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• 1.
Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
Heuristiska algoritmer för schemaläggning i real-tidssystem med hänsyn till data beroenden2018Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis

The schedule for the jobs in a real-time system can have a huge impact on how the system behave. Since real-time systems are common in safety applications it is important that the scheduling is done in a valid way. Furthermore, one can enhance the performance of the applications by minimizing data latency and jitter. A challenge is that jobs in real-time systems usually have complex constraints making it too time consuming to minimize data latency and jitter to optimality. The purpose of this report is to investigate the possibility of creating high quality schedules using heuristics, with the goal to keep the computational time under one minute. This will be done by comparing three different algorithms that will be used on real scheduling instances provided by the company Arcticus. The first algorithm is a greedy heuristic, the second one a local search and the third one is a metaheuristic, simulated annealing. The results indicate that the data latency can be reduced whilst keeping the computational time below one minute.

• 2.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Philosophy of mathematics in “La Science et l’Hypothèse”, from Henri Poincaré.2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 3.
Linköping University, Department of Electrical Engineering, Communication Systems.
Hide and Seek in a Social Network2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

In this thesis a known heuristic for decreasing a node's centrality scores while maintaining influence, called ROAM, is compared to a modified version specifically designed to decrease eigenvector centrality. The performances of these heuristics are also tested against the Shapley values of a cooperative game played over the considered network, where the game is such that influential nodes receive higher Shapley values. The modified heuristic performed at least as good as the original ROAM, and in some instances even better (especially when the terrorist network behind the World Trade Center attacks was considered). Both heuristics increased the influence score for a given targeted node when applied consecutively on the WTC network, and consequently the Shapley values increased as well. Therefore the Shapley value of the game considered in this thesis seems to be well suited for discovering individuals that are assumed to actively trying to evade social network analysis.

• 4. Abtahi, Yasmine
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
Otherness in mathematics education2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] E. Bergqvist, M. Österholm, C. Granberg, L. Sumpter, Umeå, Sweden: PME , 2018, Vol. 1, p. 95-124Conference paper (Refereed)
• 5.
Mälardalen University, School of Education, Culture and Communication.
Risk-Efficient Portfolios; Estimation Error In Essence2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

This thesis primarily looks at estimation error problems and other related issues arising in connection with portfolio optimization. With some available assets, a portfolio program or optimizer seeks to distribute a fixed amount of capital among these available assets to optimize some cost function. In this regard, Markowitz portfolio selection basis defines the variance of the portfolio return to being that of the portfolio risk and tries to find an allocation that reduces or minimizes the risk subject to a target mean or expected return. Should the mean return vector and the covariance matrix of returns for the underlying assets be known, the Markowitz problem is said to have a closed-form solution.

In practice, however, an estimation is made from historical data for unknown expected returns and the covariance matrix of the returns, and this brings into the domain several problems such as estimation problems and renders the Markowitz theory impracticable in real-life portfolio applications. Estimators necessary to remedy these problems would be made bare to show how possible it is to tackle such issues.

In the concept demonstration sections, the analysis starts with the price data of 40 stocks and the S\&P index. The efficient frontier is introduced and used to show how the estimators take effect.

Finally, implementation is made possible using the R Programming Language to demonstrate the necessary concepts with the conclusion presented at the end.

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.

• 7.
Stockholm University, Faculty of Science, Department of Mathematics.
Hardy and spectral inequalities for a class of partial differential operators2014Doctoral thesis, monograph (Other academic)

This thesis is devoted to the study of Hardy and spectral inequalities for the Heisenberg and the Grushin operators. It consists of five chapters. In chapter 1 we present basic notions and summarize the main results of the thesis. In chapters 2-4 we deal with different types of Hardy inequalities for Laplace and Grushin operators with magnetic and non-magnetic fields. It was shown in an article by Laptev and Weidl that for some magnetic forms in two dimensions, the Hardy inequality holds in its classical form. More precisely, by considering the Aharonov-Bohm magnetic potential, we can improve the constant in the respective Hardy inequality. In chapter 2 we establish an Lp - Hardy inequality related to Laplacians with magnetic fields with Aharonov-Bohm vector potentials. In chapter 3 we introduce a suitable notion of a vector field for the Grushin sub-elliptic operator G and obtain an improvement of the Hardy inequality, which was previously obtained in the paper of N. Garofallo and E. Lanconelli. In chapter 4 we find an Lp version of the Hardy inequality obtained in chapter 2. Finally in chapter 5 we aim to find the CLR and Lieb-Thirringbninequalities for harmonic Grushin-type operators. As the Grushin operator is non-elliptic, these inequalities will not take their classical form.

• 8.
University of Oslo, Norway;University of Biskra, Algeria.
Dynamic risk measure for BSVIE with jumps and semimartingale issues2019In: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 37, no 3, p. 361-376Article in journal (Refereed)

Risk measure is a fundamental concept in finance and in the insuranceindustry. It is used to adjust life insurance rates. In this article,we will study dynamic risk measures by means of backward stochasticVolterra integral equations (BSVIEs) with jumps. We prove a comparisontheorem for such a type of equations. Since the solution of aBSVIEs is not a semimartingale in general, we will discuss some particularsemimartingale issues.

• 9.
Linnaeus University, Faculty of Technology, Department of Mathematics.
Stochastic optimal control of McKean-Vlasov equations with anticipating law2019In: Afrika Matematika, ISSN 1012-9405, E-ISSN 2190-7668, Vol. 30, no 5-6, p. 879-901Article in journal (Refereed)

We are interested in Pontryagin’s stochastic maximum principle of controlled McKean–Vlasov stochastic differential equations. We allow the law to be anticipating, in the sense that, the coefficients (the drift and the diffusion coefficients) depend not only of the solution at the current time t, but also on the law of the future values of the solution PX(t+&#x03B4;)" role="presentation">PX(t+δ), for a given positive constant &#x03B4;" role="presentation">δ. We emphasise that being anticipating w.r.t. the law of the solution process does not mean being anticipative in the sense that it anticipates the driving Brownian motion. As an adjoint equation, a new type of delayed backward stochastic differential equations (BSDE) with implicit terminal condition is obtained. By using that the expectation of any random variable is a function of its law, our BSDE can be written in a simple form. Then, we prove existence and uniqueness of the solution of the delayed BSDE with implicit terminal value, i.e. with terminal value being a function of the law of the solution itself.

• 10.
University of Oslo, Norway;University of Mohamed Khider, Algeria.
University of Oslo, Norway. University of Oslo, Norway. University of Oslo, Norway.
Singular Control Optimal Stopping of Memory Mean-Field Processes2019In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 51, no 1, p. 450-468Article in journal (Refereed)

The purpose of this paper is to study the following topics and the relation between them: (i) Optimal singular control of mean-field stochastic differential equations with memory; (ii) reflected advanced mean-field backward stochastic differential equations; and (iii) optimal stopping of mean-field stochastic differential equations. More specifically, we do the following: (1) We prove the existence and uniqueness of the solutions of some reflected advanced memory backward stochastic differential equations; (2) we give sufficient and necessary conditions for an optimal singular control of a memory mean-field stochastic differential equation (MMSDE) with partial information; and (3) we deduce a relation between the optimal singular control of an MMSDE and the optimal stopping of such processes.

• 11.
University of Oslo, Norway.
University of Biskra, Algeria.
Optimal control of forward–backward mean-field stochastic delayed systems2018In: Afrika Matematika, ISSN 1012-9405, E-ISSN 2190-7668, Vol. 29, no 1-2, p. 149-174Article in journal (Refereed)

We study methods for solving stochastic control problems of systems offorward–backward mean-field equations with delay, in finite and infinite time horizon.Necessary and sufficient maximum principles under partial information are given. The resultsare applied to solve a mean-field recursive utility optimal problem.

• 12.
University Med Khider, Algeria.
Linnaeus University, Faculty of Technology, Department of Mathematics. University of Oslo, Norway. University Med Khider, Algeria. University of Oslo, Norway.
A maximum principle for infinite horizon delay equations2013In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 45, no 4, p. 2499-2522Article in journal (Refereed)

We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our results with an application to the optimal consumption rate from an economic quantity.

• 13.
University of Oslo, Norway;University of Biskra, Algeria.
University of Oslo, Norway.
A Hida-Malliavin white noise calculus approach to optimal control2018In: Infinite Dimensional Analysis Quantum Probability and Related Topics, ISSN 0219-0257, Vol. 21, no 3, article id 1850014Article in journal (Refereed)

The classical maximum principle for optimal stochastic control states that if a control û is optimal, then the corresponding Hamiltonian has a maximum at u = û. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently, it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the first-order derivative was extended to include an extra BSDE for the second-order derivatives. In this paper, we present an alternative approach based on Hida-Malliavin calculus and white noise theory. This enables us to handle the general case with jumps, allowing both the diffusion coefficient and the jump coefficient to depend on the control, and we do not need the extra BSDE with second-order derivatives. The result is illustrated by an example of a constrained linear-quadratic optimal control.

• 14.
University Med Khider, Algeria.
University of Oslo, Norway.
Infinite horizon optimal control of forward–backward stochastic differential equations with delay2014In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 259, no Part B, p. 336-349Article in journal (Refereed)

We consider a problem of optimal control of an infinite horizon system governed by forward–backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial information in infinite horizon are derived. We illustrate our results by an application to a problem of optimal consumption with respect to recursive utility from a cash flow with delay.

• 15.
University Med Khider, Algeria.
University of Oslo, Norway.
Malliavin calculus and optimal control of stochastic Volterra equations2015In: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 167, no 3, p. 1070-1094Article in journal (Refereed)

Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore, classical methods, such as dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that using Malliavin calculus, it is possible to formulate modified functional types of maximum principle suitable for such systems. This principle also applies to situations where the controller has only partial information available to base her decisions upon. We present both a Mangasarian sufficient condition and a Pontryagin-type maximum principle of this type, and then, we use the results to study some specific examples. In particular, we solve an optimal portfolio problem in a financial market model with memory.

• 16.
University of Oslo, Norway.
Univeristy of Oslo, Norway.
Stochastic control of memory mean-field processes2019In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 79, no 1, p. 181-204Article in journal (Refereed)

By a memory mean-field process we mean the solution X(&#x22C5;)" role="presentation">X(⋅) of a stochastic mean-field equation involving not just the current state X(t) and its law L(X(t))" role="presentation">L(X(t)) at time t,  but also the state values X(s) and its law L(X(s))" role="presentation">L(X(s)) at some previous times s&lt;t." role="presentation">s<t. Our purpose is to study stochastic control problems of memory mean-field processes. We consider the space M" role="presentation">M of measures on R" role="presentation">R with the norm ||&#x22C5;||M" role="presentation">||⋅||M introduced by Agram and Øksendal (Model uncertainty stochastic mean-field control. arXiv:1611.01385v5, [2]), and prove the existence and uniqueness of solutions of memory mean-field stochastic functional differential equations. We prove two stochastic maximum principles, one sufficient (a verification theorem) and one necessary, both under partial information. The corresponding equations for the adjoint variables are a pair of (time-advanced backward stochastic differential equations (absdes), one of them with values in the space of bounded linear functionals on path segment spaces. As an application of our methods, we solve a memory mean–variance problem as well as a linear–quadratic problem of a memory process.

• 17.
University of Oslo, Norway;University Mohamed Knider of Biskra, Algeria.
University of Oslo, Norway. University Mohamed Khider of Biskra, Algeria.
New approach to optimal control of stochastic Volterra integral equations2019In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 91, no 6, p. 873-894Article in journal (Refereed)

We study optimal control of stochastic Volterra integral equations(SVIE) with jumps by using Hida-Malliavin calculus.

• We give conditions under which there exist unique solutions ofsuch equations.

• Then we prove both a sufficient maximum principle (a verificationtheorem) and a necessary maximum principle via Hida-Malliavincalculus.

• As an application we solve a problem of optimal consumptionfrom a cash flow modelled by an SVIE.

• 18.
Linnaeus University, Board of Education Science.
Hur används den utökade resursen till matematikämnet i grundskolan?2014Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis
• 19.
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
Elevers möjlighet att utveckla matematiska förmågor utifrån läromedlet Pixel2012Student paper other, 10 credits / 15 HE creditsStudent thesis

Syftet med arbetet är att ta reda på i vilken utsträckning elever ges förutsättningar att utveckla de olika förmågor som beskrivs i kursplanen för ämnet matematik, LGR11, när undervisningen bygger på ett vanligt förekommande läromedel, Pixel. Metoden är kvalitativ och det har skett en textanalys på geometriavsnitten i läromedlet. De förmågor som eleverna når upp till är att använda sig av olika matematiska begrepp, samt att formulera och lösa problem. Eleverna har goda möjligheter att själva kunna välja olika sätt att lösa uppgifter. De får även kunskap att förstå och använda olika uttrycksformer. Eleverna uppmuntras inte med hjälp av detta läromedel, att föra egna matematiska diskussioner.

• 20.
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
Matematik från grunden: sortering och klassificering med de yngsta barnen i förskolan2009Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Syftet med examensarbetet är att med hjälp av enkätintervjuer och observationer få mer kunskap om hur man arbetar med sortering och klassificering med de yngsta barnen i förskolan. Vi har intervjuat arbetslag som nyligen fått kompetensutveckling i matematik. I vår bakgrund har vi utifrån ett teoretiskt perspektiv förklarat sortering och klassificering, pedagogens roll samt den pedagogiska miljön samt hur dessa faktorer kan påverka barns matematiska förmåga.  Resultatet visar att det förekommer mycket sortering och klassificering i verksamheten på förskolor i vardagsmatematiken. Pedagogerna i undersökningen menar att de vill ha mer kunskap om matematiska begrepp för att på ett bättre sätt ge barnen kunskap i matematik. Undersökningen visar hur betydelsefull pedagogen är och denna roll är inte alltid pedagogerna ute i verksamheten medvetna om.

• 21.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
Lärarstyrd lek i matematikundervisningen: Dess möjligheter och begränsningar för elevens lärande.2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

Avsikten med min studie är att veta hur lärarstyrd lek påverkar matematikundervisningen samt se vilka möjligheter och begränsningar som metoden lärarstyrd lek har. För detta syfte har jag intervjuat ett antal lärare om detta arbetssätt, hur de planerar för en undervisning som bygger på lärarstyrd lek, vad de menar med lärarstyrd lek, vilka möjligheter och begränsningar de ser samt om de märker att de stimulerar eleven i matematikundervisningen med den lärarstyrda leken.Det resultatet som jag ser i min studie är att i huvudsak anser samtliga pedagoger att det finns en positiv påverkan på lärandet när lärarstyrd lek genomförs i undervisningen. De pekar på några begränsande faktorer som tidsbrist, höga arbetsbelastning, problem med elevers sociala sampel. Trots att arbetssättet möter vissa utmaningar så bedömer samtliga pedagoger att lärarstyrd lek i matematikundervisningen ökar elevens motivation i lärandet och gör ämnet roligt och intressant.

• 22.
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
Hur kan elevers kunskapsutveckling i matematik förbättras: Formativ bedömning i matematikundervisning2010Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

Syftet med examensarbetet är att fördjupa vår kunskap om och förståelse för formativ bedömning i matematik. Vidare vill vi undersöka om den formativa bedömningen kan förbättra eleverna i klassens kunskapsutveckling i matematik. Vi har gjort en fallstudie i en klass som arbetar formativt för att undersöka hur det kan se ut i praktiken. Underlaget för det samlade materialet består av observation och intervju för att besvara våra två frågeställningar som följer. Hur kan en formativ bedömning se ut i praktiken? Hur kan en koppling mellan lärares och elevers uppfattningar om den pedagogiska verksamheten se ut? Vi har kommit fram till att den formativa bedömningen kan förbättra eleverna i klassens kunskapsutveckling i matematik. I den formativa bedömningen har vi sett vikten av mötet mellan lärare och elev. Att arbeta formativt är tidskrävande.

• 23.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Analytical and Numerical Study of the Poincaré Map with Applications on the Computation of Periodic Orbits2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 24.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). The University of Edinburgh.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Applications of Fourier Analysis in Homogenization of the Dirichlet Problem: L-p Estimates2015In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 215, no 1, p. 65-87Article in journal (Refereed)

Let u(epsilon) be a solution to the system div(A(epsilon)(x)del u(epsilon)(x)) = 0 in D, u(epsilon)(x) = g(x, x/epsilon) on partial derivative D, where D subset of R-d (d >= 2), is a smooth uniformly convex domain, and g is 1-periodic in its second variable, and both A(epsilon) and g are sufficiently smooth. Our results in this paper are twofold. First we prove L-p convergence results for solutions of the above system and for the non-oscillating operator A(epsilon)(x) = A(x), with the following convergence rate for all 1 <= p < infinity parallel to u(epsilon) - u(0)parallel to (LP(D)) <= C-P {epsilon(1/2p), d = 2, (epsilon vertical bar ln epsilon vertical bar)(1/p), d = 3, epsilon(1/p), d >= 4, which we prove is (generically) sharp for d >= 4. Here u(0) is the solution to the averaging problem. Second, combining our method with the recent results due to Kenig, Lin and Shen (Commun Pure Appl Math 67(8): 1219-1262, 2014), we prove (for certain class of operators and when d >= 3) ||u(epsilon) - u(0)||(Lp(D)) <= C-p[epsilon(ln(1/epsilon))(2)](1/p) for both the oscillating operator and boundary data. For this case, we take A(epsilon) = A(x/epsilon), where A is 1-periodic as well. Some further applications of the method to the homogenization of the Neumann problem with oscillating boundary data are also considered.

• 25.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
Matematik och estetiska lärprocesser: en studie om ämnesintegration av estetiska verktyg i matematikundervisning.2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis

Syftet med undersökningen var att observera hur lärarna arbetar med matematik i årskurserna F-3, med fokus på hur estetiska verktyg används i matematikundervisningen. Studien är baserad på klassobservationer i två årskurser i de tidigare skolåren F-3 samt elev- och lärarintervjuer och ämnade lyfta estetiska lärprocesser samt hur de spelar in på elevernas upplevelser vad gäller ämnesintegration i matematikundervisning. Resultaten visar att estetiska verktyg används mer med yngre elever och mindre ju äldre eleverna blir. Lärarna i denna studie påpekade att ett ämnesövergripande arbetssätt och att blanda in olika sinnen främjar elevernas inlärning. Majoriteten av de intervjuade lärarna betonade att det gäller att hitta en balans mellan olika metoder för att skapa en varierad undervisning.

• 26.
Linnaeus University, Faculty of Technology, Department of Mathematics.
Linnaeus University, Faculty of Technology, Department of Mathematics.
Tal och tanke: hur problemlösningsdiskurser förändras genom samarbete2019Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis

Syftet med denna studie är att beskriva processen som sker när elever arbetar tillsammans med en problemlösningsuppgift de tidigare inte kunnat lösa vid enskilt arbete. Fokus har varit på förändrad användning av Sfards (2008) nyckelbegrepp: ämnesspecifika ord, visuella mediatorer, rutiner och berättelser samt vilka diskursförändringar som synliggjorts. Studien är kvalitativ och empirin har samlats in genom observationer av problemlösningsarbetet, ljudinspelningar under pararbeten och bildupptagningar av elevmaterialet. Totalt tio observationer av gemensamt arbete genomfördes och transkriberades och av dessa djupanalyserades fem transkriberingar med hjälp av flödesscheman och Sfards (2008) nyckelbegrepp. Resultatet visar att eleverna i studien använde fler nyckelbegrepp vid den gemensamma problemlösningen och därmed ingick i diskursförändringar som bidrog till att föra problemlösningen framåt. Visuella mediatorer och användningen av tid visade sig vara viktiga aspekter för användning av fler nyckelbegrepp och förändring av diskurser.

• 27.
Izmir University, Izmir, Turkey. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
On the global solution of a fuzzy linear system2014In: Journal of Fuzzy Set Valued Analysis, ISSN 2193-4169, article id jfsva-00190Article in journal (Other academic)

The global solution of a fuzzy linear system contains the crisp vector solution of a real linear system. So discussion about the global solution of a $n\times n$ fuzzy linear system $A\tilde{x}=\tilde{b}$ with a fuzzy number vector $b$ in the right hand side and crisp a coefficient matrix $A$ is considered. The advantage of the paper is developing a new algorithm to find the solution of such system by considering a global solution based upon the concept of a convex fuzzy numbers. At first the existence and uniqueness of the solution are introduced and then the related theorems and properties about the solution are proved in details. Finally the method is illustrated by solving some numerical examples.

• 28.
Stockholm University, Faculty of Science, Department of Mathematics and Science Education, PRIM-gruppen.
På upptäcktsfärd i elevernas  värld av tal2007In: Matematikdidaktiska texter – Beprövad erfarenhet och vetenskaplig grund / [ed] Lena Alm ..., Stockholm: PRIM-gruppen, Institutionen för undervisningsprocesser, kommunikation och lärande, Lärarhögskolan i Stockholm , 2007, p. 43-55Chapter in book (Other academic)
• 29. Almquist, Martin
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
Atmospheric Sound Propagation Over Large-Scale Irregular Terrain2014In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 61, no 2, p. 369-397Article in journal (Refereed)

A benchmark problem on atmospheric sound propagation over irregular terrain has been solved using a stable fourth-order accurate finite difference approximation of a high-fidelity acoustic model. A comparison with the parabolic equation method and ray tracing methods is made. The results show that ray tracing methods can potentially be unreliable in the presence of irregular terrain.

• 30.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Harmonic Lyapunov functions in the analysis of periodically switched systems2006In: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, p. 2759-2764Conference paper (Refereed)

The dynamic phasor model of a time-periodic system is used to derive a stability test involving a harmonic Lyapunov function. This reveals a new interpretation of the harmonic Lyapunov function with an appealing time-domain representation. Most importantly, it indicates that the ideas behind the harmonic Lyapunov equation can be generalized to include cyclic switching systems that have different pulse form in each period.

• 31.
Linnaeus University, Faculty of Engineering and Technology, Department of Mathematics Education.
Muntlig bedömning: Med fokus på elevers representationer2013Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis

Muntlig bedömning är, från och med höstterminen 2011, något som alla matematiklärare inom gymnasieskolan kommer att få genomföra då en muntlig del läggs som obligatorisk för alla elever inom årskurs 1. Syftet med den här studien är därför att konstruera kriterier som lärare kan använda som hjälp vid muntlig bedömning. Fokus kommer att ligga på elevers representationsformer och transformationer däremellan utifrån ett sociokulturellt perspektiv. Elevgrupper filmades då de löste en problemlösningsuppgift och analyserades utifrån ett begreppsligt ramverk. Resultatet visar att elevers transformationer mellan representationer visar både missuppfattningar och förståelse beroende på hur dessa transformationer ter sig. Elever som obehindrat lyckas vandra mellan olika representationer visar på god förståelse för det matematiska innehållet. Även elevers förmåga att skapa sig ett multimodalt arbetssätt visar sig, för läraren, vara värd att uppmärksamma.

• 32.
KTH, School of Electrical Engineering (EES), Electric Power Systems.
Texas Tech University.
The Feedback Control of Glucose: On the road to type II diabetes2006In: Proceedings of the 45th IEEE Conference on Decision & Control, 2006, p. 685-690Conference paper (Refereed)

This paper develops a mathematical model for the feedback control of glucose regulation in the healthy human being and is based on the work of Sorensen (1985). The proposed model serves as a starting point for modeling type H diabetes. Four agents - glucose and the three hormones insulin, glucagon, and incretins - are assumed to have an effect on glucose metabolism. By letting compartments represent anatomical organs, the model has a close resemblance to a real human body. Mass balance equations that account for blood flows, exchange between compartments, and metabolic sinks and sources are written, and these result in simultaneous differential equations that are solved numerically. The metabolic sinks and sources - removing or adding glucose, insulin, glucagon, and incretins - describe physiological processes in the body. These processes function as feedback control systems and have nonlinear behaviors. The results of simulations performed for three different clinical test types indicate that the model is successful in simulating intravenous glucose, oral glucose, and meals containing mainly carbohydrates.

• 33.
Dalarna University, School of Education and Humanities, Educational Work.
Att uttrycka matematik: En observationsstudie av vilka uttrycksformer och matematiska aktiviteter som uppmuntras och används i förskolan2013Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

Syftet med studien är att fördjupa kunskaperna om vilka matematiska aktiviteter ochuttrycksformer pedagogerna i förskolan använder sig av i planerade matematikaktiviteter.Utgångspunkt för undersökningen var uttrycksformerna som finns beskrivna i förskolansläroplan samt sex historiskt och kulturellt grundade matematiska aktiviteter.Syftet konkretiseras i följande frågeställningar: Vilka matematiska aktiviteter och vilka uttrycksformer uppmuntras och stöds avpedagogerna i planerade matematikaktiviteter? Vilka likheter och skillnader finns beroende på barnens ålder?För att få svar på dessa frågor genomfördes strukturerade observationer av planeradematematikaktiviteter på tre olika förskoleavdelningar. Barnens åldrar var 1-5 år och varjeavdelning observerades vid ett tillfälle under 45 minuter. Tekniker som användes vidgenomförandet av observationerna var papper, penna, kamera och videokamera.Studiens resultat visar att samtal och rörelse är de vanligast förekommande uttrycksformerna iplanerade matematikaktiviteter. Ingen pedagog använde sig av uttrycksformerna lek/drama ellerdans. Av de matematiska aktiviteterna var lokalisera och mäta de mest förekommande, följt avkonstruera hos de äldsta barnen.En slutsats som kan dras av studien är att det behövs en ökad medvetenhet och kunskap hospedagogerna om hur förskolan kan använda alla de uttrycksformer som beskrivs i Lpfö 98/2010för att stimulera och utveckla barnens matematiklärande.

• 34.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Auction Theory2018Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 35. Anco, S.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
Solutions of gasdynamic equations associated with classical and new conservation laws2015In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 268, p. 52-58Article in journal (Refereed)

Exact solutions of the one-dimensional gasdynamic equations are constructed by applying the method of conservation laws to all point-wise conserved vectors of the equations under consideration. Â© 2015 Elsevier Inc.

• 36. Andersen, Jorgen Ellegaard
Reducibility of quantum representations of mapping class groups2010In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 91, p. 215-239Article in journal (Refereed)

In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture this decomposition is a complete decomposition into irreducible representations for high enough levels.

• 37.
CTQM, Department of Mathematical Sciences, Aarhus University, Aarhus, Denmark.
On Reducibility of Mapping Class Group Representations: The SU(N) case2010In: Noncommutative structures in mathematics and physics / [ed] Stefaan Caenepeel, Jürgen Fuchs, Simone Gutt, Christophe Schweigert, Alexander Stolin, Freddy Van Oystaeyen, Brussels: Koninklijke vlaamse academie van Belgie voor Wetenschappen en kunsten, 2010, p. 27-45Conference paper (Refereed)

We review and extend the results of [1] that gives a condition for reducibility of quantum representations of mapping class groups constructed from Reshetikhin-Turaev type topological quantum field theories based on modular categories. This criterion is derived using methods developed to describe rational conformal field theories, making use of Frobenius algebras and their representations in modular categories. Given a modular category C, a rational conformal field theory can be constructed from a Frobenius algebra A in C. We show that if C contains a symmetric special Frobenius algebra A such that the torus partition function Z(A) of the corresponding conformal field theory is non-trivial, implying reducibility of the genus 1 representation of the modular group, then the representation of the genus g mapping class group constructed from C is reducible for every g\geq 1. We also extend the number of examples where we can show reducibility significantly by establishing the existence of algebras with the required properties using methods developed by Fuchs, Runkel and Schweigert. As a result we show that the quantum representations are reducible in the SU(N) case, N>2, for all levels k\in \mathbb{N}. The SU(2) case was treated explicitly in [1], showing reducibility for even levels k\geq 4.

• 38.
Center for Quantum Geometry of Moduli Spaces, University of Aarhus, Århus, Denmark.
Reducibility of quantum representations of mapping class groups2010In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 91, no 3, p. 215-239Article in journal (Refereed)

In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture this decomposition is a complete decomposition into irreducible representations for high enough levels.

• 39.
Chalmers .
University of Borås, Faculty of Textiles, Engineering and Business.
Approximate solution of a Thomas-Fermi model equation for bulk self-gravitating stellar objects in two dimensions2017In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 38, p. 1-8, article id 015406Article in journal (Refereed)

Direct variational methods are used to find simple approximate solutions of the Thomas–Fermi equations describing the properties of self-gravitating radially symmetric stellar objects both in the non-relativistic and ultra-relativistic cases. The approximate solutions are compared and shown to be in good agreement with exact and numerically obtained solutions.

• 40.
Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.
Linnaeus university, Vaxjö, Sweden. Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.
Fourier methods for harmonic scalar waves in general waveguides2016In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 98, no 1, p. 21-38Article in journal (Refereed)

A set of semi-analytic techniques based on Fourier analysis is used to solve wave-scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are the newly developed conformal mapping methods, wave splitting, Fourier series expansions in eigenfunctions to non-normal operators, the building block method or the cascade technique, Dirichlet-to-Neumann operators, and reformulation in terms of stable differential equations for reflection and transmission matrices. For an example, the results show good correspondence with a finite element method solution to the same problem in the low- and medium-frequency domains. The Fourier method complements finite element analysis as a waveguide simulation tool. For inverse engineering involving tuning of straight waveguide parts joining complicated waveguide elements, the Fourier method is an attractive alternative including time aspects. The prime motivation for the Fourier method is its added physical understanding primarily at low frequencies.

• 41.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Validated Enclosures of Rotation Numbers2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 42.
WorldLight.com AB, Sweden.
Mälardalen University, School of Education, Culture and Communication.
The mathematics of internet search engines2008In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 104, no 2, p. 211-242Article in journal (Refereed)

This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.

• 43.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
On the Theorem of Uniform Recovery of Random Sampling Matrices2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 3, p. 1700-1710Article in journal (Refereed)

We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an s-sparse signal from linear measurements (with high probability) is known to be m greater than or similar to s(ln s)(3) ln N. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of m x N-matrices, by considering what is called effective sparsity. We also present a condition on the so-called restricted isometry constants, delta s, ensuring sparse recovery via l(1)-minimization. We show that delta(2s) < 4/root 41 is sufficient and that this can be improved further to almost allow for a sufficient condition of the type delta(2s) < 2/3.

• 44.
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
Att arbeta med begreppsinlärning: Tillsammans med elever med annat modersmål än svenska2012Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis

Elever med annat modersmål än svenska besitter oftast inte den språkliga kompetens som förväntas av dem när de når skolåldern. Detta blir problematiskt vid begreppsinlärningen i matematik. Syftet med denna studie är att beskriva hur verksamma lärare arbetar med begreppsinlärning i klasser som har elever med annat modersmål än svenska. I studien har verksamma lärare intervjuats och observerats med fokus på begreppsinlärning och på elever med annat modersmål än svenska. Resultatet av studien visar att de verksamma lärarna är överens om att i klasser med elever med annat modersmål än svenska går det inte utgå ifrån att alla elever förstår begrepp genom ord. Istället behöver dessa elever arbeta med flera olika sinnen för att skapa förståelse.

• 45.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Economics. Res Inst Ind Econ, Stockholm, Sweden..
Tilburg Univ, CentER, Tilburg, Netherlands.;Tilburg Univ, TILEC, Tilburg, Netherlands.. Stockholm Sch Econ, Stockholm, Sweden.;Inst Adv Study Toulouse, Toulouse, France.;KTH Royal Inst Technol, Stockholm, Sweden..
Robustness to strategic uncertainty in the Nash demand game2018In: Mathematical Social Sciences, ISSN 0165-4896, E-ISSN 1879-3118, Vol. 91, p. 1-5Article in journal (Refereed)

This paper studies the role of strategic uncertainty in the Nash demand game. A player's uncertainty about another player's strategy is modeled as an atomless probability distribution over that player's strategy set. A strategy profile is robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in which every player's strategy is optimal under his or her uncertainty about the others (Andersson et al., 2014). In the context of the Nash demand game, we show that robustness to symmetric (asymmetric) strategic uncertainty singles out the (generalized) Nash bargaining solution. The least uncertain party obtains the bigger share. (C) 2017 Elsevier B.V. All rights reserved.

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Robustness to strategic uncertainty2014In: Games and Economic Behavior, ISSN 0899-8256, E-ISSN 1090-2473, Vol. 85, no 1, p. 272-288Article in journal (Refereed)

We introduce a criterion for robustness to strategic uncertainty in games with continuum strategy sets. We model a player's uncertainty about another player's strategy as an atomless probability distribution over that player's strategy set. We call a strategy profile robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in which every player's strategy is optimal under his or her uncertainty about the others. When payoff functions are continuous we show that our criterion is a refinement of Nash equilibrium and we also give sufficient conditions for existence of a robust strategy profile. In addition, we apply the criterion to Bertrand games with convex costs, a class of games with discontinuous payoff functions and a continuum of Nash equilibria. We show that it then selects a unique Nash equilibrium, in agreement with some recent experimental findings.

• 47.
Halmstad University, School of Education, Humanities and Social Science.
Laborativa material i grundskolans matematik: En kunskapsöversikt om hur laborativa material kan utveckla elevers förståelse och intresse för tal i bråkform2019Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
• 48.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.
För att eleverna verkar tänka bättre när de får prata: Vilka metoder kan man hitta hos lärare som främjar diskussioner i matematik2018Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis

Syftet med arbetet är att söka reda på olika metoder lärare använder i klassrumssituationer för att stödja elevernas utveckling i matematiska uttryck gällande muntlig kommunikation mellan elever och lärare. Arbetet är baserat på observationer av tre lärare i årskurs 4, 6 och 9. Insamlad information från observationerna har resulterat i tre olika lektionsstrukturer och ett antal frågemodeller. Gemensamt i samtliga lektioner är att eleverna får först diskutera och berätta innan läraren blanda sig i; läraren har använt elevernas samtal för att bygga vidare och utgår på det sättet utifrån elevernas kunskaper. Vissa lektioner har fokus legat i diskussionen och elevers presentation av sina lösningar för klassen. I andra lektioner har läraren använt en specifik didaktisk metod för att stimulera diskussionen och elevernas förståelse. Samtliga lärare uttrycker att ett mål de haft är att eleverna skall få chansen att diskutera och ge uttryck för sina tankar verbalt.

• 49.
University of Cambridge, UK.
Comparative studies of mathematics teachers’ observable learning objectives: validating low inference codes2009In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 71, no 2, p. 97-122Article in journal (Refereed)

Videotape is an increasingly used tool in cross-national studies of mathematics teaching. However, the means by which videotaped lessons are coded and analysed remains an underdeveloped area with scholars adopting substantially different approaches to the task. In this paper we present an approach based on generic descriptors of mathematics learning objectives. Exploiting live observations in five European countries, the descriptors were developed in a bottom-up recursive manner for application to videotaped lessons from four of these countries, Belgium (Flanders), England, Hungary and Spain. The analyses showed not only that the descriptors were consistently operationalised but also that they facilitated the identification of both similarities and differences in the ways in which teachers conceptualise and present mathematics that resonated with the available literature. In so doing we make both methodological and theoretical contributions to comparative mathematics research in general and debates concerning the national mathematics teaching script in particular.

• 50.
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
European mathematics curricula and classroom practices2014In: Masterclass in mathematics education: international perspectives on teaching and learning / [ed] Paul Andrews, Tim Rowland, London: Bloomsbury Academic, 2014, p. 179-190Chapter in book (Refereed)
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