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• 1.
University Pretoria, South Africa.
University of the Basque Country, Spain. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces2015In: Discrete dynamics in nature and society, ISSN 1026-0226, E-ISSN 1607-887X, Vol. 2015, article id 532725Article in journal (Refereed)

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

• 2.
Ton Duc Thang University, Ho Chi Minh City, Viet Nam.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Kragujevac, Serbia. University of Belgrade, Belgrade.
On Weakly Commuting Set-Valued Mappings on a Domain of Sets Endowed with Directed Graph2017In: Results in Mathematics, ISSN 1422-6383, Vol. 71, no 3-4, p. 1277-1295Article in journal (Refereed)

The aim of this paper is to present coincidence and common fixed point results of set-valued mappings satisfying certain generalized graphic F-contractive conditions on a family of sets endowed with a graph. It is worth mentioning that these results are obtained without appealing to any form of continuity of mappings involved herein. Some examples are presented to support the results proved in this paper. Our results unify, generalize and extend various comparable results in the existing literature. Â© 2016, Springer International Publishing.

• 3.
Ton Duc Thang Univ, Ho Chi Minh City, Vietnam..
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Fac Sci, Dept Math, Radoja Domanovica 12, Kragujevac 34000, Serbia. State Univ Novi Pazar, Serbia..
Common fixed points of set-valued F-contraction mappings on domain of sets endowed with directed graph2017In: Computational and Applied Mathemathics, ISSN 0101-8205, Vol. 36, no 4, p. 1607-1622Article in journal (Refereed)

The aim of this paper is to present common fixed point results of set-valued graphic F-contraction mappings on a family of sets endowed with a graph. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.

• 4.
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
Black-Litterman Model: Practical Asset Allocation Model Beyond Traditional Mean-Variance2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This paper consolidates and compares the applicability and practicality of Black-Litterman model versus traditional Markowitz Mean-Variance model. Although well-known model such as Mean-Variance is academically sound and popular, it is rarely used among asset managers due to its deficiencies. To put the discussion into context we shed light on the improvement made by Fisher Black and Robert Litterman by putting the performance and practicality of both Black- Litterman and Markowitz Mean-Variance models into test. We will illustrate detailed mathematical derivations of how the models are constructed and bring clarity and profound understanding of the intuition behind the models. We generate two different portfolios, composing data from 10-Swedish equities over the course of 10-year period and respectively select 30-days Swedish Treasury Bill as a risk-free rate. The resulting portfolios orientate our discussion towards the better comparison of the performance and applicability of these two models and we will theoretically and geometrically illustrate the differences. Finally, based on extracted results of the performance of both models we demonstrate the superiority and practicality of Black-Litterman model, which in our particular case outperform traditional Mean- Variance model.

• 5. Abramov, V.
Paal, E.Tallinn University of Technology.Silvestrov, Sergei D.Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.Stolin, A.Chalmers University of Techology.
Proceedings of the 3rd Baltic-Nordic Workshop “Algebra, Geometry, and Mathematical Physics”2008Conference proceedings (editor) (Refereed)
• 6. Abramov, Viktor
Mälardalen University, School of Education, Culture and Communication.
Preface [Special issue devoted to the 4th Baltic-Nordic Workshop “Algebra, Geometry and Mathematical Physics”]2010In: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, no 4Article in journal (Refereed)
• 7.
Mälardalen University, Department of Mathematics and Physics.
Java Applet for the Pricing of Exotic Options by Monte-Carlo Simulations in a Levy market with Stochastic Volatility2006Independent thesis Basic level (professional degree), 10 points / 15 hpStudent thesis
• 8.
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.

• 9.
Mälardalen University, Department of Mathematics and Physics.
Lärares syn på lässvaga elever inom matematik2008Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis

Syftet med detta arbete är att ta reda på hur lärarna upplever att lässvaga elever påverkas av sina lässvårigheter inom matematiken samt hur lärarna hanterar de problem som uppstår för att hjälpa eleven. Jag har valt den kvalitativa arbetsmetoden med semistrukturerade intervjufrågor. Resultatet visar att svag läsförmåga påverkar eleven inom matematiken men också inom andra ämnen. Inom matematiken påverkas eleven särskilt vid lästal samt vid problemlösning om eleven lämnas ensam med en text som den inte klarar av att läsa eller tyda. För att stödja eleven kan läraren eller någon annan läsa texten eller så arbetar eleverna i grupp där samarbetet mot resultatet är viktigast, inte att kunna läsa texten. Slutsatsen visar att eleven aldrig bör lämnas ensam med en text som den inte förstår, då eleven utestängs från den matematiska processen och det matematiska tänkandet.

• 10.
Mälardalen University, Department of Mathematics and Physics.
Problemlösning, kontext och kompetens2007Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis

Syftet med arbetet är att undersöka hur matematiklärarstudenter ska introducera problemlösning för sina elever och vad som påverkar studenternas tolkningar av problem. Jag har även undersökt vilka kompetenser studenterna anser att en matematiklärare behöver ha för att genomföra en framgångsrik undervisning i matematik genom problemlösning. I undersökningen diskuterar tre grupper med matematiklärarstudenter hur de ska introducera ett problem för eleverna och vilka komprtenser de anser att en matematiklärare behöver ha för att undervisa i matematik genom problemlösning. Resultaten visar att studenterna har olika strategier för att introducera problemlösning för eleverna och att studenternas tolkningar av problemet påverkar introduktionen. Studenterna gör olika tolkningar av problemet beroende av i vilken kontext de tolkar problemet. De har ingen enhetlig bild av vilka kompetenser som krävs av en matematiklärare, för att genomföra en undervisning som svarar mot skolverkets mål.

• 11.
Mälardalen University, Department of Mathematics and Physics.
Laborativt material i matematikundervisningen - med fokus på geobrädet2006Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis

yftet med detta arbete var att undersöka hur geobrädet fungerar i praktiken. För att få en inblick i hur det kan vara att arbeta med geobrädet, valde jag att gå ut på min partnerskola i 2 och utföra en kvalitativ undersökning. Denna undersökning bestod i att hålla ett antal lektioner där geobrädet var i fokus. Jag har också utfört en litteraturstudie för att få bättre inblick i det laborativa materialets betydelse för elevers matematikutveckling. Resultatet av min undersökning visade att eleverna blev mycket engagerade och aktiva och att de tyckte att arbetet med geobrädet var roligt och spännande. Jag som blivande lärare lärde mig också mycket om hur jag kan använda geobrädet i mitt kommande yrke och vad som är bra att tänka på när man arbetar med detta laborativa material. De slutsatser som jag kan dra efter att ha utfört detta examensarbete är att elever verkligen uppskattar att få laborera och prova saker på egen hand. Dessutom har jag som blivande pedagog blivit ännu mer övertygad om att det laborativa materialet har stor betydelse för elevernas matematiska utveckling.

• 12.
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
Matematik i förskolan: - ur förskollärares perspektiv2013Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis

Syftet med denna studie var att utforska förskollärares perspektiv på arbetet med matematiken i förskolan. Studien har utforskat hur förskollärare arbetar med matematik för att tillvarata, synliggöra och främja barns lärande och utveckling i förskolans verksamhet. Detta är en kvalitativ studie där sex stycken förskollärare intervjuats för att ta reda på deras perspektiv kring arbetet med att synliggöra och tillvarata matematik för att främja barnens lärande och utveckling. Resultatet visade att matematiken har en naturlig del i förskollärares vardagsarbete och att matematiska begrepp var en central del i barns lärande och utveckling i matematik. Att skapa möjligheter att uppleva matematik på ett positivt sätt har förskollärarna uttryckt som betydelsefullt. Förskollärarna i studien har beskrivit att barnen redan i förskolan kan ges förutsättning till ett lustfyllt lärande i matematik som grund för vidare lärande. Slutsatser som kan ställas utifrån denna studie är att en medvetenhet kring arbetet med matematik i förskolan är viktigt för att främja barns lärande och utveckling i matematik.

• 13.
Azad University, Teheran, Iran.
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.

• 14.
Mälardalen University, School of Education, Culture and Communication.
Nonlinear Least-Square Curve Fitting of Power-Exponential Functions: Description and comparison of different fitting methods2017Independent thesis Advanced level (degree of Master (Two Years)), 80 credits / 120 HE creditsStudent thesis

This thesis examines how to find the best fit to a series of data points when curve fitting using power-exponential models. We describe the different numerical methods such as the Gauss-Newton and Levenberg-Marquardt methods to compare them for solving non-linear least squares of curve fitting using different power-exponential functions. In addition, we show the results of numerical experiments that illustrate the effectiveness of this approach.Furthermore, we show its application to the practical problems by using different sets of data such as death rates and rocket-triggered lightning return strokes based on the transmission line model.

• 15.
University of California, Berkeley, USA.
Mälardalen University, Department of Mathematics and Physics. University of Latvia, Latvia. University of Latvia, Latvia. University of Bonn, Germany.
Quantum finite multitape automata1999In: SOFSEM’99: Theory and Practice of Informatics: 26th Conference on Current Trends in Theory and Practice of Informatics Milovy, Czech Republic, November 27 — December 4, 1999 Proceedings, 1999, Vol. 1725, p. 340-348Conference paper (Refereed)

Quantum finite automata were introduced by C. Moore, J. P. Crutchfield [4], and by A. Kondacs and J. Watrous [3]. This notion is not a generalization of the deterministic finite automata. Moreover, in [3] it was proved that not all regular languages can be recognized by quantum finite automata. A. Ambainis and R. Freivalds [1] proved Chat for some languages quantum finite automats may be exponentially more concise rather than both deterministic and probabilistic finite automata. In this paper we introduce the notion of quantum finite multi-tape automata and prove that there is a language recognized by a quantum finite automaton but not by deterministic or probabilistic finite automats. This is the first result on a problem which can be solved by a quantum computer but not by a deterministic or probabilistic computer. Additionally we discover unexpected probabilistic automata recognizing complicated languages.

• 16.
Faculté des Sciences, Université de Sfax, Tunisia .
Université de Haute Alsace, France . Lund University.
Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras2010In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 43, no 26, p. 265204-Article in journal (Refereed)

In this paper we construct ternary q-Virasoro-Witt algebras which q-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using su(1, 1) enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary q-Virasoro-Witt algebras constructed in this paper are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield a Hom-Nambu-Lie algebra structure for q-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary q-Virasoro-Witt algebras we construct, carry a structure of the ternary Hom-Nambu-Lie algebra for all values of the involved parameters.

• 17.
Mälardalen University, Department of Mathematics and Physics.
En analys av en mattestuga: - elever med matematiksvårigheter2007Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis
• 18.
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.

• 19.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
University of Copenhagen.
On the universality of the Epstein zeta functionManuscript (preprint) (Other academic)

We study universality properties of the Epstein zeta function En(L,s) for lattices L of large dimension n and suitable regions of complex numbers s . Our main result is that, as n→∞ , En(L,s) is universal in the right half of the critical strip as L varies over all n -dimensional lattices L . The proof uses an approximation result for Dirichlet polynomials together with a recent result on the distribution of lengths of lattice vectors in a random lattice of large dimension and a strong uniform estimate for the error term in the generalized circle problem. Using the same basic approach we also prove that, as n→∞ , En(L1,s)−En(L2,s) is universal in the full half-plane to the right of the critical line as (L1,L2) varies over all pairs of n -dimensional lattices. Finally, we prove a more classical universality result for En(L,s) in the s -variable valid for almost all lattices L of dimension n . As part of the proof we obtain a strong bound of En(L,s) on the critical line that is subconvex for n≥5 and almost all n -dimensional lattices L.

• 20.
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
Forecasting the Stock Market: A Neural Network Approch2009Student thesis

Forecasting the stock market is a complex task, partly because of the random walk behavior of the stock price series. The task is further complicated by the noise, outliers and missing values that are common in financial time series. Despite of this, the subject receives a fair amount of attention, which probably can be attributed to the potential rewards that follows from being able to forecast the stock market.

Since artificial neural networks are capable of exploiting non-linear relations in the data, they are suitable to use when forecasting the stock market. In addition to this, they are able to outperform the classic autoregressive linear models.

The objective of this thesis is to investigate if the stock market can be forecasted, using the so called error correction neural network. This is accomplished through the development of a method aimed at finding the optimum forecast model.

The results of this thesis indicates that the developed method can be applied successfully when forecasting the stock market. Of the five stocks that were forecasted in this thesis using forecast models based on the developed method, all generated positive returns. This suggests that the stock market can be forecasted using neural networks.

• 21.
Riga Technical University, Latvia.
Riga Technical University, Latvia. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Algorithms of the Copula Fit to the Nonlinear Processes in the Utility Industry2017In: Procedia Computer Science, ISSN 1877-0509, E-ISSN 1877-0509, Vol. 104, p. 572-577Article in journal (Refereed)

Our research studies the construction and estimation of copula-based semi parametric Markov model for the processes, which involved in water flows in the hydro plants. As a rule analyzing the dependence structure of stationary time series regressive models defined by invariant marginal distributions and copula functions that capture the temporal dependence of the processes is considered. This permits to separate out the temporal dependence (such as tail dependence) from the marginal behavior (such as fat tails) of a time series. Dealing with utility company data we have found the best copula describing data - Gumbel copula. As a result constructed algorithm was used for an imitation of low probability events (in a hydro power industry) and predictions.

• 22.
Umeå University.
Umeå University. Umeå University.
Fast multiplication of matrices over a finitely generated semiring2008In: Information Processing Letters, ISSN 0020-0190, E-ISSN 1872-6119, Vol. 107, no 6, p. 230-234Article in journal (Refereed)
• 23.
Mälardalen University, Department of Mathematics and Physics.
Mälardalen University, Department of Mathematics and Physics.
Integer Partitions2004Book (Other (popular science, discussion, etc.))
• 24.
Mälardalen University, Department of Mathematics and Physics.
Mälardalen University, Department of Mathematics and Physics.
Nationella prov i matematik utan miniräknare?: Med fokus på huvudräkning och miniräknare i anknytning till matematikundervisning och B1-delen i ämnesprovet för år 92008Student thesis

Vi började med att ställa oss frågan varför man valt att utesluta miniräknaren i det obligatoriska Nationella ämnesprovet i matematik för år 9. Enligt PRIM-gruppen, de som konstruerat Nationella prov i matematik, var avsikten att följa målen i styrdokumenten vad gäller huvudräkning och även synpunkter från arbetslivet har bidragit till detta beslut. Vi undrade då vidare hur lärare definierar begreppet huvudräkning och om det finns en generell uppfattning kring miniräknaren som orsak till försämrad huvudräkning. I styrdokumenten står det uttryckligen att eleven skall bruka miniräknaren och använda den som hjälpmedel. Vi har valt en kvalitativ metod i vår studie med intervjuer av lärare och PRIM-gruppen. Alla lärare vi intervjuade hänvisade till styrdokumenten vad gäller den miniräknarfria delen. Vi fann att lärare uppfattar att elever använder miniräknaren ofta även vid enklare beräkningar. Några av de intervjuade lärarna hade speciella lektioner för att träna huvudräkning utan hjälpmedel medans andra ansåg det falla sig naturligt i undervisningen.

• 25.
Mälardalen University, School of Education, Culture and Communication.
Multiplikationstabellen: Multiplikationstabellen2010Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis

Syftet med mitt arbete är att belysa vilka metoder som finns för att eleven ska lära sig multiplikationstabellen, och vikten av utantill kunnande av multiplikationstabellen för eleven. Arbetet tar upp viktiga faktorer som påverkar kunnandet av multiplikationstabellen t.ex. miniräknaren och forskning om minnet. För att kunna uppfylla mitt syfte intervjuade jag tre erfarna pedagoger som uttalar sig om detta. Jag studerade vad pedagogerna anser om utantill kunnande av multiplikationstabellen, vilka metoder de använder för att lära ut tabellerna och vad de anser om miniräknaren som hjälpmedel. Jag har också använt mig av litteratur som handlar om minnet och vad som finns för grund inom forskningen för inlärningen av multiplikationstabellerna. Genom en kvalitativ analys av mitt resultat har jag kommit fram till att utantill kunnande av multiplikationstabellen förenklar och underlättar för eleven. Det ger ett bra verktyg för eleven för en fortsatt utveckling inom matematik.

• 26.
Université de Haute-Alsace, Mulhouse, France. Université de Haute-Alsace, Mulhouse, France . Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras2014In: Springer Proceedings in Mathematics and Statistics, Berlin, Heidelberg: Springer, 2014, Vol. 85, p. 123-144Conference paper (Refereed)

The aim of this paper is to compare the structure and the cohomology spaces of Lie algebras and induced 3-Lie algebras

• 27.
Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
Université de Haute Alsace, Lab. de Mathématiques Informatique et Applications, 4, rue des Frères Lumière, F-68093 Mulhouse, France. Mälardalen University, School of Education, Culture and Communication.
Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 12, p. 123502-Article in journal (Refereed)

As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]

• 28.
Max Planck Institute for Gravitational Physics (AEI), Germany.
Université de Haute Alsace, France . Lund University, Sweden.
Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras2010In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, no 4, p. 043515-11Article in journal (Refereed)

The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n-ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n-Lie structures) constructed from the binary multiplication of a Hom-Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom-Nambu-Lie algebras obtained using this construction.

• 29.
Albert Einstein Institute, Golm, Germany.
Lund University.
Affine transformation crossed product type algebras and noncommutative surfaces2009In: Operator structures and dynamical systems: July 21-25 2008, Lorentz Center, Leiden, The Netherlands, satellite conference of the fifth European Congress of Mathematics, Amer. Math. Soc. , 2009, Vol. 503, p. 1-25Chapter in book (Refereed)
• 30.
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
Lärobokens inflytande över matematikundervisningen: en studie av läroboksförfattares åsikter och tankar bakom utformandet av läroböcker2008Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis

Den här studien syftar till att undersöka hur olika författare resonerar kring författandet av en lärobok, angående utformning och påverkan. För att undersöka detta har vi genomfört kvalitativa intervjuer med sex läroboksförfattare. Resultatet av intervjuerna visar att läroboksförfattarna har en väl utarbetad tanke med hur deras läroböcker ska användas i undervisningen. Vi kan också se att författarna strävar efter att följa gällande styrdokument för skolan. Vidare har vi identifierat några av de olika faktorer som påverkar författarna i deras skrivande, något som ger utslag i läroböckerna. De viktigaste faktorerna visar sig vara styrdokument, nationella prov samt författarnas syn på matematik och lärande. Denna syn ligger även till grund för författarnas tankar med hur läroboken ska användas i undervisningen.

• 31.
Universit́e de Haute Alsace, France .
Universit́e de Haute Alsace, France . Lund University.
Generalization of n-ary Nambu algebras and beyond2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 8, p. Article number 083501-Article in journal (Refereed)

The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.

• 32.
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
Undervisning om negativa tal i mellanstadiet: En kvalitativ studie om hur lärare i mellanstadiet introducerar negativa tal2017Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis

Det övergripande syftet med denna studie är att undersöka hur ett antal lärare i åk 4-6 introducerar negativa tal i matematikundervisningen med hänsyn till sammanhang (t.ex. addition eller prioriteringsregler) och metaforer (t.ex. termometern), och deras orsaker till varför de gör på just dessa sätt. Metoder som används i studien är för att samla in data är observationer och intervjuer. Resultaten visar att de lärare som observerades och intervjuades främst använder sig av tallinjen som sammanhang och termometer samt tallinjen som metaforer för att introducera negativa tal. Enligt de observerade lärarna använder de sig av just dessa sammanhang och metaforer (t.ex. tallinjen och termometern) eftersom dessa lätt kan kopplas till elevernas vardagsliv. Vissa sammanhang och metaforer valdes bort eftersom lärarna anser att de är svåra att koppla till elevernas vardagsliv och de anser att det blir överkurs för deras elever.

• 33.
Mälardalen University, School of Education, Culture and Communication.
A comparison of a Lazy PageRank and variants for common graph structures2018Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis

The thesis first reviews the mathematics behind the Google’s PageRank, which is the state-of-the-art webpage ranking algorithm. The main focus of the thesis is on exploring a lazy PageRank and variants, related to a random walk, and by realizing that, they can be computed using the very same algorithm, find lazy PageRank and variants' expressions for some common graph structures, for example, a line-graph, a complete-graph, a complete-bipartite graph including a star graph, and try to get some understanding of the behavior of the PageRank, when a network evolves, for example either by a contraction or an expansion of graphs’ nodes or links.

• 34.
Danderyds Gymnasium, Danderyd, Sweden.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Umeå University, Umeå, Sweden. Uppsala University, Uppsala, Sweden.
Semi-Bloch Functions in Several Complex Variables2016In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 26, no 1, p. 463-473Article in journal (Refereed)

Let M be an n-dimensional complex manifold. A holomorphic function f:M→C is said to be semi-Bloch if for every λ∈C the function (Formula presented.) is normal on M. We characterize semi-Bloch functions on infinitesimally Kobayashi non-degenerate M in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.

• 35.
Danderyd gymnasium.
Mälardalen University, School of Education, Culture and Communication. Umeå University. Uppsala University.
Semi-Bloch functions in several complex variables2013Report (Other academic)

Let $M$ be an $n$-dimensional complex manifold. A holomorphic function $f:M\to \mathbb C$ is said to be semi-Bloch if for every $\lambda\in \mathbb C$ the function $g_\lambda=\exp(\lambda f(z))$ is normal on $M$. We characterise Semi-Bloch functions on infinitesimally Kobayashi non-degenerate $M$ in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.

• 36.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
American Option pricing under Mutiscale Model using Monte Carlo and Least-Square approach2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

In the finance world, option pricing techniques have become an appealing topic among researchers, especially for pricing American options. Valuing this option involves more factors than pricing the European style one, which makes it more computationally challenging. This is mainly because the holder of American options has the right to exercise at any time up to maturity. There are several approaches that have been proved to be efficient and applicable for maximizing the price of this type of options. A common approach is the Least squares method proposed by Longstaff and Schwartz. The purpose of this thesis is to discuss and analyze the implementation of this approach under the Multiscale Stochastic Volatility model. Since most financial markets show randomly variety of volatility, pricing the option under this model is considered necessary. A numerical study is performed to present that the Least-squares approach is indeed effective and accurate for pricing American options.

• 37.
Mälardalen University, School of Education, Culture and Communication.
Twisted derivations, quasi-hom-Lie algebras and their quasi-deformations2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

Quasi-hom-Lie algebras (qhl-algebras) were introduced by Larsson and Silvestrov (2004) as a generalisation of hom-Lie algebras, which are a deformation of Lie algebras. Lie algebras are defined by an operation called bracket, [·,·], and a three-term Jacobi identity. By the theorem from Hartwig, Larsson, and Silvestrov (2003), this bracket and the three-term Jacobi identity are deformed into a new bracket operation, <·,·>, and a six-term Jacobi identity, making it a quasi-hom-Lie algebra.

Throughout this thesis we deform the Lie algebra sl2(F), where F is a field of characteristic 0. We examine the quasi-deformed relations and six-term Jacobi identities of the following polynomial algebras: F[t], F[t]/(t2), F[t]/(t3), F[t]/(t4), F[t]/(t5), F[t]/(tn), where n is a positive integer ≥2, and F[t]/((t-t0)3). Larsson and Silvestrov (2005) and Larsson, Sigurdsson, and Silvestrov (2008) have already examined some of these cases, which we repeat for the reader's convenience.

We further investigate the following σ-twisted derivations, and how they act in the different cases of mentioned polynomial algebras: the ordinary differential operator, the shifted difference operator, the Jackson q-derivation operator, the continuous q-difference operator, the Eulerian operator, the divided difference operator, and the nilpotent imaginary derivative operator. We also introduce a new, general, σ-twisted derivation operator, which is σ(t) as a polynomial of degree k.

• 38.
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
Måluppfyllelse genom konkret material i matematikundervisning: Hur fyra lärare använder konkret material för att uppnå ett visst matematiskt mål och hur de bedömer att detta mål är uppnått.2017Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

Syftet med denna studie är att undersöka varför och hur lärare använder konkret material i matematikundervisningen för att uppfylla ett matematiskt mål. Genom att observera och intervjua fyra lärare med erfarenheter inom ämnet, framkommer resultat som visar att lärare är positiva till laborativa arbetssätt men att läroboken upplevs allt för styrande och på så sätt utgör ett hinder. Syftet med det konkreta materialet lyfts inte alltid fram, vilket resulterar i att syftet blir underordnat själva användandet av konkret material. Slutsatsen blir således att måluppfyllelsen inte går att bedöma i de fall aktiviteterna med konkret material inte har ett givet syfte.

• 39.
Mälardalen University, Department of Mathematics and Physics.
Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank2005In: Proceedings of the Royal Society of London, ISSN 0035-9017, Vol. 461, no 2059, p. 2181-2195Article in journal (Refereed)

We present a study of Rainich-like conditions for symmetric and trace-free tensors T. For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source-free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to gain a complete set of algebraic and differential conditions on T for it to be a superenergy tensor of a Weyl candidate tensor, satisfying the Bianchi vacuum equations. By a result of Bell and Szekeres, this implies that in vacuum, generically, T must be the Bel-Robinson tensor of the spacetime. For the rank 3 case, we derive a complete set of necessary algebraic and differential conditions for T to be the superenergy tensor of a massless spin-3/2 field, satisfying the source-free field equation.

• 40.
Mälardalen University, Department of Mathematics and Physics.
Unique characterization of the Bel-Robinson tensor2004In: Classical and Quantum Graviry, ISSN 0264-9381, Vol. 21, no 14, p. 3499-3503Article in journal (Refereed)

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.

• 41.
Mälardalen University, Department of Mathematics and Physics.
Skriftliga redovisningar av matematikuppgifternas lösningar, viktiga eller inte?: `Vilka ambitioner har lärare med sin undervisning och vilka krav ställer de på sina elever?2007Student thesis

Syftet med undersökningen är att ta reda på i vilken utsträckning lärare kräver av sina elever att de skriftligen redovisar lösningar på matematikuppgifter de arbetar med, samt i vilken utsträckning lärarna tror att eleverna går tillbaka och reflekterar över sina uppgifter där skriftliga lösningar saknas när de rättar själva. Undersökningen är utförd genom en enkät samt tillhörande möjligheter för respondenterna att lämna egna kommentarer till frågorna. Studien visar att lärarnas önskan är att eleverna på något vis ska redovisa sina lösningar skriftligen samt gå tillbaka och reflektera när de rättar, men de kräver det inte av eleverna i någon större utsträckning. Eleverna rättar oftast själva, men lärarna kontrollerar emellanåt.

• 42.
Maastricht University .
Stockholm School of Economics. Stockholm University. Mälardalen University, School of Education, Culture and Communication.
The subgroup problem: When can binding voting on extractions from a common resource pool overcome the tragedy of the commons?2013In: Journal of Economic Behavior and Organization, ISSN 0167-2681, E-ISSN 1879-1751, Vol. 91, p. 122-130Article in journal (Refereed)

Using a common pool resource game protocol with voting we examine experimentally how cooperation varies with the level at which (binding) votes are aggregated. Our results are broadly in line with theoretical predictions. When players can vote on the behavior of the whole group or when leaders from each group can vote for the group as a whole, extraction levels from the common resource pool are close to the social optimum. When players extract resources individually, there is substantial overextraction. When players vote in subgroups, there is initially less overextraction but it increases over time. This suggests that in order for binding voting to overcome the tragedy of the commons in social dilemmas, it should ideally affect the group as a whole.

• 43.
University of Latvia, Latvia.
Mälardalen University, Department of Mathematics and Physics.
Ambainis-Freivalds’ algorithm for measure-once automata2001In: Fundamentals of Computation Theory: 13th International Symposium, FCT 2001 Riga, Latvia, August 22–24, 2001 Proceedings, 2001, Vol. 2183, p. 83-93Conference paper (Refereed)

An algorithm given by Ambainis and Freivalds [1] constructs a quantum finite automaton (QFA) withO(logp) states recognizing the language L p = a i |i is divisible by p with probability 1 − ε, for any ε > 0 and arbitrary prime p. In [4] we gave examples showing that the algorithm is applicable also to quantum automata of very limited size. However, the Ambainis-Freivalds algoritm is tailored to constructing a measure-many QFA (defined by Kondacs and Watrous [2]), which cannot be implemented on existing quantum computers. In this paper we modify the algorithm to construct ameasure-once QFA of Moore and Crutchfield [3] and give examples of parameters for this automaton. We show for the language L p that a measure-once QFA can be twice as space efficient as measure-many QFA’s.

• 44. Biffi, Elena
Mälardalen University, School of Education, Culture and Communication.
Monte Carlo semi-Markov methods  for credit risk migration and Basel II rules II2008In: Journal of Numerical and Applied Mathematics, Vol. 96, p. 59-86Article in journal (Refereed)
• 45. Biffi, Elena
Mälardalen University, School of Education, Culture and Communication.
Monte Carlo semi-Markov methods  for credit risk migration and Basel II rules. I.2008In: Journal of Numerical and Applied Mathematics, ISSN 0868-6912, Vol. 1, p. 28-58Article in journal (Refereed)
• 46.
Mälardalen University, Department of Mathematics and Physics.
Mälardalen University, Department of Mathematics and Physics.
A Quantitative Risk Optimization of Markowitz Model: An Empirical Investigation on Swedish Large Cap List2007Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis

This paper is an empirical study on Harry Markowitz work on Modern Portfolio Theory. The model introduced by him assumes the normality of assets’ return. We examined the OMX Large Cap List1 by mathematical and statistical methods for normality of assets’ returns. We studied the effect of the parameters, Skewness and Kurtosis for different time series data. We tried to figure it out which data series is better to construct a portfolio and how these extra parameters can make us better informed in our investments.

• 47.
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
Jag skulle ju också vilja tänka lite: En kvalitativ studie om matematiskt begåvade elevers uppfattningar kring matematikundervisning2013Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

The mathematic gifted pupil needs support, variation and challenge as much as other children. Therefore it is important that these children do not end up in the background and that the teacher does not think that ”they can handle it on their own”. The aims of this study are to explore the mathematic gifted pupils´ beliefs about mathematics teaching, their learning styles and how they want to work to have the opportunity to develop their full mathematical capacity.  With support from theory and earlier research we chose six mathematical gifted pupils in the fourth grade to participate in the study. As the research method we chose to interview these pupils in order to get a deeper understanding of how they believe that their own learning in mathematic looks like, how they think they learn the best and how they want to work to have the opportunity to develop their full mathematical capacity. The result and conclusion of the interviews show that according to the pupils, a majority of the learning situations includes the pupils’ individual work and by that these children do not get the help and support that they need. The results from the interviewees also show that these pupils have different ways of learning, like everybody else, and therefore the learning situations have to be varying.  Finally, the result shows that the pupils want to have challenges, work together in groups and more support from teachers to be able to develop their full mathematical capacity.

• 48.
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
Hur man utvecklar automatiserad kunskap av multiplikationstabellerna: En jämförelse av två undervisningsaktiviteter i årskurs 32016Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis

För att eleverna ska nå de kunskapsmål som Skolverket suttit upp inom matematik, behöver de utveckla och behärska flera matematiska förmågor. För att kunna lösa uppgifter utifrån de fyra grundläggande räknesätten underlättar det om elever har utvecklat utantillkunskaper för b.la. multiplikationstabellerna. Syftet med denna studie är att jämföra två olika undervisningsaktiviteter, grundade i behaviorismen respektive pragmatismen, för att se vilken som är mest framgångsrik för automatisering av multiplikationstabeller. Studien har genomförts i årskurs 3 i två parallellklasser inriktat på sjuans, åttans och nians multiplikationstabell. Varje klass fick ta del av varsin undervisningsaktivitet och det genomfördes flera skriftliga tester för att jämföra resultaten. Resultaten visade en marginell skillnad mellan de två grupperna som båda hade förbättrat sina kunskaper av multiplikationstabellerna. Slutsatsen blev därför att båda aktiviteterna var lika framgångsrika för studiens syfte.

• 49.
Mälardalen University, School of Education, Culture and Communication.
Is it all in their heads?: A study of the strategies used in mental arithmetic by Swedish pupils in their last years of the obligatory school and in the upper secondary school2008Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Competence in mental arithmetic is recognised by many as essential to be active participants in the fast flowing, high technological society we live in today.  Many have noticed pupils’ unwillingness to set their calculators aside and practice this aspect of mathematics when possible.  Furthermore, some studies show that pupils’ ability to compute mentally deteriorates as they pass through the school system.  Through testing classes in a Swedish obligatory school and an upper secondary school, the aim of this thesis is to see if the goals set by The National [Swedish] Agency for Education regarding mental arithmetic, are being fulfilled.  Through using questionnaires to collect the strategies and ideas of the pupils, a wide range of problematic mathematical misconceptions became evident.  These are highlighted since they are important aspects teachers should be aware of.  The results of this study show that the obligatory school classes are far from reaching the goals set for them whereas the upper secondary classes show good results.  Furthermore, there is an apparent improvement in their progression, resulting in a fulfilment the official goals.  Many pupils however, seem reluctant to rely on their mental arithmetic capabilities and resort to algorithmic strategies.  Other problems to emerge are in carrying out table calculations and in a lack of number sense when deeming if the answers are reasonable.

• 50.
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
Samband mellan de fyra räknesätten- en läromedelsanalys2012Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis

Sambandet mellan de fyra räknesätten är en del i utvecklingen av den matematiska förståelsen. Syftet med denna studie är att analysera hur ett antal olika läromedel i matematik riktade till årskurs 1-3 tar upp dessa samband. Med läromedel menas då läroböcker, samt tillhörande lärarhandledningar. Resultatet visar att flertalet av de analyserade läromedlen inte tar upp alla samband, medan ett fåtal tar upp alla samband men i olika stor omfattning. Dessutom visar analysen hur viktig lärarhandledningen är för att ge eleverna fler övningstillfällen i att träna de fyra sambanden, eftersom en stor del av dessa tillfällen förekommer i lärarhandledningen och inte i läroböckerna. Lärare som endast följer ett enskilt läromedel i sin undervisning kan alltså gå miste om mycket när det gäller sambandet mellan de fyra räknesätten.

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