the modules were also investigated.The conceptual framework used to study this process of design, implementation, and evaluation is built up of design-based research methodology, cultural historical activity theory (CHAT), and co-learning agreement between the researcher and the participants.The teachers as well as the students expressed that they enjoyed working on the modules and found the experience positive and rewarding. However, some doubt concerning the learning outcome on behalf of the students were raised among the teachers, and the wish to incorporate more scheduled time into the modules was expressed by the students.It is concluded that the participating teachers could had difficulties in expressing a clear conception of the notions of mathematical models or modelling and no affirmative conclusions could be drawn that the participation of the teachers changed their attitudes towards mathematical models and modelling. The designing process was often was restrained by constraints originating from the local school context, and working with modelling highlights many systemic tensions in the established school practice. Also, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.
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| 6. |
- Bergman Ärlebäck, Jonas, 1972-
(författare)
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Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
- 2009
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Denna rapport studerar hur begreppen matematisk modell och matematisk modellering behandlats i kursplanerna i matematik för motsvarande svenska gymnasieskolans naturvetenskapliga program mellan åren 1965 och 2000. En översikt över sex kursplaners olika form och innehåll ges och tre olika analyser på tre olika nivåer genomförs; en innehållsanalys, en kvalitativ analys, och en analys som beaktar relationen mellan begreppen modellering, tillämpningar och problemlösning. Analysen visar att matematiska modeller och modellering förekommit implicit sedan kursplanen från 1965, men att begreppen främst i de två senaste kursplanerna lyfts fram explicit och fått en central position i kursplanerna. I den nuvarande kursplanen Gy2000 framgår att matematiska modeller kan tolkas både som ett undervisningsmål i sig och som ett didaktiskt hjälpmedel att lära matematik.
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| 7. |
- Berntsson, Fredrik, et al.
(författare)
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Numerical Solution of the Cauchy Problem for the Helmholtz Equation
- 2014
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The Cauchy problem for the Helmholtz equation appears in applications related to acoustic or electromagnetic wave phenomena. The problem is ill–posed in the sense that the solution does not depend on the data in a stable way. In this paper we give a detailed study of the problem. Specifically we investigate how the ill–posedness depends on the shape of the computational domain and also on the wave number. Furthermore, we give an overview over standard techniques for dealing with ill–posed problems and apply them to the problem.
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| 8. |
- Frenander, Hannes, et al.
(författare)
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Spurious solutions for the advection-diffusion equation using wide stencils for approximating the second derivative.
- 2014
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A one dimensional steady-state advection-diffusion problem using summation-by-parts operators has been investigated. For approximating the second derivative, a wide stencil has been used, which has spurious, oscillating, modes for all mesh-sizes. We show that the size of the spurious modes are equal to the size of the truncation error for a stable approximation. The theoretical results are veried with numerical experiments.
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| 9. |
- Ghasemi Zinatabadi, Fatemeh, 1988-, et al.
(författare)
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An Energy Stable Coupling Procedure for the Compressible and Incompressible Navier-Stokes Equations
- 2019
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Ingår i: Journal of Computational Physics. - Linköping : Linköping University Electronic Press. - 0021-9991 .- 1090-2716. ; 396, s. 280-302
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The coupling of the compressible and incompressible Navier-Stokes equations is considered. Our ambition is to take a first step towards a provably well posed and stable coupling procedure. We study a simplified setting with a stationary planar interface and small disturbances from a steady background ow with zero velocity normal to the interface.The simplified setting motivates the use of the linearized equations, and we derive interface conditions such that the continuous problem satisfy an energy estimate. The interface conditions can be imposed both strongly and weakly. It is shown that the weak and strong interface imposition produce similar continuous energy estimates.We discretize the problem in time and space by employing finite difference operators that satisfy a summation-by-parts rule. The interface and initial conditions are imposed weakly using a penalty formulation. It is shown that the results obtained for the weak interface conditions in the continuous case, lead directly to stability of the fully discrete problem.
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| 10. |
- Ghasemi Zinatabadi, Fatemeh, 1988-, et al.
(författare)
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On conservation and dual consistency for summation-by-parts based approximations of parabolic problems
- 2019
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We consider the coupling of parabolic problems discretized using difference operators on summation-by-parts (SBP) form with interface conditions imposed weakly. In, it was shown that conservation and dual consistency are equivalent concepts for linear conservation laws. Here, we show that these concepts are equivalent also for symmetric or symmetrizable parabolic problems, exemplified by the heat equation. We rewrite the heat equation as first order system as in the local discontinuous Galerkin method and show the equivalence of dual consistency and conservation for both the first and second order forms.
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