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• 1. Abramovich, S
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Some new Hermite-Hadamard and Fejer typeinequalities without convexity/concavityIn: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966Article in journal (Refereed)
• 2. Abravomich, S
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Rearrangements andJensen type inequalities related to convexity, superquadracity, strongconvexity and 1-quasiconvexityIn: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966Article in journal (Refereed)
• 3. Acedo, L.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
On the derivation of a high-velocity tail from the Boltzmann-Fokker-Planck equation for shear flow2002In: J. Statist. Phys, Vol. 109:5-6Article in journal (Refereed)
• 4. Ackelh, A.S.
Institute for Complex Molecular Systems & Centre for Analysis, Scientific computing and Applications, Eindhoven University of Technology.
Preface to "modeling with measures"2015In: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 12, no 2Article in journal (Refereed)
• 5.
University of Louisiana at Lafayette, USA.
University of Brescia, Italy. Team ACUMES, INRIA, France. Leiden University, The Netherlands. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Mathematical modeling with measures2019In: Nieuw Archief voor Wiskunde, ISSN 0028-9825, Vol. 20, no September, p. 218-220Article in journal (Refereed)
• 6.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
En Montessori-inspirerad pedagogik utmanar högpresterande elever matematiskt: En kvalitativ studie om vilka strategier lärare som använder en Montessori- inspirerad pedagogik i årskurs 1-3 anser utmanar och stimulerar högpresterande elever i matematik.2016Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis

Studiens syfte var att ta reda på vilka strategier lärare som använder en Montessori-inspirerad pedagogik anser stimulerar och utmanar högpresterande elever i matematik samt om de upplevde några svårigheter eller problem med att undervisa högpresterande elever i matematik. För att undersöka det har sex kvalitativa intervjuer genomförts med lärare som har varit eller som är verksamma i årskurserna 1-3. Resultatet av intervjuerna visar att lärarna har en gemensam uppfattning om att en Montessori-inspirerad pedagogik utmanar och stimulerar högpresterande elever i matematik eftersom grundtanken i Montessori-pedagogiken är "eleven i centrum". Det här innebär att lärarna måste utgå från varje elevs förutsättningar, behov och aktuella kunskapsnivå. I resultatet framkommer också att lärarna använder sig av olika strategier i form av matematikbok från en högre årskurs, special- och fördjupningsområden, åldersintegrering och lärande med flera sinnen för att stimulera och utmana de högpresterande eleverna matematiskt. Det framgår också i resultatet att lärarna inte upplever några större problem eller svårigheter i undervisningen av högpresterande elever i matematik. De belyser ändå att den egna matematiska kompetensen, tidsbrist och eget kontrollbehov ibland kan utgöra hinder för att stimulera och utmana de högpresterande eleverna tillräckligt. Utifrån studien kan man dra slutsatserna att lärare som använder en Montessori-inspirerad pedagogik lägger stor vikt vid att hitta rätt strategi för rätt elev, vilket bidrar till att de högpresterande eleverna får utmaning och stimulans. De olika hindren som lärarna belyser skulle kunna minskas med fortbildning och samarbete mellan årskurserna.

Matematikverkstad: hur kan lärare och elever arbeta där?2010Student paper other, 10 credits / 15 HE creditsStudent thesis

The starting point of this work has been to get knowledge about teachers working in a mathematical workshop with the students. I also wanted to investigate what students think about math, both within the workshop and in traditional teaching.

To achieve this I chose to interview a teacher in charge within the framework of a mathematical workshop, and six students in the 5th grade. I also did a lesson observation with the purpose to see how well the teacher’s tutoring agrees with the results of the interview.

In this study I have discovered that the lessons in the mathematical workshop are planned after what the students are working with in the textbook. The teacher opens the lessons with the whole class and then splits it up in groups. In the interview the respondent conveys the importance of discussions among the students where they can explain their thoughts, especially for the weaker students that, thanks to the discussions are able to show their knowledge more. This is something I did not see during my lesson observation, however. The students also seemed to miss this when I spoke to them in the interview. They describe that they cannot see the connection between what they learn in the workshop and the textbook.

• 8.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Nyanlända elevers möte med textbaserade matematikuppgifter: En studie om hur lärare och studiehandledare för åk 1-3 undervisar nyanlända elever i textbaserade matematikuppgifter, samt deras syn på elevernas utmaningar.2019Independent thesis Basic level (degree of Bachelor), 20 credits / 30 HE creditsStudent thesis

Abstract

The purpose of this study is to investigate how teachers and study supervisors for year 1-3 teach newly arrived students’ in mathematical word problems and

their views on the students’ challenges. The method used for this study is

qualitative semi-structures interviews aimed at teachers and study supervisors. The study is based upon ten interviews, six teachers and four study supervisors. The sociocultural perspective on learning is used, as this perspective is implemented in Swedish school system.

The result of the study show the importance of the Swedish language for newly arrived students to be able to take on mathematical word problems. Furthermore, the result shows that the difficulties for newly arrived students lie mainly in their language skills rather than their mathematical skills. Previous research and the result of the interviews also confirm this and emphasize the importance of study guidance in the students’ native language.

Keywords

Word problems, socio-cultural perspective, newly arrived students, bilingual teaching

• 9. Aiki, T.
Technische Universiteit Eindhoven, Department of Mathematics and Computer Science, Eindhoven, Netherlands .
Preface2012In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, discrete and cont, Vol. 5, no 1, p. 1-Article in journal (Refereed)
• 10.
Japan Womens Univ, Fac Sci, Dept Math, Bunkyo Ku, Tokyo.
Vrije Univ Amsterdam, Fac Sci, Dept Math, Amsterdam, Netherlands. Bukkyo Univ, Sch Educ Math, Kita Ku, Kyoto. Eindhoven Univ Technol, Dept Math & Comp Sci,.
Analysis of non-equilibrium evolution problems: Selected topics in material and life sciences2014In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 7, no 1Article in journal (Refereed)
• 11. Aiki, T.
Eindhoven Univ Technol, Dept Math & Comp Sci.
A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the root t-law of propagation2013In: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 15, no 2, p. 167-180Article in journal (Refereed)
• 12. Aiki, T.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures2009In: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 19, p. 119-129Article in journal (Refereed)
• 13.
Gifu University, Japan.
Eindhoven University Technology, Netherlands. Eindhoven University Technology, Netherlands.
On a one-dimensional shape-memory alloy model in its fast-temperature- activation limit2012In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 5, no 1, p. 15-28Article in journal (Refereed)
• 14.
Gifu University, Japan.
Eindhoven University of Technology.
Large time behavior of solutions to a moving-interface problem modeling concrete carbonation2010In: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 9, no 5, p. 1117-1129Article in journal (Refereed)
• 15.
Tokyo Womens University.
Netherlands.
Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 93, p. 3-14Article in journal (Refereed)

We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the t-behavior of reaction penetration depths by including nonlinear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data.

• 16. Aiki, Toyohiko
Eindhoven University of Technology.
Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation2014In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 38, no 7, p. 1451-1464Article in journal (Refereed)
• 17.
Japan.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions2017In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 5, no 5, p. 3009-3026Article in journal (Refereed)

We prove the large time behavior of solutions to a coupled thermo-diffusion arising in the modeling of the motion of hot colloidal particles in porous media. Additionally, we also ensure the uniqueness of solutions of the target problem. The main mathematical difficulty is due to the presence in the right-hand side of the equations of products between temperature and concentration gradients. Such terms mimic the so-called thermodynamic Soret and Dufour effects. These are cross-coupling terms emphasizing in this context a strong interplay between heat conduction and molecular diffusion.

• 18.
Gifu University, Japan.
Eindhoven University of Technology.
On uniqueness of a weak solution of one-dimensional concrete carbonation problem2011In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 29, no 4, p. 1345-1365Article in journal (Refereed)

In our previous works we studied a one-dimensional free-boundary model related to the aggressive penetration of gaseous carbon dioxide in unsaturated concrete. Essentially, global existence and uniqueness of weak solutions to the model were obtained when the initial functions are bounded on the domain. In this paper we investigate the well-posedness of the problem for the case when the initial functions belong to a $\displaystyle{{L}}^{{2}}-$ class. Specifically, the uniqueness of weak solutions is proved by applying the dual equation method.

• 19.
Karlstad University, Faculty of Technology and Science, Department of Mathematics. Osaka Kyoiku Univ, Dept Math, Kashiwara, Osaka 5828582, Japan.. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Advances in Operator Cauchy-Schwarz Inequalities and their Reverses2015In: Annals of Functional Analysis, ISSN 2008-8752, E-ISSN 2008-8752, Vol. 6, no 3, p. 275-295Article in journal (Refereed)

The Cauchy-Schwarz (C-S) inequality is one of the most famous inequalities in mathematics. In this survey article, we first give a brief history of the inequality. Afterward, we present the C-S inequality for inner product spaces. Focusing on operator inequalities, we then review some significant recent developments of the C-S inequality and its reverses for Hilbert space operators and elements of Hilbert C*-modules. In particular, we pay special attention to an operator Wielandt inequality.

• 20.
Karlstad University, Faculty of Technology and Science, Avdelningen för matematik.
Embedding Theorems for Mixed Norm Spaces and Applications2010Doctoral thesis, monograph (Other academic)

This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of Sobolev and Besov type spaces. We study different structural, integrability, and smoothness properties of functions satisfying certain mixed norm conditions. Conditions of this type are determined by the behaviour of linear sections of functions. The work in this direction originates in a paper due to Gagliardo (1958), and was further developed by Fournier (1988), by Blei and Fournier (1989), and by Kolyada (2005).

Here we continue these studies. We obtain some refinements of known embeddings for certain mixed norm spaces introduced by Gagliardo, and we study general properties of these spaces. In connection with these results, we consider a scale of intermediate mixed norm spaces, and prove intrinsic embeddings in this scale.

We also consider more general, fully anisotropic, mixed norm spaces. Our main theorem states an embedding of these spaces to Lorentz spaces. Applying this result, we obtain sharp embedding theorems for anisotropic Sobolev-Besov spaces, and anisotropic fractional Sobolev spaces. The methods used are based on non-increasing rearrangements, and on estimates of sections of functions and sections of sets. We also study limiting relations between embeddings of spaces of different type. More exactly, mixed norm estimates enable us to get embedding constants with sharp asymptotic behaviour. This gives an extension of the results obtained for isotropic Besov spaces by Bourgain, Brezis, and Mironescu, and for anisotropic Besov spaces by Kolyada.

We study also some basic properties (in particular the approximation properties) of special weak type spaces that play an important role in the construction of mixed norm spaces, and in the description of Sobolev type embeddings.

In the last chapter, we study mixed norm spaces consisting of functions that have smooth sections. We prove embeddings of these spaces to Lorentz spaces. From this result, known properties of Sobolev-Liouville spaces follow.

• 21.
Karlstad University, Faculty of Technology and Science, Avdelningen för matematik.
Embedding Theorems for Mixed Norm Spaces and Applications2008Licentiate thesis, monograph (Other scientific)

This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of Sobolev and Besov type spaces. The work in this direction originates in a paper due to Gagliardo (1958), and was continued by Fournier (1988) and by Kolyada (2005).

We consider fully anisotropic mixed norm spaces. Our main theorem states an embedding of these spaces into Lorentz spaces. Applying this result, we obtain sharp embedding theorems for anisotropic fractional Sobolev spaces and anisotropic Sobolev-Besov spaces. The methods used are based on non-increasing rearrangements and on estimates of sections of functions and sections of sets. We also study limiting relations between embeddings of spaces of different type. More exactly, mixed norm estimates enable us to get embedding constants with sharp asymptotic behaviour. This gives an extension of the results obtained for isotropic Besov spaces $B_p^\alpha$ by Bourgain, Brezis, and Mironescu, and for Besov spaces $B^{\alpha_1,\dots,\alpha_n}_p$ by Kolyada.

We study also some basic properties (in particular the approximation properties) of special weak type spaces that play an important role in the construction of mixed norm spaces and in the description of Sobolev type embeddings.

• 22.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Tid och klockan i läromedel: En läromedelsanalys med fokus på de matematiska förmågorna och representationsformer2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis

The purpose of the study was to analyse time and clock and its progression in textbooks, for grades 4–6. The study also aimed, based on tasks linked to clock and time, to analyse which representation forms and mathematical competencies are trained in the selected textbooks. To studying as well as analysing different mathematics teaching textbooks, a document and textbook analysis was used to build up the approach for the study.

The results of the study showed that in the selected teaching materials, a mixture of the forms of representation, however, often lacked a concrete model. Concrete model existed in a few single tasks. The study's results also show that students are given the opportunity to practice the five mathematical skills but to varying extents. Communication and reasoning ability are the skills that are least trained in teaching materials.

The conclusion that can be drawn is that the role of teachers in the use of teaching materials in mathematics is of great im-portance because certain abilities are highlighted more in the workbook. The use of different representations might help the student to get good knowledge about time and the clock. Another conclusion is that the reasoning ability and communication skills need to be lifted more, so that students can learn to reason and communicate with each other.

• 23.
Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Portugal.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
Inflationary alpha-attractor cosmology: A global dynamical systems perspective2017In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 95, no 8, article id 083517Article in journal (Refereed)

We study flat Friedmann-Lemaitre-Robertson-Walker alpha-attractor E- and T-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both illustrative figures and a complete description of the entire solution spaces of these models, including asymptotics. In particular, it is shown that observational viability, which requires a sufficient number of e-folds, is associated with a particular solution given by a one-dimensional center manifold of a past asymptotic de Sitter state, where the center manifold structure also explains why nearby solutions are attracted to this "inflationary attractor solution." A center manifold expansion yields a description of the inflationary regime with arbitrary analytic accuracy, where the slow-roll approximation asymptotically describes the tangency condition of the center manifold at the asymptotic de Sitter state.

• 24.
University of Zagreb, Croatia.
University of Zagreb, Croatia. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Josip Pecaric- and his life in mathematics and politics2019In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 22, no 4, p. 1067-1080Article in journal (Refereed)

It is impossible in limited number of pages to give a fair picture of such a remarkable man, great mathematician and human being as Josip Pecaric. Our intention is instead to complement the picture of him in various ways. We hope that our paper will give also someflavor of Josip as family man, fighter, supervisor,international authority, author (also in other subjects than mathematics), fan of the Croatian football team, and not only as his obvious role as our King of Inequalities.

• 25.
UT Austin, Ctr Subsurface Modeling, ICES, Austin, TX 78712 USA.;Saudi Arabian Oil Co, Dhahran, Saudi Arabia..
Univ Bergen, Math Inst, N-5020 Bergen, Norway.. Saudi Arabian Oil Co, Dhahran, Saudi Arabia.. UT Austin, Ctr Subsurface Modeling, ICES, Austin, TX 78712 USA.. UT Austin, Ctr Subsurface Modeling, ICES, Austin, TX 78712 USA..
Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics2016In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 311, p. 180-207Article in journal (Refereed)

We consider multirate iterative schemes for the Biot system modeling coupled flow and geomechanics in a poro-elastic medium. The multirate iterative coupling scheme exploits the different time scales for the mechanics and flow problems by taking multiple finer time steps for flow within one coarse mechanics time step. We adapt the fixed stress split algorithm that decouples the flow and mechanics equations for the multirate case and perform an iteration between the two problems until convergence. We provide a fully discrete scheme that uses Backward Euler time discretization and mixed spaces for flow and conformal Galerkin for mechanics. Our analysis is based on studying the equations satisfied by the difference of iterates and using Banach contraction argument to prove that the corresponding scheme is a fixed point contraction. The analysis provides the value of an adjustable coefficient used in the proposed iterative coupling algorithms. Furthermore, we show that the converged quantities satisfy the variational weak form for the coupled discrete system. (C) 2016 Elsevier B.V. All rights reserved.

• 26.
Austin, USA.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). University of Bergen, Norway. Austin, USA. Austin, USA.
Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium2019In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 78, no 8, p. 2682-2699Article in journal (Refereed)

We consider single rate and multirate explicit schemes for the Biot system modeling coupled flow and geomechanics in a poro-elastic medium. These schemes are widely used in practice that follows a sequential procedure in which the flow and mechanics problems are fully decoupled. In such a scheme, the flow problem is solved first with time-lagging the displacement term followed by the mechanics solve. The multirate explicit coupling scheme exploits the different time scales for the mechanics and flow problems by taking multiple finer time steps for flow within one coarse mechanics time step. We provide fully discrete schemes for both the single and multirate approaches that use Backward Euler time discretization and mixed spaces for flow and conformal Galerkin for mechanics. We perform a rigorous stability analysis and derive the conditions on reservoir parameters and the number of finer flow solves to ensure stability for both schemes. Furthermore, we investigate the computational time savings for explicit coupling schemes against iterative coupling schemes.

• 27.
Center for Subsurface Modeling, ICES, UT-Austin, Austin, USA; Saudi Arabian Oil Company (Aramco), Dhahran, Saudi Arabia.
Mathematics Institute, University of Bergen, Bergen, Norway. Center for Subsurface Modeling, ICES, UT-Austin, Austin, USA.
Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics2017In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499, Vol. 21, no 5-6, p. 1157-1172Article in journal (Refereed)

In this paper, we consider an iterative coupling scheme for solving a fully discretized Biot system based on the fixed-stress split coupling algorithm. Specifically, we derive a priori error estimates for quantifying the error between the solution obtained at any iterate and the true solution. Our approach is based on studying the equations satisfied by the difference of iterates and utilizing a Banach contraction argument to show that the corresponding scheme is a fixed point iteration. Obtained contraction results are then used to derive theoretical convergence error estimates for the single rate iterative coupling scheme. We compare our numerical computations against the theoretically derived contraction estimates and show a good agreement with theory.

• 28.
Saudi Arabian Oil Company (Aramco), Saudi Arabia.
Saudi Arabian Oil Company (Aramco), Saudi Arabia. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). University of Bergen, Norway. Saudi Arabian Oil Company (Aramco), Saudi Arabia; MIT, USA.
Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media2019In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499Article in journal (Refereed)

Recently, an accurate coupling between subsurface flow and reservoir geomechanics has received more attention in both academia and industry. This stems from the fact that incorporating a geomechanics model into upstream flow simulation is critical for accurately predicting wellbore instabilities and hydraulic fracturing processes. One of the recently introduced iterative coupling algorithms to couple flow with geomechanics is the undrained split iterative coupling algorithm as reported by Kumar et al. (2016) and Mikelic and Wheeler (Comput. Geosci. 17: 455–461 2013). The convergence of this scheme is established in Mikelic and Wheeler (Comput. Geosci. 17:455–461 2013) for the single rate iterative coupling algorithm and in Kumar et al. (2016) for the multirate iterative coupling algorithm, in which the flow takes multiple finer time steps within one coarse mechanics time step. All previously established results study the convergence of the scheme in homogeneous poroelastic media. In this work, following the approach in Almani et al. (2017), we extend these results to the case of heterogeneous poroelastic media, in which each grid cell is associated with its own set of flow and mechanics parameters for both the single rate and multirate schemes. Second, following the approach in Almani et al. (Comput. Geosci. 21:1157–1172 2017), we establish a priori error estimates for the single rate case of the scheme in homogeneous poroelastic media. To the best of our knowledge, this is the first rigorous and complete mathematical analysis of the undrained split iterative coupling scheme in heterogeneous poroelastic media.

• 29.
Karlstad University, Faculty of Economic Sciences, Communication and IT, Department of Economics and Statistics.
A Approach for Analysing the Fractional Difference Processes2006Conference paper (Refereed)
• 30.
Karlstad University, Faculty of Economic Sciences, Communication and IT, Department of Economics and Statistics.
Some aspects of wavelet analysis in time series2000Licentiate thesis, monograph (Other academic)
• 31.
Karlstad University, Faculty of Economic Sciences, Communication and IT, Department of Economics and Statistics.
Testing for Periodicity and Trend in Long-Memory Processes2003Doctoral thesis, monograph (Other academic)
• 32.
Karlstad University, Faculty of Economic Sciences, Communication and IT, Department of Economics and Statistics.
A study of residential radon in Sweden using multilevel analysis2008In: Health Physics Journal, to appear 2008Article in journal (Refereed)

A Swedish radon data set, consisting of more than 8000 measurements of residential radon levels in about 50% of the Swedish municipalities were analysed using a multilevel approach.

The results were compared with those of a single-level analysis. We found that there was a significant variability between municipalities. The point estimates of the population mean radon levels were similar (geometric mean 60 Bq/m3 and arithmetic mean 106 Bq/m3).

The analysis shows the advantages of multilevel modeling compared with a single-level OLS model.

A single-level model results in too optimistic standard errors, about 25% of those of the multilevel

model which can lead to erroneous conclusions.

In a multilevel model including house type as a fixed effect (single-family house, row house, or apartment in multi-family house), the estimates of the fixed effect of house type were similar for the single-level and the multi-level models

• 33.
Karlstad University, Faculty of Economic Sciences, Communication and IT, Department of Economics and Statistics.
Impact of the Periodicity and Trend on the FD Parameter Estimation2007In: Journal of Statistical Computation and Simulation. 2007, 77, 79-87Article in journal (Refereed)
• 34.
Karlstad University, Faculty of Economic Sciences, Communication and IT, Department of Economics and Statistics.
Testing for climate warming in Sweden during 1850-1999, using wavelets analysis2008In: Journal of Applied Statistics, 2008, vol. 35, issue 4, pages 431-443Article in journal (Refereed)

This paper describes an alternative approach for testing for the existence of trend among time series. The test method has been constructed using wavelet analysis which has the ability of decomposing a time series into low frequencies (trend) and high-frequency (noise) components. Under the normality assumption, the test is distributed as F. However, using generated empirical critical values, the properties of the test statistic have been investigated under different conditions and different types of wavelet. The Harr wavelet has shown to exhibit the highest power among the other wavelet types. The methodology here has been applied to real temperature data in Sweden for the period 1850-1999. The results indicate a significant increasing trend which agrees with the 'global warming' hypothesis during the last 100 years.

• 35.
Karlstad University, Faculty of Economic Sciences, Communication and IT, Department of Economics and Statistics.
An Illustration of the Causality Relation between Government Spending and Revenue Using Wavelets Analysis on Finish Data2003In: Journal of Applied Statistics, 2003, 30, 571-584Article in journal (Refereed)

Quarterly data for the period 1960:1 to 1997:2, conventional tests, a bootstrap simulation approach and a multivariate Rao's F-test have been used to investigate if the causality between government spending and revenue in Finland was changed at the beginning of 1990 due to future plans to create the European Monetary Union (EMU). The results indicate that during the period before 1990, the government revenue Granger-caused spending, while the opposite happened after 1990, which agrees better with Barro's tax smoothing hypothesis. However, when using monthly data instead of quarterly data for almost the same sample period, totally different results have been noted. The general conclusion is that the relationship between spending and revenue in Finland is still not completely understood. The ambiguity of these results may well be due to the fact that there are several time scales involved in the relationship, and that the conventional analyses may be inadequate to separate out the time scale structured relationships between these variables. Therefore, to investigate empirically the relation between these variables we attempt to use the wavelets analysis that enables us to separate out different time scales of variation in the data. We find that time scale decomposition is important for analysing these economic variables.

• 36.
Karlstad University, Faculty of Economic Sciences, Communication and IT, Department of Economics and Statistics.
Testing the Causal Relation between Sunspots and Temperature Using Wavelets Analysis2005In: Journal of Modern Applied Statistical Methods, 2005, 4, 134-139Article in journal (Refereed)
• 37.
Karlstad University, Faculty of Economic Sciences, Communication and IT, Department of Economics and Statistics.
Clustering Using Wavelet Transformation2008In: Handbook of Research on Cluster Theory / [ed] Charlie Karlsson, Edward Elgar , 2008Chapter in book (Refereed)
• 38.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Kan en lärare hinna med alla elever i dagens matematikundervisning?: En intervjustudie av hur lärare beskriver undervisningen av elever som presterar lågt i matematik.2017Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

In this study I want to illustrate how teachers describe their preventions and interventions when teaching students with low achievement in mathematics. This is a qualitative study based on a series of group interviews of teachers in the Swedish compulsory school. Mathematics teachers still hold a traditional compensatory perspective on students with low achievement thus placing the responsibility for learning with the students. The general opinion is that special pedagogics is necessary to enable support enough to help students with low achievement in mathematics to reach a passing grade. Thanks to further training, primarily through “Matematiklyftet”, the view on the possibility to include low achieving students in the classroom in a good way is more positive. There is an ongoing work in schools to improve the mathematics teaching, but one cannot see a complete or common plan for the schools neither from the school administration nor the teachers. The preventive measures made to include the low achieving students does have a positive effect for all students. Much of the implemented changes have its origin in talking mathematics in the classroom and not following the textbook as slavishly as previously done.

• 39.
Karlstad University, Faculty of Economic Sciences, Communication and IT.
Prognostisering av Sveriges inflation: Med hjälp av ARIMA-modeller2007Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Syftet med min uppsats är att redogöra för de steg som krävs för att prognostisera den svenska inflationen med hjälp av Autoregressive Integrated Moving Average (ARIMA), för att sedan bestämma den modell som ger den bästa prognosen. Jag använder mig av månadsdata av Konsumentprisindex (KPI) som mått på inflation. För att man ska kunna prognostisera en tidsserie är det viktigt att den är stationär  och efter att ha utforskat korrelogram drar jag slutsatsen att dels en förstadifferens och dels en tolvmånadersdifferens måste tas för att kunna prognostisera KPI.

Jag följer Box-Jenkins-metodologin tämligen väl, där modellidentifikation, diagnostiska test och prognostisering är centrala begrepp.  Jag rankar de tio bästa modellerna enligt Bayesian Information Criterion (BIC) för att sedan utföra diagnostiska test på den bästa modellen i synnerhet och de andra modellerna i allmänhet. Slutligen utvärderas de olika modellerna bl.a. med hjälp av ”Root Mean Square Error” (RMSE). Den modell som bäst prognostiserar  inflationen  är en säsongsbetonad Moving Average  process  av order  ett förutom differentieringarna.

Matematisk begåvning och läroboken: En analys av läromedel för gymnasiet2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

The coursebook plays a key role in the mathematics education in the Swedish school.

Because it has such an important role in the students’ abilities to practice and fortify their

mathematical knowledge and abilities, there are high standards to be met for the

coursebook to accommodate all of the students’ needs in the classroom. Despite this, there

is no national review of coursebooks, which means that it is up to the teachers themselves

to review them. According to the law, the education in schools should contribute to

knowledge development to all students, regardless of their prior level of knowledge. For

the subject mathematics, this means that the exercises and tasks being worked on by the

students need to meet the needs of students with difficulties as well as giftedness. This

study has examined to what extent four coursebooks in mathematics at the upper

secondary level can support the knowledge development of gifted students. The results of

the study show that the coursebooks meet one or some of the criteria research has shown

supports mathematically gifted students. At the same time it is important to stress that the

results of this study only show the potential that the coursebooks have, it is still up to the

teacher to use the materials available to them and use them in such a way that they can

contribute to the gifted students’ knowledge development.

• 41.
Karlstad University, Faculty of Technology and Science.
Att välja variationsrik matematikundervisning.: En enkätstudie av lärares undervisning2012Independent thesis Advanced level (degree of Master (Two Years)), 10 credits / 15 HE creditsStudent thesis
• 42.
Karlstad University, Faculty of Technology and Science.
Nivågruppering i matematik: vad tycker eleverna?2008Student thesis

Sammanfattning

Ett problem som alla lärare ställs inför är hur man ska anpassa undervisningen till varje elevs individuella behov.

För att belysa denna fråga har jag valt att undersöka ett specifikt fall där en skola har valt att, under en begränsad tid, nivågruppera matematikundervisningen i åk 9. De deltagande eleverna har besvarat en enkät med frågor kring hur de ser på denna organisationsform.

Resultatet av undersökningen visar att en stor majoritet av eleverna har en positiv inställning till nivågruppering i detta specifika fall. Eleverna är även positiva till att deras fortsatta undervisning ska bedrivas nivågrupperat.

Nyckelord: Nivågruppering, Matematik.

• 43.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Hur väl uppfyller läroboken lärarnas behov i undervisningen?How well does the textbook fulfill teh teachers´ needs in the teaching?: En studie kring lärarnas syn på läroboken i matematikA study of the teachers´ view on the textbook in mathematics2016Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis

In the Swedish school the textbook is seen as a central teaching material in mathematics. In many classrooms individual, silent work in the textbook is particularly common during mathematics lessons. Silent work is often a large part of the lesson, although research shows that the teaching of mathematics should include variation and communication and that the pupils should at an early age be given the opportunity to understand the relation between mathematics and daily life.The teacher has a central role in choosing which teaching material are best suited for each teaching situation and each individual pupil. The teacher is also supposed to adapt instruction to individual's ability in a way that enhances the pupil´s curiosity, thus contributing to an increased inner motivation.The aim of this study was to get teachers' perspective on textbooks. In school mathematic the textbook is a common teaching material and because of that there were a questions about how well the textbook actually lives up to the teachers' needs.The chosen method was both qualitative and quantitative. A survey was sent out to mathematics teachers in grade 1-3. A simple survey with a reduced number of predetermined answers was supposed to attract many teachers to answer them. Unfortunately there was low participation among the respondents, which made it difficult to answer the research questions. As a complement a more in-depth survey was sent out to only a few respondents. The two different surveys were coordinated in the analysis.The result showed that teachers in mathematics in year 1-3 often use a textbook. A big part of them believe the textbook is a motivating factor for the pupils, and that younger pupils like to work with their textbook. The results also showed that there is a difference of opinion as to whether or not the textbook itself gives good opportunities to adaptive instruction, as well as concerning. How well it is aligned with their own understanding of the required knowledge goals for class 3. All teachers see their own teaching as varied and that the communicative aspect of the subject is important. The results also showed that the teachers that work without textbooks don't see any advantages with it, except as a help for their own planning.The conclusion is that the textbook is an important teaching material, not least as a support in one's own planning.Teachers in class 1-3 believe themselves to have a varied mathematics pedagogy and also that they have motivated pupils. The teachers agree on the importance to anchor mathematics in daily life since it is always there, around us.

• 44.
Karlstad University, Division for Engineering Sciences, Physics and Mathematics.
Matematik i förskolan: Hur arbetar man med matematik i förskolan?2006Independent thesis Basic level (professional degree), 10 points / 15 hpStudent thesis

The word mathematics is often associated to addition, subtraction, division or multiplication. This is not the kind of mathematics that belongs to pre-school. In my essay I have chosen to write about how mathematics is used in pre-school. In the literature it is written that the best way of becoming familiar with mathematics, is to integrate it in the every day life but that there are educators that use traditional mathematics education in pre-school. The questions I would like to answer are:

1. How is mathematic used in pre-school?

2. What are the educators’ opinions in pre-school regarding the introduction of the

curriculum?

In order to answer the questions I will use qualitative interviews. I have interviewed six pre-school teachers in two different schools in a middle sized town in Sweden. I have chosen six departments in order to get two educators’ views on three types of children groups, infants, siblings and an integrated group.

The answers showed that the level of using specific mathematics education is very low. Instead mathematics is integrated with everyday life situations such as when laying the table or portioning food.

The investigation also showed that all persons interviewed expressed a positive attitude towards the implementation of the curriculum for several reasons. The addition has given them a sense of acknowledgement in their earlier work, given their jobs a higher status and also strengthened and broadened their view on mathematics in pre-school.

• 45.
All Russia Res Inst Automat VNIIA, Moscow, Russia.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. All Russia Res Inst Automat VNIIA, Moscow, Russia.;RAS, PN Lebedev Phys Inst, Moscow 117901, Russia. All Russia Res Inst Automat VNIIA, Moscow, Russia.;RAS, PN Lebedev Phys Inst, Moscow 117901, Russia. All Russia Res Inst Automat VNIIA, Moscow, Russia. RAS, MV Keldysh Appl Math Inst, Moscow 117901, Russia.
Stochastic simulation of the nonlinear kinetic equation with high-frequency electromagnetic fields2013In: PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, ISSN 1562-6016, no 4, p. 233-237Article in journal (Refereed)

A general approach to Monte Carlo methods for Coulomb collisions is proposed. Its key idea is an approximation of Landau-Fokker-Planck (LFP) equations by Boltzmann equations of quasi-Maxwellian kind. High-frequency fields are included into consideration and comparison with the well-known results are given.

• 46.
Umeå universitet.
Locally D-optimal Designs for Bivariate Logistic Regression2004Licentiate thesis, monograph (Other academic)
• 47. Arcozzi, N
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Hardys inequalities for monotone functions on partly ordered measure spaces2006In: Proc. Roy. Soc. Edingburgh Sect. A, 136 (2006), no.5Article in journal (Refereed)
• 48.
Università di Roma La Sapienza.
Università di Roma La Sapienza. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Eindhoven University of Technology.
Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media2017In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 82, no 1, p. 224-250Article in journal (Refereed)

We study the weak solvability of a system of coupled Allen–Cahn-like equations resembling cross-diffusion which arises as a model for the consolidation of saturated porous media. Besides using energy-like estimates, we cast the special structure of the system in the framework of the Leray–Schauder fixed-point principle and ensure in this way the local existence of strong solutions to a regularized version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.

• 49.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
"I slutet av varje dag förstår alla elever matematiken": En kvalitativ studie om matematiklärares syn på barn i behov av särskilt stöd i Kenya2014Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

The purpose of the study was to find out how teachers in a school in Kenya conducted the education of mathematics in standard 4-6. The focus was how the teachers worked with children in need of special support in mathematics.To find out the purpose a case study was made with two interviews and seven observations with four teachers on a rural school in Kenya. The following issues were: Which standards were there in the classrooms during lessons in mathematics in Kenya? How did the teachers express the view of children in need of special support? The main conclusion was that different teachers teaching in mathematics looked the same.The teacher was standing in front of the blackboard where the teaching occurred and the pupils were sitting lined up in their benches. The teaching of the pupils was about repetition and imitates the teacher and mostly filling the gap that the teacher made them say. Pupils in need of special support got their help through extra lessons and homework but the teachers thought that it was hard to help every child when there was only one teacher in the classroom.

• 50.
Karlstad University, Faculty of Technology and Science.
Laborativ matematik: Att variera undervisningen med alternativa metoder2009Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

This report investigates various ways of diversifying mathematics teaching, especially elaborative mathematics. Primarily it focuses upper secondary school, but the results should have an impact on lower and higher levels as well. From an account of teacher and student views the report provides some concrete suggestions for improvement. The purpose of the report is to investigate alternatives for the traditional ways of teaching. Five teachers known for their experience on alternative teaching methods and on laboratory mathematics have been interviewed.

The result shows that mathematics teaching is uniform and that it needs to be diversified. The report presents a sample of ideas for such teaching. Many teachers are willing to try this type of teaching but hesitate since there are no proofs of positive results or because there is too little time for such methods. A diversified, laboratory teaching seems to contribute good results but this has not been proved.

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