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  • 1.
    Abdulla, Ariyan
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Andersson, Erik
    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
    Abstract [en]

    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.

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  • 2.
    Aboud, Mathilde
    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
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  • 3.
    Abrahamsson, Olle
    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
    Abstract [en]

    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.

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  • 4. Abtahi, Yasmine
    et al.
    Adler, J.
    Guillemette, D.
    Herheim, R.
    Lerman, S.
    Maheux, J-F.
    Valero, Paola
    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.
    Ackeflo, Olle
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Digitala verktyg i matematikundervisningen: Lärares användning av digitala verktyg vid problemlösningsuppgifter i matematik2020Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med denna kvalitativa studie var att genom semi-strukturerade intervjuer med fem matematiklärare undersöka hur, varför och när lärarna väljer att använda digitala verktyg vid problemlösning i matematik. Detta är relevant på grund av ökade krav att använda digitala verktyg i skolan och för att forskning pekat ut nödvändigheten av att de digitala verktygen används på rätt sätt i undervisningen. Det teoretiska ramverket TPACK (teknisk, pedagogisk och ämnesmässig kunskap) har använts för att analysera lärarnas intervjusvar för att synliggöra i vilken grad lärarna besitter teknisk, pedagogisk och ämnesmässig kunskap och vilken betydelse dessa kunskaper har för den undervisning som innefattar digitala verktyg i samband med problemlösning. Resultatet i denna studie visar att digitala verktyg är ett stöd för läraren i undervisningen eftersom dessa kan öka elevernas motivation för ämnet. Genom att använda digitala verktyg kan läraren också lättare individanpassa sin undervisning för de elever som har svårt för matematik eller för de som behöver mer utmanande uppgifter. Lärarna måste på egen hand införskaffa den kunskap som krävs gällande de digitala verktygen för att kunna bedriva en så bra matematikundervisning som möjligt, vilket lärarna upplever som problematiskt. Det är tydligt att avsaknaden av utbildning om digitala verktyg hos lärarna är ett problem då de måste utbilda sig själva om de skulle behöva det.

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  • 6.
    Adobah-Otchey, Daniel
    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
    Abstract [en]

    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.

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  • 7. Adolfsson, Sandra
    Matematikverkstad: hur kan lärare och elever arbeta där?2010Student paper other, 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    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.

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  • 8.
    Aermark, Lior Alexandra
    Stockholm University, Faculty of Science, Department of Mathematics.
    Hardy and spectral inequalities for a class of partial differential operators2014Doctoral thesis, monograph (Other academic)
    Abstract [en]

    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.

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  • 9.
    Aerts, Diederik
    et al.
    Brussels Free University, Belgium.
    Khrennikov, AndreiLinnaeus University, Faculty of Technology, Department of Mathematics.Melucci, MassimoUniversity of Padova, Italy.Bourama, ToniHoward University, USA.
    Quantum-Like Models for Information Retrieval and Decision-Making2019Collection (editor) (Refereed)
    Abstract [en]

    Recent years have been characterized by tremendous advances in quantum information and communication, both theoretically and experimentally. In addition, mathematical methods of quantum information and quantum probability have begun spreading to other areas of research, beyond physics. One exciting new possibility involves applying these methods to information science and computer science (without direct relation to the problems of creation of quantum computers). 

    The aim of this Special Volume is to encourage scientists, especially the new generation (master and PhD students), working in computer science and related mathematical fields to explore novel possibilities based on the mathematical formalisms of quantum information and probability.  The contributing authors, who hail from various countries, combine extensive quantum methods expertise with real-world experience in application of these methods to computer science. The problems considered chiefly concern quantum information-probability based modeling in the following areas: information foraging; interactive quantum information access; deep convolutional neural networks; decision making, quantum dynamics; open quantum systems; and theory of contextual probability. 

    The book offers young scientists (students, PhD, postdocs) an essential introduction to applying the mathematical apparatus of quantum theory to computer science, information retrieval, and information processes. 

  • 10.
    Agram, Nacira
    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)
    Abstract [en]

    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.

  • 11.
    Agram, Nacira
    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)
    Abstract [en]

    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+δ)" role="presentation">PX(t+δ), for a given positive constant δ" 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.

  • 12.
    Agram, Nacira
    et al.
    University of Oslo, Norway;University of Mohamed Khider, Algeria.
    Bachouch, Achref
    University of Oslo, Norway.
    Oksendal, Bernt
    University of Oslo, Norway.
    Proske, Frank
    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)
    Abstract [en]

    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.

  • 13.
    Agram, Nacira
    et al.
    University of Oslo, Norway.
    Engen Rose, Elin
    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)
    Abstract [en]

    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.

  • 14.
    Agram, Nacira
    et al.
    University Med Khider, Algeria.
    Haadem, Sven
    Linnaeus University, Faculty of Technology, Department of Mathematics. University of Oslo, Norway.
    Oksendal, Bernt
    University Med Khider, Algeria.
    Proske, Frank
    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)
    Abstract [en]

    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.

  • 15.
    Agram, Nacira
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Oksendal, Bernt
    University of Oslo, Norway.
    Introduction to White Noise, Hida-Malliavin Calculus and ApplicationsManuscript (preprint) (Other academic)
    Abstract [en]

    The purpose of these lectures is threefold: We first give a short survey of the Hida white noise calculus, and in this context we introduce the Hida-Malliavin derivative as a stochastic gradient with values in the Hida stochastic distribution space (S. We show that this Hida-Malliavin derivative defined on L2(FT,P) is a natural extension of the classical Malliavin derivative defined on the subspace D1,2 of L2(P). The Hida-Malliavin calculus allows us to prove new results under weaker assumptions than could be obtained by the classical theory. In particular, we prove the following: (i) A general integration by parts formula and duality theorem for Skorohod integrals, (ii) a generalised fundamental theorem of stochastic calculus, and (iii) a general Clark-Ocone theorem, valid for all F∈L2(FT,P). As applications of the above theory we prove the following: A general representation theorem for backward stochastic differential equations with jumps, in terms of Hida-Malliavin derivatives; a general stochastic maximum principle for optimal control; backward stochastic Volterra integral equations; optimal control of stochastic Volterra integral equations and other stochastic systems.

  • 16.
    Agram, Nacira
    et al.
    University of Oslo, Norway;University of Biskra, Algeria.
    Øksendal, Bernt
    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)
    Abstract [en]

    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.

  • 17.
    Agram, Nacira
    et al.
    University Med Khider, Algeria.
    Øksendal, Bernt
    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)
    Abstract [en]

    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.

  • 18.
    Agram, Nacira
    et al.
    University Med Khider, Algeria.
    Øksendal, Bernt
    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)
    Abstract [en]

    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.

  • 19.
    Agram, Nacira
    et al.
    University of Oslo, Norway.
    Øksendal, Bernt
    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)
    Abstract [en]

    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.

  • 20.
    Agram, Nacira
    et al.
    University of Oslo, Norway;University Mohamed Knider of Biskra, Algeria.
    Øksendal, Bernt
    University of Oslo, Norway.
    Yakhlef, Samia
    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)
    Abstract [en]

    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.

  • 21.
    Ahijado, Susana
    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
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  • 22.
    Ahlberg, Sandra
    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
    Abstract [sv]

    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. 

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  • 23.
    Ahlgren Veinfors, Elin
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Lang, Karolina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Andersson, Malin
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Matematisk fallenhet, problemlösning och motivation: En systematisk litteraturstudie om hur problemlösning kan motivera elever med matematisk fallenhet2019Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I denna systematiska litteraturstudie fokuseras elever med fallenhet för matematik, problemlösning samt motivation och sambanden mellan dessa. Syftet med studien är att kartlägga hur elever med matematisk fallenhet kan utmärka sig, att undersöka hur problemlösning kan utmana och utveckla dessa elever samt att undersöka sambanden mellan elever med matematisk fallenhet, problemlösning och motivation. För att besvara studiens syfte samt frågeställningar baseras studien på ett flertal vetenskapliga publikationer som har analyserats utifrån tre teoretiska perspektiv. Studiens resultatanalys visar på flera utmärkande drag hos elever med matematisk fallenhet, vissa mer förekommande än andra. Resultatanalysen i studien redogör även för kännetecken för problemlösningsuppgifter, med vilka faser en problemlösningsuppgift kan lösas samt hur arbete med problemlösning kan bidra till utmaning och fortsatt utveckling hos elever med matematisk fallenhet. Avslutningsvis redogör studiens resultatanalys för sambandet mellan elever med matematisk fallenhet, problemlösning och motivation. Studien visar att motivationen hos elever med matematisk fallenhet ökar vid arbete med problemlösning.

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  • 24.
    Ahlqvist, Susanne
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Johansson, Maria
    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
    Abstract [sv]

    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.

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  • 25.
    Ahmed, Lisa
    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
    Abstract [sv]

    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.

  • 26.
    Ahrnbom, Moa
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics and Science Education.
    Eklund, Maria
    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
    Abstract [sv]

    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.

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  • 27.
    Albahaca, Juan Carlos
    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
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  • 28.
    Aleksanyan, Hayk
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). The University of Edinburgh.
    Shahgholian, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Sjölin, Per
    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)
    Abstract [en]

    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.

  • 29.
    Ali, Rafef
    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
    Abstract [sv]

    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. 

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  • 30.
    All Carreberg, Susanna
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Karlsson, Lina
    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
    Abstract [sv]

    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.

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    Tal och tanke
  • 31.
    Allahviranloo, Tofigh
    et al.
    Azad University, Teheran, Iran.
    Arjan, Skuka
    Izmir University, Izmir, Turkey.
    Tahvili, Sahar
    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)
    Abstract [en]

    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  fuzzy linear system  with a fuzzy number vector  in the right hand side and crisp a coefficient matrix  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.

  • 32.
    Alm, Lena
    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)
  • 33. Almquist, Martin
    et al.
    Karasalo, Ilkka
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.
    Mattsson, Ken
    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)
    Abstract [en]

    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.

  • 34.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    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)
    Abstract [en]

    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.

  • 35.
    Alriksson, Madeleine
    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
    Abstract [sv]

    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. 

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  • 36.
    Alvehag, Karin
    et al.
    KTH, School of Electrical Engineering (EES), Electric Power Systems.
    Martin, Clyde
    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)
    Abstract [en]

    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.

  • 37.
    Amcoff, Linda
    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
    Abstract [sv]

    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.

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  • 38.
    An, Filip
    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
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  • 39. Anco, S.
    et al.
    Ibragimov, Nail
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Imamutdinova, K.V.
    Karimova, E.N.
    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)
    Abstract [en]

    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. © 2015 Elsevier Inc.

  • 40.
    Anderberg, Lina
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Bogren, Elin
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Nivågruppering inom matematikämnet: Hur påverkas elevers lärande av undervisning i homogena grupper?2020Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Detta är en systematisk litteraturstudie som fokuserar på nivågruppering inom matematikämnet i grundskolan. Syftet är att undersöka hur sådana grupperingar kan tillämpas samt hur det påverkar elevers lärande. Den data som samlats in har sammanställts i en innehållsanalys. Koppling har sedan gjorts till det sociokulturella perspektivet och dess beskrivning av scaffolding och lärande i samspel med andra. Resultatet ger ingen entydig bild av huruvida elever påverkas av nivågruppering, då skilda uppfattningar presenteras i de olika studierna. Vad som dock kunnat urskiljas är att flertalet faktorer har betydelse för hur eleverna påverkas av nivågruppering. Elevernas kunskapsnivå är en av dessa faktorer. Ytterligare faktorer som har betydelse för utfallet är på vilket sätt nivågruppering tillämpas, elevernas självbild samt lärarens förväntningar.

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    Nivågruppering inom matematikämnet
  • 41. Andersen, Jorgen Ellegaard
    et al.
    Fjelstad, Jens
    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)
    Abstract [en]

    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.

  • 42.
    Andersen, Jørgen Ellegaard
    et al.
    CTQM, Department of Mathematical Sciences, Aarhus University, Aarhus, Denmark.
    Fjelstad, Jens
    Department of Physics, Karlstad University, Karlstad, Sweden.
    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)
    Abstract [en]

    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.

  • 43.
    Andersen, Jørgen Ellegaard
    et al.
    Center for Quantum Geometry of Moduli Spaces, University of Aarhus, Århus, Denmark.
    Fjelstad, Jens
    Department of Physics, Karlstad University, Karlstad, Sweden.
    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)
    Abstract [en]

    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.

  • 44.
    Anderson, Dan
    et al.
    Chalmers .
    Desaix, Mats
    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)
    Abstract [en]

    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.

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  • 45.
    Andersson, Anders
    et al.
    Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.
    Nilsson, Börje
    Linnaeus university, Vaxjö, Sweden.
    Biro, Thomas
    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)
    Abstract [en]

    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.

  • 46.
    Andersson, Björn
    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
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  • 47.
    Andersson, Fredrik K.
    et al.
    WorldLight.com AB, Sweden.
    Silvestrov, Sergei
    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)
    Abstract [en]

    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.

  • 48.
    Andersson, Jesper
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Bråk i läromedel: En läromedelsanalys med utgångspunkt i variationsteorin2020Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med denna studie är att undersöka vilka möjligheter elever har att utveckla sin förståelse för bråk i en läroboksstyrd undervisning. Forskning visar att läroböcker har en stor inverkan på matematikundervisningen, och undersökningar visar att även i Sverige används läroböcker i stor utsträckning. Det är därför av intresse att undersöka hur väl ett område som bråk, som ofta ses som ett problematiskt område, behandlas i läromedlen. I studien har tre olika läromedel undersökts och totalt 15 böcker. Denna studie är således en innehållsanalys, och variationsteorin har valts som utgångspunkt. I studien har fem kritiska aspekter för bråk valts ut från olika forskningsresultat. Läromedlen har sedan undersökts för att se om uppgifter rörande de olika aspekterna förekommer, och om något variationsmönster används för att förtydliga den kritiska aspekten. Resultatet visar att vissa aspekter behandlas i större utsträckning än andra, men också att läromedlen ofta missar viktiga delar.

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  • 49.
    Andersson, Joakim
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.
    Representationsformer i algebrans värld: En läromedelsanalys om representationers progression i år 4-62020Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med den här studien är att analysera olika läromedels uppbyggnad och struktur med fokus på representationsformernas progression i kunskapsområdet algebra. Anledningen till att studien handlar om just detta är för att algebra är ett väldigt viktigt område i matematiken för att förbereda elever för framtida matematiska områden. Dagens undervisning är också i hög grad läromedelsstyrd, vilket också motiverar till studien. För att undersöka de olika läromedlen användes en innehållsanalys där väsentliga uppgifter valdes ut och analyserades. Resultatet visade att det var svårt att få en tydligt bild av progressionen, men att uppgifterna i samtliga läromedel i hög grad representerades fullständigt symboliskt. Slutsatsen som dras är att den läromedelsstyrda skola vi har idag kan vara bristfällig och att det är lärarens uppgift att inkludera de relevanta representationsformerna elever behöver för att ta till sig algebra.

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  • 50.
    Andersson, Joel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Strömberg, Jan-Olov
    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)
    Abstract [en]

    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.

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