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  • 1. Accardi, L.
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Ohya, M.
    The problem of quantum-like representation in economy, cognitive science, and genetics2009In: Quantum Bio-Informatics II: from Quantum Information toBio-Informatics, Singapore: WSP , 2009, p. 1-8Chapter in book (Refereed)
  • 2. Accardi, Luigi
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Ohya, Masanori
    Quantum Markov Model for Data from Shafir-Tversky Experiments in Cognitive Psychology2009In: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 16, no 4, p. 371-385Article in journal (Refereed)
    Abstract [en]

    We analyze, from the point of view of quantum probability, statistical data from two interesting experiments, done by Shafir and Tversky [1, 2] in the domain of cognitive psychology. These are gambling experiments of Prisoner Dilemma type. They have important consequences for economics, especially for the justification of the Savage "Sure Thing Principle" [3] (implying that agents of the market behave rationally). Data from these experiments were astonishing, both from the viewpoint of cognitive psychology and economics and probability theory. Players behaved irrationally. Moreover, all attempts to generate these data by using classical Markov model were unsuccessful. In this note we show (by inventing a simple statistical test — generalized detailed balance condition) that these data are non-Kolmogorovian. We also show that it is neither quantum (i.e., it cannot be described by Dirac-von Neumann model). We proceed towards a quantum Markov model for these data.

  • 3.
    Accardi, Luigi
    et al.
    Univ Rome Torvergata, Italy.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo Univ Sci, Japan.
    Tanaka, Yoshiharu
    Tokyo Univ Sci, Japan.
    Yamato, Ichiro
    Tokyo Univ Sci, Japan.
    Application of Non-Kolmogorovian Probability and Quantum Adaptive Dynamics to Unconscious Inference in Visual Perception Process2016In: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 23, no 2, article id 1650011Article in journal (Refereed)
    Abstract [en]

    Recently a novel quantum information formalism - quantum adaptive dynamics - was developed and applied to modelling of information processing by bio-systems including cognitive phenomena: from molecular biology (glucose-lactose metabolism for E.coli bacteria, epigenetic evolution) to cognition, psychology. From the foundational point of view quantum adaptive dynamics describes mutual adapting of the information states of two interacting systems (physical or biological) as well as adapting of co-observations performed by the systems. In this paper we apply this formalism to model unconscious inference: the process of transition from sensation to perception. The paper combines theory and experiment. Statistical data collected in an experimental study on recognition of a particular ambiguous figure, the Schroer stairs, support the viability of the quantum(-like) model of unconscious inference including modelling of biases generated by rotation-contexts. From the probabilistic point of view, we study (for concrete experimental data) the problem of contextuality of probability, its dependence on experimental contexts. Mathematically contextuality leads to non-Komogorovness: probability distributions generated by various rotation contexts cannot be treated in the Kolmogorovian framework. At the same time they can be embedded in a "big Kolmogorov space" as conditional probabilities. However, such a Kolmogorov space has too complex structure and the operational quantum formalism in the form of quantum adaptive dynamics simplifies the modelling essentially.

  • 4.
    Achek, Jennie
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Geometri: Hur lärare undervisar i geometri i de tidigare skolåren2012Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    A number of both international and national enquires shows that Swedish pupils are getting worse results in mathematics. One area that’s frequently pointed out is geometry. This enquiry intends to find out how the subject of geometry has developed in the Swedish school and witch methods and concepts teachers who teach in preschool and the early school years grade use in their teaching. This enquiry is based upon eight semi structured interviews and from studying previous curriculums. The result shows that teachers use a great deal of concepts and methods in their teaching but that there are a need for further education among teachers. The enquiry also shows that the significance of the subject has changed over time.

  • 5.
    Adenier, Guillaume
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Local Realist Approach and Numerical Simulations of Nonclassical Experiments in Quantum Mechanics2008Doctoral thesis, monograph (Other academic)
    Abstract [en]

    Local Realist Approach and Numerical Simulations of Nonclassical Experiments in Quantum Mechanics was constructed.

  • 6.
    Adenier, Guillaume
    et al.
    INRiM, Italy.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Test of the no-signaling principle in the Hensen loophole-free CHSH experiment2017In: Fortschritte der Physik, ISSN 0015-8208, E-ISSN 1521-3978, Vol. 65, no 9, article id 1600096Article in journal (Refereed)
    Abstract [en]

    We analyze the data from the loophole-free CHSH experiment performed by Hensen et al., and show that it is actually not exempt of an important loophole. By increasing the size of the sample of event-ready detections, one can exhibit in the experimental data a violation of the no-signaling principle with a statistical significance at least similar to that of the reported violation of the CHSH inequality, if not stronger. The data from the loophole-free CHSH experiment performed by Hensen et al. are analysed, It is shown that it is actually not exempt of an important loophole. By increasing the size of the sample of event-ready detections, one can exhibit in the experimental data a violation of the no-signaling principle with a statistical significance at least similar to that of the reported violation of the CHSH inequality, if not stronger.

  • 7.
    Adenier, Guillaume
    et al.
    University of Oslo, Norway.
    Watanabe, Noboru
    Tokyo University of Science, Japan.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Multiple-photon absorption attack on entanglement-based quantum key distribution protocols2013In: Quantum Bio-Informatics V: Proceedings of the Quantum Bio-Informatics 2011 : Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Luigi Accardi, Wolfgang Freudenberg, Masanori Ohya, Singapore: World Scientific, 2013, vol. 30, p. 171-180Conference paper (Refereed)
    Abstract [en]

    We propose a multiple-photon absorption attack on Quantum Key Distribution protocols. In this attack, the eavesdropper (Eve) is in control of the source and sends pulses correlated in polarization (but not entangled) containing several photons at frequencies for which only multiple-photon absorptions are possible in Alice's and Bob's detectors. Whenever the number of photons from one pulse are dispatched in insufficient number to trigger a multiple-photon absorption in either channel, the pulse remains undetected. We show that this simple feature is enough to reproduce the type of statistics on the detected pulses that are considered as indicating a secure quantum key distribution in entangled-based protocols, even though the source is controlled by Eve, and we discuss possible countermeasures.

  • 8.
    Aghababa, Somayeh
    Linnaeus University, Faculty of Engineering and Technology, Department of Mathematics.
    Extremal dependency:The GARCH(1,1) model and an Agent based model2013Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis focuses on stochastic processes and some of their properties are investigated which are necessary to determine the tools, the extremal index and the extremogram. Both mathematical tools measure extremal dependency within random time series. Two different models are introduced and related properties are discussed. The probability function of the Agent based model is surveyed explicitly and strong stationarity is proven. Data sets for both processes are simulated and clustering of the data is investigated with two different methods. Finally an estimation of the extremogram is used to interpret dependency of extremes within the data.

  • 9.
    Ahijado, Susana
    Linnaeus University, Board of Education Science.
    Hur används den utökade resursen till matematikämnet i grundskolan?2014Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis
  • 10.
    Ahlberg, Sandra
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Elevers möjlighet att utveckla matematiska förmågor utifrån läromedlet Pixel2012Student paper other, 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

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

  • 11.
    Ahlqvist, Susanne
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Johansson, Maria
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Matematik från grunden: sortering och klassificering med de yngsta barnen i förskolan2009Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

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

  • 12.
    Ahmad, Qadeer
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    CUBIC CONGRUENCE EQUATIONS2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Let Nm(f(x)) denote the number of solutions of the congruence equation f(x)≡0 (modm), where m≥2 is any composite integer and f(x) is a cubic polynomial. In this thesis, we use different theorems and corollaries to find a number of solutions of the congruence equations without solving then we also construct the general expression of corresponding congruence equations to demonstrate the solutions of the equations. In this thesis, we use Mathematica software as a tool.

  • 13. Albeverio, S.
    et al.
    Cianci, R.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Operator calculus for p-adic valued symbols and quantization2009In: Rendicoti Del Seminario Matematico, ISSN 0373-1243, Vol. 67, no 2, p. 137-150Article in journal (Refereed)
    Abstract [en]

    The aim of this short review is to attract the attention of the pseudo-differentialcommunity to possibilities in the development of operator calculus for symbols (dependingon p-adic conjugate variables) taking values in fields of p-adic numbers. Essentials of thiscalculus were presented in works of the authors of this paper in order to perform p-adic valuedquantization. Unfortunately, this calculus still has not attracted a great deal of attentionfrom pure mathematicians, although it opens new and interesting domains for the theory ofpseudo-differential operators.

  • 14. Albeverio, S
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Shelkovich, M
    Nonlinear singular problems of $p$-adic analysis: associative algebras of $p$-adic distributions2005In: Izvestiya. Mathematics, ISSN 1064-5632, E-ISSN 1468-4810, Vol. 69, no 2, p. 221-263Article in journal (Refereed)
  • 15. Albeverio, S
    et al.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Shelkovich, V
    Theory of p-adic distributions: linear and nonlinear models2010Book (Refereed)
  • 16. Albeverio, S
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Shelkovich, V.M.
    p-adic Colombeau-Egorov type theory of generalized functions2005In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 278, no 1-2, p. 3-16Article in journal (Refereed)
  • 17. Albeverio, Sergio
    et al.
    Cianci, Roberto
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    p-Adic valued quantization2009In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 1, no 2, p. 91-104Article, review/survey (Refereed)
    Abstract [en]

    This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ℚ p , operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrödinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ℚ p . A physical interpretation of p-adic quantities is provided through approximation by rational numbers.

  • 18. Albeverio, Sergio
    et al.
    Gundlach, Mathias
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Lindahl, Karl-Olof
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    On the Markovian Behavior of p-Adic Random Dynamical Systems2001In: Russ. J. Math. Phys., Vol. 8, no 2, p. 135-152Article in journal (Refereed)
  • 19. Albeverio, Sergio
    et al.
    Hilbert, Astrid
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Kolokoltsov, Vassili
    Warwick University, Department of Statistics.
    Estimates uniform in time for the transition probability ofdiusions with small drift and for stochastically perturbed Newton equations1999In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 12, no 2, p. 293-300Article in journal (Refereed)
    Abstract [en]

    An estimate uniform in time for the transition probability of di®usion processes with small drift is given. This also covers the case of a degenerate di®usion describing a stochastic perturbation of a particle moving according to the Newton's law. Moreover the random wave operator for such a particle is described and the analogue of asymptotic completeness is proven, the latter in the case of a su±ciently small drift.

  • 20.
    Albeverio, Sergio
    et al.
    University of Bonn, Institute of Applied Mathematics.
    Hilbert, Astrid
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Kolokoltsov, Vassili
    University of Warwick, Department of Statistics.
    Uniform Asymptotic Bounds for the Heat Kernel and the Trace of a Stochastic Geodesic Flow2012In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 84, no 2-3, p. 315-333Article in journal (Refereed)
    Abstract [en]

    We analyze the asymptotic behaviour of the heat kernel dened by a stochastically perturbedgeodesic ow on the cotangent bundle of a Riemannian manifold for small time and smalldiusion parameter. This extends WKB-type methods to a particular case of a degenerateHamiltonian. We give uniform bounds for the solution of the degenerate Hamiltonian boundaryvalue problem for small time. The results are exploited to derive two sided estimates andmultiplicative asymptotics for the heat kernel semigroup and its trace.

  • 21. Albeverio, Sergio
    et al.
    Hilbert, Astrid
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Kolokoltsov, Vassily
    The small time asymptotics of the transition density of some degenerate diffusions on the cotangent bundle2009In: arXiv:0912.4683v2, no arXiv:0912.4683v2Article in journal (Other academic)
  • 22. Albeverio, Sergio
    et al.
    Hilbert, Astrid
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Kolokoltsov, Vassily
    Transcience of stochastically perturbed classical Hamiltonian systems and random wave operators1997In: Stochastics and Stochastics Reports, ISSN 1045-1129, E-ISSN 1029-0346, no 1-2, p. 41-55Article in journal (Refereed)
  • 23. Albeverioa, S.
    et al.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Shelkovichg,, V.M.
    The Cauchy problems for evolutionary pseudo-differential equations over p-adic field and the wavelet theory2011In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 375, no 1, p. 82-98Article in journal (Refereed)
  • 24.
    Albinsson, Anneli
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Sundberg, Maria
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Wiktorsson, Veronika
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Matematik i förskolan: Om synsätt och arbetssätt efter kompetensutveckling2007Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med vårt arbete är att undersöka hur synsätt och arbetssätt kring matematik i förskolan förhåller sig i en kommun där det medvetet har satsats på kompetensutveckling i matematik. Vi vill veta vad matematik i förskolan innebär för lärarna och hur de arbetar med matematik samt hur de ser på kompetensutvecklingens betydelse.

    Som metod har vi använt oss av en kvantitativ metod i form av enkäter samt en kvalitativ metod i form av semistrukturerade intervjuer. Enkäterna har besvarats av lärare som deltagit i kompetensutvecklingen. Intervjuer har sedan genomförts med några av dessa samt med en rektor.

    Resultatet visar på att lärarna tycker att matematik hör hemma i förskolan. Förskolematematik innebär att synliggöra och lyfta fram matematiken i vardagliga situationer som är meningsfulla för barnen. Detta görs genom att utgå från barnens egna tankar och intressen. Enligt lärarna är det viktigt att sätta ord på matematiken och använda rätt begrepp samt att barnen lär sig under lekfulla former. Lärarna ser också sin egen roll som betydelsefull. I undersökningen framkommer att kompetensutvecklingen har haft stor betydelse för hur det arbetas med matematik i verksamheten.

  • 25.
    Alfelt, Gustav
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Lövdahl, Susanna
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Undersökning av metoder för att analysera och modellera efter stora datamaterial, hantering av programmet SPSS samt en studie i Kronoberg läns gymnasieelevers psykiska ohälsa2008Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Landstinget i Kronobergs län utförde 2006 en enkätundersökning bland elever i årskurserna 5, 8 och gymnasiets årskurs 2. Datamaterialet för gymnasieeleverna har studerats i detta arbete där den psykiska ohälsan och alkoholkonsumtion varit i fokus.

    Det statistiska arbetet är uppdelat i tre delar: Metodbeskrivning, hantering av programmet SPSS samt en undersökning av gymnasieelevers psykiska ohälsa och alkoholkonsumtion. I metodbeskrivningen har metoderna dikotomisering, logistisk regression, Wald, faktorinteraktion och kategorisering beskrivits. För hantering av stora datamaterial samt för att kunna ta fram statistiska samband rörande psykisk ohälsa och alkoholkonsumtion har programmet SPSS använts och illustrerats i arbetet. De förklarande variablerna som varit mest inflytelserika mot den psykiska ohälsan var ’Tycker du att du är frisk?’, ’Har du någonsin använt läkemedel tillsammans med alkohol i berusningssyfte’ samt ’Trivs du med livet?’. När undersökningen för gymnasieelevers alkoholkonsumtion studerades var de gemensamma signifikanta faktorerna för både killar och tjejer ’Skolkar du?’, ’Känner du dig ofta irriterad eller på dåligt humör?’ och ’Har någon vuxen behandlat dig fysiskt illa?’ där samtliga förklarande faktorer bidrog till en ökad sannolikhet att konsumera mycket alkohol. Då undersökning av variabeln symtom, variabeln oro samt deras interaktion studerades för killar respektive för tjejer mot den psykiska ohälsan kunde man se att variabeln symtom för killar var inflytelserik samt interaktionen mellan oro och symtom. För tjejerna var däremot variabeln oro inflytelserik samt variabeln symtom men inte deras interaktion.

  • 26.
    Algotsson, Sarah
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Tror jag att jag kan det här?: En kvantitativ studie om elevers tilltro till sin egen matematiska förmåga i relation till faktisk prestation i metod-och problemlösningsuppgifter  2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This quantitative study focuses on how students perceive their own mathematical ability, what degree of confidence students have in their ability and how they perform in mathematical tasks that focuses on method and problem solving ability. The literature underlying the study is based on the importance of believing in your own ability, the ability to assess yourself and your ability, and the importance of mathematics to maintain and create opportunity to develop self-perception and confidence in your own ability. The research method used to answer the questions of the study is of a quantitative nature and consists of a self-assessment form that aims to visualize the students' degree of confidence in their own mathematical ability and a mathematics test where students solve method and problem solving tasks. The dissolution rate of the different types of tasks is analyzed in relation to the students' degree of confidence. The study is pervaded by a social psychological perspective and the result is theorized by starting from the social psychological theory of self-efficacy as well as symbolic interactionism. To analyze the relationships, the material has also been analyzed from a statistical perspective, using the SPSS analyzing tool. The result of the study shows that there seems to be a connection between the students' degree of confidence in their mathematical ability and how they perform in both method and problem solving tasks.

  • 27.
    Alice, Reinaudo
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Empirical testing of pseudo random number generators based on elliptic curves2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    An introduction on random numbers, their history and applications is given, along with explanations of different methods currently used to generate them. Such generators can be of different kinds, and in particular they can be based on physical systems or algorithmic procedures. The latter type of procedures gives rise to pseudo-random number generators. Specifically, several such generators which are based on elliptic curves are examined. Therefore, in order to ease understanding, a basic primer on elliptic curves over fields and the operations arising from their group structure is also provided. Empirical tests to verify randomness of generated sequences are then considered. Afterwards, there are some statistical considerations and observations about theoretical properties of the generators at hand, useful in order to use them optimally. Finally, several randomly generated curves are created and used to produce pseudo-random sequences which are then tested by means of the previously described generators. In the end, an analysis of the results is attempted and some final considerations are made.

  • 28.
    Aliu, Armend
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Matematiksvårigheter: textuppgifter inom algebra2006Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I detta arbete fördjupar jag mina kunskaper omkring elevernas svårigheter, kring dem matematiska begrepp och kring formuleringen av de olika textuppgifter som framkommer inom avsnittet algebra. Här ville jag ta reda på om det är matematiska begreppen eller om det är formuleringarna i matematikuppgifterna som eleverna har svårt att förstå samtidigt som jag ville se vilka strategier som eleverna använder sig av när de får olika typer av uppgifter inom avsnittet algebra. De klasser som jag ska göra min undersökning på är två åk 1 klasser som går handelsprogrammet. Detta medför att de läser matematik –A kursen och håller på med avsnittet som handlar om algebra och ekvationer. Jag utför en stor undersökning i form av prov som består av 8 uppgifter. Efter att provet genomförs och rättas så väljs några elever för en intervju. Förhoppningen var att med hjälp av intervjun komma underfund med vad i dessa uppgifter eleverna har problem med. Arbetet visar att elever oftast är osäkra när det gäller de olika matematiska begreppen. När det gäller formuleringen i textuppgifter har många elever i min undersökning svårt att hålla isär och hämta in rätt information för att kunna lösa uppgifterna rätt. Vidare visar arbetet att majoriteten av eleverna har problem med formuleringarna i uppgiften dvs. när uppgiften är lång och mycket information ges.

  • 29.
    Alkmark, Niklas
    Växjö University, Faculty of Humanities and Social Sciences, School of Education.
    Praktisk matematik ur ett lärarperspektiv2006Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Abstract: I rapporten intervjuas fyra mellanstadielärare på en 4-6 skola i Borås stad, om deras syn på praktisk matematik. I vilken utsträckning använder sig lärarna av praktisk matematik, när använder dom det, hur ser de på själva uppgiften samt om uppgifterna ökar elevernas motivation, lust och förståelse för matematik.

    Intervjuerna deklarerar att det finns en stor osäkerhet i hur praktisk matematik skall användas och vilka fördelar den för med sig. Lärarna anser att det bedrivs för lite praktisk matematik på skolan, bokens trygghet lockar allt för mycket. Lärarna poängterar också att vissa områden är lättare än andra att applicera praktisk matematik på. Det finns inte någon direkt uttalad linje när det gäller praktiska moment utan det kommer när det kommer. Däremot är man överens om att lusten och motivationen ofta stärks och att de svaga eleverna får möjlighet att lyckas. Vissa forskare menar att ett praktiskt arbetssätt är helt nödvändigt för att ta upp kunskapen på en ny nivå. Kunskapen måste kunna sättas in i en kontext för att djupinlärning skall erhållas.

  • 30. Allahverdyan, A
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Nieuwenhuizen, Th. M
    Brownian entanglement2005In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 72, p. 032102-Article in journal (Refereed)
  • 31.
    Almasri, Abdullah
    et al.
    Karlstad University.
    Locking, Håkan
    Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
    Forecasting risk premium using wavelet transform2015In: Festschrift in honor of Professor Ghazi Shukur on the occasion of his 60th birthday / [ed] Thomas Holgersson, Linnaeus University Press, 2015, 1, p. 1-7Chapter in book (Other academic)
  • 32.
    Almasri, Abdullah
    et al.
    Karlstad University.
    Locking, Håkan
    Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
    Shukur, Ghazi
    Linnaeus University, School of Business and Economics, Department of Economics and Statistics. Jönköping University.
    Testing for trends and causality in Swedish environmental data, using Wavelet analysis2013Conference paper (Refereed)
    Abstract [en]

    This paper utilizes Wavelet based methodology to estimate and test for trends and granger causality in temperature andprecipitation. We use quarterly data from Sweden for the period 1884 up to 2011. The analysis suggests that temperatureand precipitation in Sweden currently have a positive trend in 2011. Thus the recent lower levels of the variables 2009-2010are estimated to be temporary fluctuations or deviations from the trend. Moreover, in the short run there are feedbackeffects between the variables and over longer periods, 4-8 years, temperature granger cause precipitation.

  • 33.
    Almasri, Abdullah
    et al.
    Växjö University, Faculty of Humanities and Social Sciences, School of Management and Economics.
    Locking, Håkan
    Växjö University, Faculty of Humanities and Social Sciences, School of Management and Economics.
    Shukur, Ghazi
    Växjö University, Faculty of Humanities and Social Sciences, School of Management and Economics.
    Wavelet Based Forecasting Approach, with Application2009In: 2009 International Conference on Financial Theory and Engineering / [ed] Patrick Kellenberger, 2009Conference paper (Refereed)
    Abstract [en]

    In this paper we outline a framework for forecasting using maximal overlap discrete wavelet transform (MODWT) based multiresoulution analysis (MRA). This framework has been applied for forecasting the tourism arrival series from Denmark to Norway. We compare forecasted values obtained from modeling the data in the time domain with the forecasted values from the wavelet domain using the traditional Box-Jenkins methodology. In both cases, diagnostic tests have been conducted to insure the specification of the model. The results have shown that the wavelet based forecasts outperforms the traditional Box-Jenkins approach in term of forecasts accuracy.

  • 34.
    Almgren, Annika
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Vilka erfarenheter kan ligga till grund för valet att gå en spetsutbildning i matemaik2016Independent thesis Advanced level (degree of Master (One Year)), 40 credits / 60 HE creditsStudent thesis
    Abstract [sv]

    Denna undersöknings syfte var att ge ett elevperspektiv på vilka faktorer som kan ligga till grund för valet att gå en spetsutbildning i matematik samt om man kan skönja gemensamma uttryck i vad som kan ha varit avgörande för detta val.

    Följande forskningsfrågor har legat till grund för studien:

    • Vilka faktorer uttrycker elever för valet att gå en spetsutbildning i matematik?

    • Vilken syn på matematik och matematikundervisning uttrycks hos dessa elever?

    • Går det att finna några kopplingar mellan de faktorer eleverna uttrycker för sitt val att gå en spetsutbildning i matematik och deras uttryckta syn på matematik och matematikundervisning?

       

    En hermeneutiska tolkningsansats användes och en enkätundersökning gjord på elever på spetsutbildningar i årskurs 7 låg till grund som data. Resultaten visade att den elev som väljer att gå en spetsutbildning i matematik kan ha grundat sina val på en mängd skiljda faktorer men det finns också faktorer som visade sig finnas hos majoriteten av dem. En generell bild av en elever som väljer att gå en spetsutbildning i matematik gör det för sin lusta att lära och att de söker utmaningar i ett ämne de inte nödvändigtvis har som favoritämne men känner en stor tillfredställelse att ägna sig åt. Ofta finns det föräldrar som uppmuntrar och är delaktiga i sina barns utbildning och det är i större utsträckning syskon som haft påverkan än kompisar. Användbarhet av matematik är inte alltid synlig för eleven i den egna vardagen men en majoritet anser att ämnet är en mycket viktig del i dagen samhälle.

  • 35.
    Almquist, Rebecka
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Lindgren, Josefine
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Multiplikation: användningen av och uppfattningar om olika metoder inom multiplikation2017Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Multiplikation är ett av de fyra räknesätten inom matematik som elever ska utveckla kunskap och förståelse inom. Utifrån lärarens undervisning ska eleverna ges möjlighet att i slutet av årskurs 6 kunna behärska olika metoder inom multiplikation. Syftet med studien är att urskilja vilka metoder inom multiplikation som är vanligast förekommande i två stycken årskurs 5-klasser samt vilka metoder som matematikläraren för dessa klasser använder mest i genomgången av multiplikation. Syftet är även att försöka tolka olika elevers uppfattningar inom dessa metoder. Studien genomfördes med hjälp av en kvalitativ analys utifrån en fenomenografisk ansats.

  • 36.
    Alriksson, Madeleine
    Linnaeus University, Faculty of Engineering and Technology, Department of Mathematics Education.
    Muntlig bedömning: Med fokus på elevers representationer2013Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

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

  • 37.
    Alsteryd, Karin
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Matematiska prefix: Hur läromedel tar upp kunskapen om de matematiska prefixen och vilka kunskaper elever i år 6 har i ämnet2007Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med mitt examensarbete var att ta reda på hur läromedel i matematik för år 4-6 tar upp kunskapen om prefixen kring vikt, längd och volym och vilka kunskaper elever i år 6 har i ämnet.

    Jag har analyserat fem olika läromedel och gjort en enkätundersökning i fem klasser. Genom min undersökning har jag kommit fram till att läromedlen ger eleverna för få tillfällen att praktiskt erfara kunskaper om de olika enheterna. De flesta informerar om vad prefixen betyder men det förekommer inga arbetsuppgifter där eleverna får lära och förstå sammanhanget och nyttan med att kunna dem. Resultatet av min enkätundersökning visade att många elever vet vad enheterna för längd, vikt och volym heter, men har dåliga kunskaper i vad prefixen betyder och svårigheter med att omvandla enheterna. I slutet av mitt examensarbete ger jag några förslag på hur undervisningen kan läggas upp för att ge eleverna större möjlighet att förstå prefixens betydelse och nyttan med kunskapen.

  • 38.
    Al-Talibi, Haidar
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    A Differentiable Approach to Stochastic Differential Equations: the Smoluchowski Limit Revisited2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis we generalize results by Smoluchowski [43], Chandrasekhar[6], Kramers, and Nelson [30]. Their aim is to construct Brownian motion as a limit of stochastic processes with differentiable sample paths by exploiting a scaling limit which is a particular type of averaging studied by Papanicolao [35]. Their construction of Brownian motion differs from the one given by Einstein since it constitutes a dynamical theory of Brownian motion. Nelson sets off by studying scaled standard Ornstein-Uhlenbeck processes. Physically these describe classical point particles subject to a deterministic friction and an external random force of White Noise type, which models perpetuous collisions with surrounding(water) molecules. Nelson also studies the case when the particles are subject to an additional deterministic nonlinear force. The present thesis generalizes the work of Chandrasekhar in that it deals with finite dimensional α-stable Lévy processes with 0 < α < 2, and Fractional Brownian motion as driving noises and mathematical techniques like deterministic time change and a Girsanov theorem. We consider uniform convergence almost everywhere and in -sense. In order to pursue the limit we multiply all vector fields in the cotangent space by the scaling parameter including the noise. For α-stable Lévy processes this correspondsto scaling the process in the tangent space, , , according to . Sending β to infinity means sending time to infinity. In doing so the noise evolves with a different speed in time compared to the component processes. For α≠2, α-stable Lévy processes are of pure jump type, therefore the approximation by processes having continuous sample paths constitutes a valuable mathematical tool. α-stable Lévy processes exceed the class studied by Zhang [46]. In another publication related to this thesis we elaborate on including a mean-field term into the globally Lipschitz continuous nonlinear part of the drift while the noise is Brownian motion, whereas Narita [28] studied a linear dissipation containing a mean-field term. Also the classical McKean-Vlasov model is linear in the mean-field. In a result not included in this thesis the scaling result of Narita [29], which concerns another scaling limit of the tangent space process (velocity) towards a stationary distribution, is generalized to α-stable Lévy processes. The stationary distribution derived by Narita is related to the Boltzmann distribution. In the last part of this thesis we study Fractional Brownian motion with a focus on deriving a scaling limit of Smoluchowski-Kramers type. Since Fractional Brownian motion is no semimartingale the underlying theory of stochastic differential equations is rather involved. We choose to use a Girsanov theorem to approach the scaling limit since the exponent in the Girsanov denvsity does not contain the scaling parameter explicitly. We prove that the Girsanov theorem holds with a linear growth condition alone on the drift for 0 < H < 1, where H is the Hurst parameterof the Fractional Brownian motion.

  • 39.
    Al-Talibi, Haidar
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Differentiable Approximation of Diffusion Equations Driven by α-Stable Lévy Noise2013In: Brazilian Journal of Probability and Statistics, ISSN 0103-0752, E-ISSN 2317-6199, Vol. 27, no 4, p. 544-552Article in journal (Refereed)
    Abstract [en]

    Edward Nelson derived Brownian motion from Ornstein-Uhlenbeck theory by a scaling limit. Previously we extended the scaling limit to an Ornstein-Uhlenbeck process driven by an α-stable Lévy process. In this paper we extend the scaling result to α-stable Lévy processes in the presence of a nonlinear drift, an external field of force in physical terms.

  • 40.
    Al-Talibi, Haidar
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Nelson-type Limits for α-Stable Lévy Processes2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Brownian motion has met growing interest in mathematics, physics and particularly in finance since it was introduced in the beginning of the twentieth century. Stochastic processes generalizing Brownian motion have influenced many research fields theoretically and practically. Moreover, along with more refined techniques in measure theory and functional analysis more stochastic processes were constructed and studied. Lévy processes, with Brownian motionas a special case, have been of major interest in the recent decades. In addition, Lévy processes include a number of other important processes as special cases like Poisson processes and subordinators. They are also related to stable processes.

    In this thesis we generalize a result by S. Chandrasekhar [2] and Edward Nelson who gave a detailed proof of this result in his book in 1967 [12]. In Nelson’s first result standard Ornstein-Uhlenbeck processes are studied. Physically this describes free particles performing a random and irregular movement in water caused by collisions with the water molecules. In a further step he introduces a nonlinear drift in the position variable, i.e. he studies the case when these particles are exposed to an external field of force in physical terms.

    In this report, we aim to generalize the result of Edward Nelson to the case of α-stable Lévy processes. In other words we replace the driving noise of a standard Ornstein-Uhlenbeck process by an α-stable Lévy noise and introduce a scaling parameter uniformly in front of all vector fields in the cotangent space, even in front of the noise. This corresponds to time being sent to infinity. With Chandrasekhar’s and Nelson’s choice of the diffusion constant the stationary state of the velocity process (which is approached as time tends to infinity) is the Boltzmann distribution of statistical mechanics.The scaling limits we obtain in the absence and presence of a nonlinear drift term by using the scaling property of the characteristic functions and time change, can be extended to other types of processes rather than α-stable Lévy processes.

    In future, we will consider to generalize this one dimensional result to Euclidean space of arbitrary finite dimension. A challenging task is to consider the geodesic flow on the cotangent bundle of a Riemannian manifold with scaled drift and scaled Lévy noise. Geometrically the Ornstein-Uhlenbeck process is defined on the tangent bundle of the real line and the driving Lévy noise is defined on the cotangent space.

  • 41.
    Al-Talibi, Haidar
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    On the Relevance of Fractional Gaussian Processes for Analysing Financial Markets2007Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In recent years, the field of Fractional Brownian motion, Fractional Gaussian noise and long-range dependent processes has gained growing interest. Fractional Brownian motion is of great interest for example in telecommunications, hydrology and the generation of artificial landscapes. In fact, Fractional Brownian motion is a basic continuous process through which we show that it is neither a semimartingale nor a Markov process. In this work, we will focus on the path properties of Fractional Brownian motion and will try to check the absence of the property of a semimartingale. The concept of volatility will be dealt with in this work as a phenomenon in finance. Moreover, some statistical method like R/S analysis will be presented. By using these statistical tools we examine the volatility of shares and we demonstrate empirically that there are in fact shares which exhibit a fractal structure different from that of Brownian motion.

  • 42.
    Al-Talibi, Haidar
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Hilbert, Astrid
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Differentiable Approximation by Solutions of Newton Equations Driven by Fractional Brownian Motion.Manuscript (preprint) (Other academic)
    Abstract [en]

    We derive a Smoluchowski-Kramers type scaling limit for second order stochastic differential equations driven by Fractional Brownian motion.We show a Girsanov theorem for the solution processes with respect to corresponding Fractional Ornstein-Uhlenbeck processes which are Gaussian. This reveals existence of weak solutions as well as a weak scaling limit. Subsequently the results are strengthened.

  • 43.
    Al-Talibi, Haidar
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Hilbert, Astrid
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Kolokoltsov, Vassili
    Department of Statistics, Warwick University.
    Smoluchowski-Kramers Limit for a System Subject to a Mean-Field DriftManuscript (preprint) (Other academic)
    Abstract [en]

    We establish a scaling limit for autonomous stochastic Newton equations, the solutions are often called nonlinear stochastic oscillators,where the nonlinear drift includes a mean field term of Mckean type and the driving noise is Gaussian. Uniform convergence in  sense is achieved by applying -type estimates and the Gronwall Theorem.The approximation is also called Smoluchowski-Kramers limit and is a particular averaging technique studied by Papanicolaou. It reveals an approximation of diffusions with a mean-field contribution in the drift by diffusions with differentiable trajectories.

  • 44.
    Aminbaghai, Mehdi
    et al.
    Vienna University of Technology.
    Dorn, Michael
    Linnaeus University, Faculty of Technology, Department of Building and Energy Technology.
    Eberhardsteiner, Josef
    Vienna University of Technology.
    Pichler, Bernhard
    Vienna University of Technology.
    A Matrix-Vector Operation-Based Numerical Solution Method for Linear m-th Order Ordinary DifferentialEquations: Application to Engineering Problems2013In: Advances in Applied Mathematics and Mechanics, ISSN 2070-0733, E-ISSN 2075-1354, Vol. 5, no 3, p. 269-308Article in journal (Refereed)
    Abstract [en]

    Many problems in engineering sciences can be described by linear, inhomogeneous, m-th order ordinary differential equations (ODEs) with variable coefficients. For this wide class of problems, we here present a new, simple, flexible, and robust solution method, based on piecewise exact integration of local approximation polynomials as well as on averaging local integrals. The method is designed for modern mathematical software providing efficient environments for numerical matrix-vector operation-based calculus. Based on cubic approximation polynomials, the presented method can be expected to perform (i) similar to the Runge-Kutta method, when applied to stiff initial value problems, and (ii) significantly better than the finite difference method, when applied to boundary value problems. Therefore, we use the presented method for the analysis of engineering problems including the oscillation of a modulated torsional spring pendulum, steady-state heat transfer through a cooling web, and the structural analysis of a slender tower based on second-order beam theory. Related convergence studies provide insight into the satisfying characteristics of the proposed solution scheme.

  • 45. Anashin,, V
    et al.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Using van der Put basis to determine if a 2-adic function is measure-preserving or ergodic w.r.t. Haar measure2011In: Advances in Non-Archimedean Analysis: 11th International Conference p-adic Funcional Analysis, July 5-9, 2010, Université Blaise Pascal, Clemont-Ferrand, France / [ed] Jesus Araujo-Gomez, Bertin Diarra and Alain Escassut, American Mathematical Society (AMS), 2011, Vol. 551, p. 33-38Chapter in book (Refereed)
  • 46.
    Anashin, V. S.
    et al.
    Moscow State University, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Characterization of ergodicity of p-adic dynamical systems by using the van der Put basis.2011In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 83, no 3, p. 306-308Article in journal (Refereed)
  • 47.
    Anashin, V. S.
    et al.
    Moscow State Univeristy.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ergodicity of dynamical systems on 2-adic spheres2012In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 86, no 3, p. 843-845Article in journal (Refereed)
  • 48.
    Anashin, Vladimir
    et al.
    Russian State University.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Applied algebraic dynamics2009Book (Refereed)
  • 49.
    Anashin, Vladimir
    et al.
    Moscow MV Lomonosov State Univ, Fac Computat Math & Cybernet, Moscow 119991, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ergodicity criteria for non-expanding transformations of 2-adic spheres2014In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 34, no 2, p. 367-377Article in journal (Refereed)
    Abstract [en]

    In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems < f; S2-r (a)> on 2-adic spheres S2-r (a) of radius 2(-r), r >= 1, centered at some point a from the ultrametric space of 2-adic integers Z(2). The map f: Z(2) -> Z(2) is assumed to be non-expanding and measure-preserving; that is, f satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and f preserves a natural probability measure on Z(2), the Haar measure mu(2) on Z(2) which is normalized so that mu(2)(Z(2)) = 1.

  • 50.
    Anashin, Vladimir
    et al.
    Lomonosov Moscow State University.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    T-functions revisited: new criteria for bijectivity/transitivity2014In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 71, no 3, p. 383-407Article in journal (Refereed)
    Abstract [en]

    The paper presents new criteria for bijectivity/transitivity of T-functions and a fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz p-adic functions and to study measure-preservation/ergodicity of these.

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