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  • 1.
    Abbas, M.
    et al.
    University Pretoria, South Africa.
    De La Sen, M.
    University of the Basque Country, Spain.
    Nazir, Talat
    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)
    Abstract [en]

    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.
    Abbas, M.
    et al.
    Ton Duc Thang University, Ho Chi Minh City, Viet Nam.
    Nazir, Talat
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Popović, B.
    University of Kragujevac, Serbia.
    Radenović, S.
    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)
    Abstract [en]

    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. © 2016, Springer International Publishing.

  • 3.
    Abbas, Mujahid
    et al.
    Ton Duc Thang Univ, Ho Chi Minh City, Vietnam..
    Nazir, Talat
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Lampert, Tatjana Aleksic
    Fac Sci, Dept Math, Radoja Domanovica 12, Kragujevac 34000, Serbia.
    Radenovic, Stojan
    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)
    Abstract [en]

    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.
    Abdumuminov, Shuhrat
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Esteky, David Emanuel
    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
    Abstract [en]

    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.
    et al.
    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
    et al.
    Paal, Eugen
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication.
    Stolin, Alexander
    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.
    Acheampong, Isaac
    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.
    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.

  • 9.
    Adolfsson, Catarina
    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
    Abstract [sv]

    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.
    Ahl, Linda
    Mälardalen University, Department of Mathematics and Physics.
    Problemlösning, kontext och kompetens2007Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis
    Abstract [sv]

    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.
    Ahy, Nathaniel
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Sierra, Mikael
    Mälardalen University, School of Education, Culture and Communication.
    Implied Volatility Surface Approximation under a Two-Factor Stochastic Volatility Model2018Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Due to recent research disproving old claims in financial mathematics such as constant volatility in option prices, new approaches have been incurred to analyze the implied volatility, namely stochastic volatility models. The use of stochastic volatility in option pricing is a relatively new and unexplored field of research with a lot of unknowns, where new answers are of great interest to anyone practicing valuation of derivative instruments such as options. With both single and two-factor stochastic volatility models containing various correlation structures with respect to the asset price and differing mean-reversions of variance the question arises as to how these values change their more observable counterpart: the implied volatility. Using the semi-analytical formula derived by Chiarella and Ziveyi, we compute European call option prices. Then, through the Black–Scholes formula, we solve for the implied volatility by applying the bisection method. The implied volatilities obtained are then approximated using various models of regression where the models’ coefficients are determined through the Moore–Penrose pseudo-inverse to produce implied volatility surfaces for each selected pair of correlations and mean-reversion rates. Through these methods we discover that for different mean-reversions and correlations the overall implied volatility varies significantly and the relationship between the strike price, time to maturity, implied volatility are transformed.

  • 12.
    Aldin-Lundgren, Ida
    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
    Abstract [sv]

    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.

  • 13.
    Alexandersson, Elin
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Olsson, Johanna
    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
    Abstract [sv]

    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.

  • 14.
    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.

  • 15.
    Altoumaimi, Rasha Talal
    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
    Abstract [en]

    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.

  • 16.
    Ambainis, A.
    et al.
    University of California, Berkeley, USA.
    Bonner, R.
    Mälardalen University, Department of Mathematics and Physics.
    Freivalds, R.
    University of Latvia, Latvia.
    Golovkins, M.
    University of Latvia, Latvia.
    Karpinski, M.
    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)
    Abstract [en]

    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.

  • 17.
    Ammar, F.
    et al.
    Faculté des Sciences, Université de Sfax, Tunisia .
    Makhlouf, A.
    Université de Haute Alsace, France .
    Silvestrov, S. D.
    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)
    Abstract [en]

    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.

  • 18.
    Anari, Majid
    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
  • 19.
    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.

  • 20.
    Andersson, Johan
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Anders, Södergren
    University of Copenhagen.
    On the universality of the Epstein zeta functionManuscript (preprint) (Other academic)
    Abstract [en]

    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.

  • 21.
    Andersson, Magnus
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Palm, Johan
    Mälardalen University, School of Education, Culture and Communication.
    Forecasting the Stock Market: A Neural Network Approch2009Student thesis
    Abstract [en]

    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.

  • 22.
    Andersson, Mikael
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Andersson, Jimmy
    Mälardalen University, School of Education, Culture and Communication.
    Hur tänkte du nu?: En studie kring frågetyper i matematikundervisningen2018Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Utifrån rådande forskning och rapporter från Skolverket framstod det att det funnits och fortfarande finns brister i hur lärare ställer frågor under matematiklektioner. Det finns också studier som visar på hur lärare följer upp elevers svar och skapar diskussioner under lektionerna. Därför syftar denna studie till att studera vilka frågetyper som ställs under matematiklektioner samt hur lärare följer upp elevers svar. För att göra detta genomfördes strukturerade icke-deltagande observationer under 14 lektioner med sex stycken olika lärare. Insamlad data tolkades sedan utifrån Emanuelssons (2001) ramverk där frågor kan delas in i tre olika zoner, stoffzonen, den konceptuella zonen samt den proceduriella zonen. Frågor i stoffzonen behandlar frågor där eleven kan använda sig av memorerade fakta eller presenterar sina tankar i korta svar. Den konceptuella zonen ställer frågor där eleven behöver redogöra för sina tankar kring uträkningar och matematiska problem. Frågor i den proceduriella zonen fokuserar på att elever ska presentera tankar kring val av metod eller presentation. Uppföljning av svar ställdes mot studier där det visades att argumentation och delaktighet kunde skapa motivation och en bättre chans till inlärning hos eleverna. Studien visade att det i likhet med andra studier i samma område ställdes en hög andel frågor inom stoffzonen (93 %) och att inga frågor under matematiklektionerna ställdes inom den proceduriella zonen. Studien visade också att det inom stoffzonen och den konceptuella zonen gick att särskilja underkategorier. Inom stoffzonen är dessa begrepps- och tillämpningsfrågor, uträkningsfrågor samt korta analysfrågor. Inom den konceptuella zonen var kategorierna redogörande analysfrågor och fel svar, hur tänker eleven? Av dessa underkategorier var begrepps- och tillämpningsfrågor och uträkningsfrågor de vanligaste sett till det totala antalet frågor (73 %). Lärarna visade sig följa upp på elevernas svar med ett fokus att föra lektionen framåt. Elevernas svar togs till vara på om svaren var på den nivå som lektionen vid det tillfället handlade om. Det kunde urskiljas fem kategorier av uppföljningstyper, dessa var: att värdera rätt eller fel, förtydligande till elev eller helklass, hålla sig till fokusområde, motfråga till klassen samt ny uppgift. Den sista kategorin ny uppgift skiljde sig från de övriga till utförande men också tack vare att det endast var en av lärarna som arbetade med den metoden. Studiens slutsats var att det i likhet med tidigare studier fortfarande är så att de frågetyper som visar sig under matematikundervisningen är sådan som fokuserar på korta svar där läraren följer upp om det är rätt eller fel.

  • 23.
    Andrejs, Matveevs
    et al.
    Riga Technical University, Latvia.
    Fjodorovs, Jegors
    Riga Technical University, Latvia.
    Malyarenko, Anatoliy
    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)
    Abstract [en]

    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.

  • 24.
    Andren, Daniel
    et al.
    Umeå University.
    Hellström, Lars
    Umeå University.
    Markström, Klas
    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)
  • 25.
    Andrews, George
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Eriksson, Kimmo
    Mälardalen University, Department of Mathematics and Physics.
    Integer Partitions2004Book (Other (popular science, discussion, etc.))
  • 26.
    Anthony, Jennifer
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Jovanovic, Sladjana
    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
    Abstract [sv]

    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.

  • 27.
    Armas, Ivan
    Mälardalen University, School of Education, Culture and Communication.
    Multiplikationstabellen: Multiplikationstabellen2010Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    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.

  • 28.
    Arnlind, Joakim
    et al.
    Linköping University, Sweden.
    Kitouni, Abdennour
    Université de Haute-Alsace, Mulhouse, France.
    Makhlouf, Abdenacer
    Université de Haute-Alsace, Mulhouse, France .
    Silvestrov, Sergei
    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)
    Abstract [en]

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

  • 29.
    Arnlind, Joakim
    et al.
    Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
    Makhlouf, Abdenacer
    Université de Haute Alsace, Lab. de Mathématiques Informatique et Applications, 4, rue des Frères Lumière, F-68093 Mulhouse, France.
    Silvestrov, Sergei
    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)
    Abstract [en]

    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]

  • 30.
    Arnlind, Joakim
    et al.
    Max Planck Institute for Gravitational Physics (AEI), Germany.
    Makhlouf, Abdenacer
    Université de Haute Alsace, France .
    Silvestrov, Sergei
    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)
    Abstract [en]

    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.

  • 31.
    Arnlind, Joakim
    et al.
    Albert Einstein Institute, Golm, Germany.
    Silvestrov, Sergei
    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)
  • 32.
    Arwe, Linda
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Andersson, Mathias
    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
    Abstract [sv]

    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.

  • 33.
    Ataguema, H.
    et al.
    Universit́e de Haute Alsace, France .
    Makhlouf, A.
    Universit́e de Haute Alsace, France .
    Silvestrov, S. D.
    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)
    Abstract [en]

    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.

  • 34.
    Atif Fakhir, Hala
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Matti, Ayd
    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
    Abstract [sv]

    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. 

  • 35.
    Aziz Ali, Barkat
    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
    Abstract [en]

    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.

  • 36.
    Backlund, U.
    et al.
    Danderyds Gymnasium, Danderyd, Sweden.
    Carlsson, Linus
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Fällström, A.
    Umeå University, Umeå, Sweden.
    Persson, H.
    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)
    Abstract [en]

    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.

  • 37.
    Backlund, Ulf
    et al.
    Danderyd gymnasium.
    Carlsson, Linus
    Mälardalen University, School of Education, Culture and Communication.
    Fällström, Anders
    Umeå University.
    Persson, Håkan
    Uppsala University.
    Semi-Bloch functions in several complex variables2013Report (Other academic)
    Abstract [en]

    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.

  • 38.
    Bairkdar, Anas
    Mälardalen University, School of Education, Culture and Communication.
    A model to examine how social influence on individual grades may bias the aggregate grade in a sequential grading process.2018Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Businesses nowadays tend to ask their customers to grade a product or a service they have experienced, usually that grading is a number of stars on a scale of 5. When an individual grades a product, that grade goes into a system that calculates the average of all given grades and expose it to the next individual, and so on. Through primary data we estimated what could be a realistic distribution of uninfluenced grades as well as a realistic degree of social influence. This thesis aims to understand the social influence on individual grades and to what extent the order in which graders come may bias the aggregate grade. In addition, we aim to apply mathematical analysis and simulations to examine the social influence of a planted grade on aggregate grade, depending on the strength of social influence and the total number of graders.

    It was concluded that ordering the same set of individuals in different ways will give different aggregate grades, mostly biased when ordering from largest to smallest and the other way around. In addition, we presented a perception on how large a planted grade can affect the aggregate grade, studying different main factors such as the degree of social influence and total number of graders.

  • 39.
    Bart Adde, Tiffany
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Puspita, Kadek Maya Sri
    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
    Abstract [en]

       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.

  • 40.
    Benits, Nicolina
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Arnberg, Cassandra
    Mälardalen University, School of Education, Culture and Communication.
    Matematikundervisning för elever med språksvårigheter: Lärares erfarenheter och arbetsmetoder2018Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Elevers matematikutveckling riskerar att hindras på grund av språkliga svårigheter. Det mest centrala i matematikundervisningen bör därför vara att bygga upp ett adekvat språk hos eleverna. Lärares kunskaper gällande språkets påverkan på matematikundervisningen är därför avgörande för lärandesituationen, framförallt för elever i behov av särskilt stöd i ämnena svenska och matematik. Den här studien syftar till att få en förståelse för vilka metoder fem verksamma pedagoger använder för att identifiera och stödja elever vars språksvårigheter hindrar deras matematiska utveckling. 

  • 41.
    Bergander, Philip
    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
    Abstract [en]

    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.

  • 42.
    Bergner, Malén
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Severin, Camilla
    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
    Abstract [sv]

    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.

  • 43.
    Bergqvist, Göran
    et al.
    Linköpings Universitet.
    Lankinen, Paul
    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)
    Abstract [en]

    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.

  • 44.
    Bergqvist, Göran
    et al.
    Linköpings Universitet, Sweden.
    Lankinen, Paul
    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)
    Abstract [en]

    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.

  • 45.
    Bergström, Lena
    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
    Abstract [en]

    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.

  • 46.
    Bernard, Mark
    et al.
    Maastricht University .
    Dreber, Anna
    Stockholm School of Economics.
    Strimling, Pontus
    Stockholm University.
    Eriksson, Kimmo
    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)
    Abstract [en]

    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.

  • 47.
    Berzina, A.
    et al.
    University of Latvia, Latvia.
    Bonner, R.
    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)
    Abstract [en]

    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.

  • 48.
    Betuel, Canhanga
    et al.
    Faculty of Sciences, Dept of Mathematics and Computer Sciences, Eduardo Mondlane University, Mozambique.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach2018In: / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2018Conference paper (Refereed)
    Abstract [en]

    The development of financial markets imposes more complex models on the option pricing problems. On the previous papers by the authors, we consider a model under which the underlying asset is driven by two independent Heston-type stochastic volatility processes of multiscale (fast and slow) mean-reverting rates and we compute an approximate solution for the option pricing problem, using asymptotic expansion method. In the present paper, we aim to calibrate the model using the market prices of options on Euro Stoxx 50 index and an equity stock in the European market. Our approach is to use the market implied volatility surface for calibrating directly a set of new parameters required in our second-order asymptotic expansion pricing formula for European options. This secondorder asymptotic expansion formula provides a better approximation formula for European option prices than the first-order formula, as explained in an earlier work of the authors.

  • 49. Biffi, Elena
    et al.
    D'Amico, Guillermo
    Di Biase, G
    Janssen, J
    Manca, Raimondo
    Silvestrov, Dmitrii
    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)
  • 50. Biffi, Elena
    et al.
    D'Amigo, Guillermo
    Di Biase, Giuseppe
    Janssen, Jacques
    Manca, Raimondo
    Silvestrov, Dmitrii
    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)
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