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  • 1.
    Aghanavesi, Somayeh
    et al.
    Dalarna University, School of Technology and Business Studies, Microdata Analysis.
    Memedi, Mevludin
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Dougherty, Mark
    Dalarna University, School of Technology and Business Studies, Microdata Analysis.
    Nyholm, Dag
    Westin, Jerker
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Verification of a method for measuring Parkinson’s disease related temporal irregularity in spiral drawings2017In: Sensors, ISSN 1424-8220, E-ISSN 1424-8220, Vol. 17, no 10, article id 2341Article in journal (Refereed)
    Abstract [en]

    Parkinson's disease (PD) is a progressive movement disorder caused by the death of dopamine-producing cells in the midbrain. There is a need for frequent symptom assessment, since the treatment needs to be individualized as the disease progresses. The aim of this paper was to verify and further investigate the clinimetric properties of an entropy-based method for measuring PD-related upper limb temporal irregularities during spiral drawing tasks. More specifically, properties of a temporal irregularity score (TIS) for patients at different stages of PD, and medication time points were investigated. Nineteen PD patients and 22 healthy controls performed repeated spiral drawing tasks on a smartphone. Patients performed the tests before a single levodopa dose and at specific time intervals after the dose was given. Three movement disorder specialists rated videos of the patients based on the unified PD rating scale (UPDRS) and the Dyskinesia scale. Differences in mean TIS between the groups of patients and healthy subjects were assessed. Test-retest reliability of the TIS was measured. The ability of TIS to detect changes from baseline (before medication) to later time points was investigated. Correlations between TIS and clinical rating scores were assessed. The mean TIS was significantly different between healthy subjects and patients in advanced groups (p-value = 0.02). Test-retest reliability of TIS was good with Intra-class Correlation Coefficient of 0.81. When assessing changes in relation to treatment, TIS contained some information to capture changes from Off to On and wearing off effects. However, the correlations between TIS and clinical scores (UPDRS and Dyskinesia) were weak. TIS was able to differentiate spiral drawings drawn by patients in an advanced stage from those drawn by healthy subjects, and TIS had good test-retest reliability. TIS was somewhat responsive to single-dose levodopa treatment. Since TIS is an upper limb high-frequency-based measure, it cannot be detected during clinical assessment.

  • 2.
    Al Zoghbi, Amal
    Dalarna University, School of Education, Health and Social Studies, Educational Work.
    Problemlösning i matematik: En litteraturstudie om svårigheter i problemlösning i matematik för elever i grundskolans tidiga åldrar2016Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Elevers problemlösningsförmåga uppmärksammas i PISA undersökningar som visar att svenska elever

    inte uppnår goda resultat inom området. Problemlösning är en viktig färdighet som elever behöver i

    och utanför skolan. Problemlösning har förekommit sedan flera decennier tillbaka i skolans kursplan i

    matematik.

    Syftet med den här studien är att få kunskap om svårigheter elever kan ha när de arbetar med

    problemlösning i matematik i grundskolans tidiga skolår och, om så möjligt, vilka orsaker som kan

    påverka dessa svårigheter. Resultaten visar att språkfärdigheter som läsförmåga, förståelseförmåga,

    läsflyt samt det matematiska tänkandet påverkar elevers förmåga att förstå och lösa matematiska

    problem. Likaså är färdigheter i matematiska ord och begrepp samt matematisk text- och talförståelse

    väsentliga. Språk- och problemlösningsfärdigheter främjas av färdigheterna i tänkandet som har sin

    grund i språket. Resultaten visar även att kognitiva faktorer och föräldrars utbildningsnivå är orsaker

    som kan ha en inverkan på elevers förmågor i förståelsen och lösningen av problemlösningsuppgifter.

    Slutsatserna som dras i den här studien är att språkfärdigheter och kognitiva faktorer är de mest

    dominerande i de svårigheter elever kan ha i arbetet med problemlösning. Förståelsen av det

    matematiska problemet utgör den viktigaste delen i problemlösningsprocessen som beskrivs av

    matematikern George Polya och består av en fyra stegs process. Ytterligare en slutsats som dras i

    studien är lärarens roll och undervisningens upplägg som utgör en viktig del i elevers förståelse av

    matematiska problem samt förmågan att lösa dem. Metoden som har använts till den här studien är en

    systematisk litteraturstudie där sökningar på svenska och engelska efter vetenskaplig forskning har

    genomförts i olika databaser.

  • 3.
    Alam, Moudud
    Dalarna University, School of Technology and Business Studies, Statistics.
    An efficient algorithm for the pseudo likelihood estimation of the generalized linear mixed models (GLMM) with correlated random effects2009Report (Other academic)
    Abstract [en]

    This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with correlated random effects. The proposed estimation technique does not require reparametarisation of the model. Multivariate Taylor's approximation has been used to approximate the intractable integrals in the likelihood function of the GLMM. Based on the analytical expression for the estimator of the covariance matrix of the random effects, a condition has been presented as to when such a covariance matrix can be estimated through the estimates of the random effects. An application of the model with a binary response variable has been presented using a real data set on credit defaults from two Swedish banks. Due to the use of two-step estimation technique, proposed algorithm outperforms the conventional pseudo likelihood algorithms in terms of computational time.

  • 4.
    Alam, Moudud
    Dalarna University, School of Technology and Business Studies, Statistics.
    Feasible computation of the generalized linear mixed models with application to credit risk modelling2010Doctoral thesis, monograph (Other academic)
    Abstract [en]

    This thesis deals with developing and testing feasible computational procedures to facilitate the estimation of and carry out the prediction with the generalized linear mixed model (GLMM) with a scope of applying them to large data sets. The work of this thesis is motivated from an issue arising in credit risk modelling. We have access to a huge data set, consisting of about one million observations, on credit history obtained from two major Swedish banks. The principal research interest involved with the data analysis is to model the probability of credit defaults by incorporating the systematic dependencies among the default events. In order to model the dependent credit defaults we adopt the framework of GLMM which is a popular approach to model correlated binary data. However, existing computational procedures for GLMM did not offer us the flexibility to incorporate the desired correlation structure of defaults events. For the feasible estimation of the GLMM we propose two estimation techniques being the fixed effects (FE) approach and the two-step pseudo likelihood approach (2PL). The preciseness of the estimation techniques and their computational advantages are studied by Monte-Carlo simulations and by applying them to the credit risk modelling. Regarding the prediction issue, we show how to apply the likelihood principle to carry out prediction with GLMM. We also provide an R add-in package to facilitate the predictive inference for GLMM.

  • 5.
    Alam, Moudud
    Dalarna University, School of Technology and Business Studies, Statistics.
    Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups2010Manuscript (preprint) (Other academic)
    Abstract [en]

    This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the intractable integrals in the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study. An application of it with a binary response variable is presented using a real data set on credit defaults from two Swedish banks. Thanks to the use of two-step estimation technique, the proposed algorithm outperforms conventional pseudo likelihood algorithms in terms of computational time.

  • 6.
    Alam, Moudud
    Dalarna University, School of Technology and Business Studies, Statistics.
    Industry shocks and empirical evidences on defaults comovement2009Report (Other academic)
    Abstract [en]

    It is commonly agreed that the credit defaults are correlated. However, the mechanism of such dependence is not yet fully understood. This paper contributes to the current understanding about the defaults comovement in the following way. Assuming that the industries provides the basis of defaults comovement it provides empirical evidence as to how such comovements can be modeled using correlated industry shocks. Generalized linear mixed model (GLMM) with correlated random effects is used to model the defaults comovement. Empirical evidences are drawn through analyzing individual borrower level credit history data obtained from two major Swedish banks between the period 1994-2000. The results show that the defaults are correlated both within and between industries but not over time (quarters). A discussion has also been presented as to how a GLMM for defaults correlation can be explained.

  • 7.
    Alam, Moudud
    Dalarna University, School of Technology and Business Studies, Statistics.
    Likelihood prediction for generalized linear mixed models under covariate uncertainty2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 43, no 2, p. 219-234Article in journal (Refereed)
    Abstract [en]

    This paper presents the techniques of likelihood prediction for the generalized linear mixed models. Methods of likelihood prediction is explained through a series of examples; from a classical one to more complicated ones. The examples show, in simple cases, that the likelihood prediction (LP) coincides with already known best frequentist practice such as the best linear unbiased predictor. The paper outlines a way to deal with the covariate uncertainty while producing predictive inference. Using a Poisson error-in-variable generalized linear model, it has been shown that in complicated cases LP produces better results than already know methods.

  • 8.
    Alam, Moudud
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Carling, Kenneth
    Dalarna University, School of Technology and Business Studies, Statistics.
    Computionally feasible estimation of the covariance structure in generalized linear mixed models2008In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 78, no 12, p. 1229-1239Article in journal (Refereed)
    Abstract [en]

    In this paper, we discuss how a regression model, with a non-continuous response variable, which allows for dependency between observations, should be estimated when observations are clustered and measurements on the subjects are repeated. The cluster sizes are assumed to be large. We find that the conventional estimation technique suggested by the literature on generalized linear mixed models (GLMM) is slow and sometimes fails due to non-convergence and lack of memory on standard PCs. We suggest to estimate the random effects as fixed effects by generalized linear model and to derive the covariance matrix from these estimates. A simulation study shows that our proposal is feasible in terms of mean-square error and computation time. We recommend that our proposal be implemented in the software of GLMM techniques so that the estimation procedure can switch between the conventional technique and our proposal, depending on the size of the clusters.

  • 9.
    Alam, Moudud
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Carling, Kenneth
    Dalarna University, School of Technology and Business Studies, Statistics.
    Chen, Rui
    Liang, Yuli
    How to determine the progression of young skiers?2008In: CHANCE: New Directions for Statistics and Computing, ISSN 0933-2480, Vol. 21, no 4, p. 13-19Article in journal (Refereed)
  • 10.
    Alam, Moudud
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Carling, Kenneth
    Dalarna University, School of Technology and Business Studies, Statistics.
    Linde, Olof
    Sweco Eurofutures.
    Nääs, Ola
    Dalarna University, School of Technology and Business Studies, Statistics.
    Sandén, Peter
    Sweco Eurofutures.
    Wing, Stefan
    Sweco Eurofutures.
    Utvärdering av det arbetsmarknadspolitiska projektet "Volvo Cars och dess underleverantörer"2012Report (Other academic)
    Abstract [sv]

    Denna rapport är en utvärdering av det arbetsmarknadspolitiska projektet "Volvo Cars och dess underleverantörer", som har genomförts av Arbetsförmedlingen i samarbete med Skolverket och Svenska ESF-rådet. Den 5 juni 2009 ansökte Sveriges regering om medel hos den Europeiska globaliseringsfonen (EGF)2 för att kunna erbjuda åtgärder för personer som blivit uppsagda från Volvo Cars AB och dess underleverantörer. Syftet med projektet var att kunna erbjuda de som blivit uppsagda kompetensutveckling, nya yrkeskunskaper och möjlighet att etablera egna företag.

    På operativ nivå drevs projektet i samverkan mellan Arbetsförmedlingen och den kom-munala yrkesvuxenutbildningen ("Yrkesvux"). Yrkesvux i Göteborgs kommun fick i upp-drag av Skolverket att samordna den del av verksamheten som berörde kommunal yr-kesvuxenutbildning. Projektet startade 1 januari 2010 och avslutades 31 maj 2011. Enligt kommissionens beslut fick medel även användas retroaktivt för insatser som hade givits till de uppsagda i form av olika arbetsmarknadsutbildningar, det s.k. snabbspåret, under 2009 innan projektet hade startat.

    Av nästan 5 000 individer i målgruppen som registrerade sig vid Arbetsförmedlingen del-tog knappt en fjärdedel i projektets insatser (exkl. vägledning). Av dessa gick 55 procent i aktiviteter enbart genom Arbetsförmedlingen, 37 procent enbart genom Yrkesvux och åtta procent genom både Arbetsförmedlingen och Yrkesvux. De vanligaste förekommande utbildningsinriktningarna var industri och bygg, fordonsindustri, transport och magasine-ring, omvårdnad och handel.

  • 11.
    Alam, Moudud
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Hao, Chengcheng
    Carling, Kenneth
    Dalarna University, School of Technology and Business Studies, Statistics.
    Review of the literature on credit risk modeling: development of the past 10 years2010In: Banks and Bank Systems, ISSN 1816-7403, Vol. 5, no 3, p. 43-60Article in journal (Refereed)
    Abstract [en]

    This paper traces the developments of credit risk modeling in the past 10 years. Our work can be divided into two parts: selecting articles and summarizing results. On the one hand, by constructing an ordered logit model on historical Journal of Economic Literature (JEL) codes of articles about credit risk modeling, we sort out articles which are the most related to our topic. The result indicates that the JEL codes have become the standard to classify researches in credit risk modeling. On the other hand, comparing with the classical review Altman and Saunders(1998), we observe some important changes of research methods of credit risk. The main finding is that current focuses on credit risk modeling have moved from static individual-level models to dynamic portfolio models.

  • 12.
    Alam, Moudud
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Maengseok, Noh
    Department of Statistics, Pukyong National University, South Korea.
    Lee, Youngjo
    Department of Statistics, Seoul National University, South Korea.
    Likelihood estimate of treatment effects under selection bias2013In: Statistics and its Interface, ISSN 1938-7989, E-ISSN 1938-7997, Vol. 6, no 3, p. 349-359Article in journal (Refereed)
    Abstract [en]

    We consider methods for estimating the causal effects of treatment in the situation where the individuals in the treatment and the control group are self selected, i.e., the selection mechanism is not randomized. In this case, a simple comparison of treated and control outcomes will not generally yield valid estimates of casual effect. The propensity score method is frequently used for the evaluation of treatment effect. However, this method is based on some strong assumptions, which are not directly testable. In this paper, we present an alternative modelling approach to draw causal inferences by using a shared random-effect model and the computational algorithm to draw likelihood based inference with such a model. With small numerical studies and a real data analysis, we show that our approach gives not only more efficient estimates but also is less sensitive to model misspecifications, which we consider, than existing methods.

  • 13.
    Alam, Moudud
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Noh, Maengseok
    Department of Statistics, Pukyong National Univeristy.
    Lee, Youngjo
    Department of Statistics, Seoul National Univeristy.
    Likelihood estimate of treatment effects under selection bias2012Report (Other academic)
    Abstract [en]

    We consider methods for estimating causal effects of treatment in the situation where the individuals in the treatment and the control group are self selected, i.e., the selection mechanism is not randomized. In this case, simple comparison of treated and control outcomes will not generally yield valid estimates of casual effects. The propensity score method is frequently used for the evaluation of treatment effect. However, this method is based onsome strong assumptions, which are not directly testable. In this paper, we present an alternative modeling approachto draw causal inference by using share random-effect model and the computational algorithm to draw likelihood based inference with such a model. With small numerical studies and a real data analysis, we show that our approach gives not only more efficient estimates but it is also less sensitive to model misspecifications, which we consider, than the existing methods.

  • 14.
    Alam, Moudud
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Rönnegård, Lars
    Dalarna University, School of Technology and Business Studies, Statistics.
    Shen, Xia
    Karolinska Institutet.
    Fitting conditional and simultaneous autoregressive spatial models in hglm2015In: The R Journal, ISSN 2073-4859, Vol. 7, no 2, p. 5-18Article in journal (Refereed)
    Abstract [en]

    We present a new version (> 2.0) of the hglm package for fitting hierarchical generalized linear models (HGLMs) with spatially correlated random effects. CAR() and SAR() families for conditional and simultaneous autoregressive random effects were implemented. Eigen decomposition of the matrix describing the spatial structure (e.g., the neighborhood matrix) was used to transform the CAR/SAR random effects into an independent, but eteroscedastic, Gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR and SAR models. This gives a computationally efficient algorithm for moderately sized problems.

  • 15.
    Alam, Moudud
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Rönnegård, Lars
    Dalarna University, School of Technology and Business Studies, Statistics.
    Shen, Xia
    Swedish University of Agricultural Sciences, Uppsala.
    Fitting spatial models in the R package: hglm2014Report (Other academic)
    Abstract [en]

    We present a new version of the hglm package for fittinghierarchical generalized linear models (HGLM) with spatially correlated random effects. A CAR family for conditional autoregressive random effects was implemented. Eigen decomposition of the matrix describing the spatial structure (e.g. the neighborhood matrix) was used to transform the CAR random effectsinto an independent, but heteroscedastic, gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR model.This gives a computationally efficient algorithm for moderately sized problems (e.g. n<5000).

  • 16.
    Alshemas, Rand
    Dalarna University, School of Education, Health and Social Studies, Educational Work.
    Användning av IKT i matematikundervisning: En intervjustudie med matematiklärare 7-92017Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Studiens syfte är att undersöka de IKT med fokus på digitala verktyg som lärare använder i matematikundervisning idag och vilka mål de har med att integrera digitala verktyg. I studien presenteras olika digitala verktyg som används i matematikundervisning, följt av en kort analys.

    Studiens genomfördes genom intervjuer med åtta lärare som undervisar matematik för elever (7-9) och gymnasiet (kurser i grundnivå (7-9)/introduktionsprogrammet). Intervjuerna skedde genom träff (muntliga intervjuer) eller genom mejl(datorstödda intervjuer).

    Studien lyfter fram lärarens roll i elevens lärande med och utan digitala verktyg. Lärarna som har deltagit i studien har olika erfarenheter, arbetssätt och olika syn på användning av digitala verktyg i matematikundervisning. Vissa lärare tycker att det är värdefullt att integrera digitala verktyg i matematikundervisning och att det kan motivera eleverna samt komplettera det som görs i klassrummet. Matematiklärare som väljer att integrera digitala verktyg i undervisningen gör det för att t.ex. att öka elevernas motivation, skapa ökad måluppfyllelse och underlätta lärarens arbete. Andra visar inte samma intresse för användning av digitala verktyg. De senare anser att matematikundervisning med digitala verktyg inte kan säkerställa elevernas förståelse av ämnets innehåll. Enligt dessa mattelärare är digitala verktyg endast ett komplement till den traditionella undervisningen.

  • 17.
    Amcoff, Linda
    Dalarna University, School of Education and Humanities, Educational Work.
    Att uttrycka matematik: En observationsstudie av vilka uttrycksformer och matematiska aktiviteter som uppmuntras och används i förskolan2013Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

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

  • 18.
    Arvidson, Amanda
    Dalarna University, School of Education, Health and Social Studies, Educational Work.
    Undervisning för elever med låga prestationer i matematik: • En litteraturstudie med fokus på allmänna matematiksvårigheter2017Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med denna studie är att undersöka hur lärare i F-3 kan undervisa för att stödja elever med låga prestationer i matematik. Utifrån syftet konkretiserades en frågeställning för att göra studien undersökningsbar: Hur kan lärare undervisa för att hjälpa elever i allmänna matematiksvårigheter? Metoden som valdes för att undersöka denna fråga var en systematisk litteraturstudie. Sökning av relevant litteratur har skett genom olika databaser, litteraturen har granskats och analyserats för att sedan sammanställas till ett resultat. Resultatet visar en varierande bild på hur lärare ska arbeta för att stödja elever i allmänna matematiksvårigheter. Strategiundervisning bör vara en central roll i undervisningen. Beroende på elevers individuella förutsättningar bör antingen läraren styra inlärningen av strategier eller låta elever utveckla en flexibilitet i sin egen strategiutveckling. Resultatet visar på vikten av att läraren bör ha matematiska samtal med eleverna och användning av teknologiska spel i undervisningen visades även vara positivt för elever i låga prestationer i matematik. Slutsatserna av denna studie är att lärare måste erfara elevers individuella förutsättningar för att kunna stödja dem på bästa sätt där matematiska samtal och strategiutbildning ska vara en central roll i matematikundervisningen.

  • 19.
    Barmé, Elin
    Dalarna University, School of Education, Health and Social Studies, Mathematics Education.
    En varierad matematikundervisning: Hur matematiklärare i årskurs F-3 varierar undervisningsformer2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Denna studie behandlar hur lärare i årskurs F-3 varierar sin matematikundervisning. Syftet med studien är att utifrån ett lärarperspektiv undersöka vilka olika undervisningsformer som används av ett antal matematiklärare i årskurs F-3 samt vad dessa lärare anser om variation i matematikundervisningen.Fyra lärare, en från varje årskurs från förskoleklass till årskurs 3, har deltagit i studiens undersökningar. Undersökningsmetoder har varit icke deltagande observation av en matematiklektion med varje lärare samt en kvalitativ semistrukturerad intervju med varje lärare. Resultaten visade på att den traditionella undervisningsformen var den vanligaste undervisningsformen som användes och matematikdiskussioner var den vanligaste alternativa undervisningsformen som användes. Ju högre upp i årskurserna undersökningarna gjordes desto mindre användes alternativa undervisningsformer. En ökad andel resurser under matematiklektionerna skulle bidra till ökade möjligheter till att variera undervisningen.

  • 20.
    Bergqvist, Tomas
    et al.
    Umeå universitet, Interaktiva medier och lärande.
    Lithner, Johan
    Umeå universitet, Institutionen för matematik och matematisk statistik.
    Sumpter, Lovisa
    Umeå universitet, Institutionen för matematik och matematisk statistik.
    Upper secondary students’ task reasoning2008In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 39, no 1, p. 1-12Article in journal (Refereed)
    Abstract [en]

    Upper secondary students’ task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a random way, and guided reasoning, where progress was possible only when essentially all important strategy choices were made by the interviewer.

  • 21.
    Bergstrand, Mattias
    Dalarna University, School of Education, Health and Social Studies, Mathematics Education.
    Digitala verktyg i matematik: Elevers arbete med matematik i digitala verktyg2017Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med denna undersökning är att undersöka hur elever använder det matematiska innehållet i olika digitala verktyg. För att få svar på detta har observationer och enkätundersökningar gjorts. Resultaten har analyserats med utgångspunkt i ett teoretiskt ramverk där användningar av digitala verktyg kan vara ersättande, förstärkande och transformerande. Resultaten visar att digitala verktyg kan vara ersättande i vissa avseenden och förstärkande eller transformerande i andra.

  • 22. Besnier, Francois
    et al.
    Wahlberg, Per
    Rönnegård, Lars
    Dalarna University, School of Technology and Business Studies, Statistics.
    Ek, Weronika
    Andersson, Leif
    Siegel, Paul
    Carlborg, Örjan
    Fine mapping and replication of QTL in outbred chicken advanced intercross lines2011In: Genetics Selection Evolution, ISSN 0999-193X, E-ISSN 1297-9686, Vol. 43, article id 3Article in journal (Refereed)
    Abstract [en]

    Background: Linkage mapping is used to identify genomic regions affecting the expression of complex traits. However, when experimental crosses such as F2 populations or backcrosses are used to map regions containing a Quantitative Trait Locus (QTL), the size of the regions identified remains quite large, i.e. 10 or more Mb. Thus, other experimental strategies are needed to refine the QTL locations. Advanced Intercross Lines (AIL) are produced by repeated intercrossing of F2 animals and successive generations, which decrease linkage disequilibrium in a controlled manner. Although this approach is seen as promising, both to replicate QTL analyses and fine-map QTL, only a few AIL datasets, all originating from inbred founders, have been reported in the literature.

    Methods: We have produced a nine-generation AIL pedigree (n = 1529) from two outbred chicken lines divergently selected for body weight at eight weeks of age. All animals were weighed at eight weeks of age and genotyped for SNP located in nine genomic regions where significant or suggestive QTL had previously been detected in the F2 population. In parallel, we have developed a novel strategy to analyse the data that uses both genotype and pedigree information of all AIL individuals to replicate the detection of and fine-map QTL affecting juvenile body weight.

    Results: Five of the nine QTL detected with the original F2 population were confirmed and fine-mapped with the AIL, while for the remaining four, only suggestive evidence of their existence was obtained. All original QTL were confirmed as a single locus, except for one, which split into two linked QTL.

    Conclusions: Our results indicate that many of the QTL, which are genome-wide significant or suggestive in the analyses of large intercross populations, are true effects that can be replicated and fine-mapped using AIL. Key factors for success are the use of large populations and powerful statistical tools. Moreover, we believe that the statistical methods we have developed to efficiently study outbred AIL populations will increase the number of organisms for which in-depth complex traits can be analyzed.

  • 23.
    Breton, Daniel
    Dalarna University, School of Technology and Business Studies, Mathematics.
    Teaching Mathematics in English to Swedish Speaking Students: A systematic review of strategies for teaching mathematics to second language learners2016Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The Swedish government has authorised the teaching of mathematics in English to Swedish speaking students. Much of that teaching is performed by foreign trained native English speaking teachers lacking training in second language learners. This systematic review summarises international studies from the last ten years that deal with the teaching of mathematics to second language learners. The review shows that second language students working in a bilingual environment achieve higher rates of content and language knowledge than learners in a monolingual environment. This study also summarises some of the teacher practices that are effective for teaching mathematics in English to second language learners.

  • 24.
    Breton, Daniel
    Dalarna University, School of Education, Health and Social Studies, Educational Work.
    Teaching Mathematics in English to Swedish Speaking Students: The Use of Second Language Teaching Practices in the Teaching of Mathematics in English to Swedish Speaking Students in Lower Secondary School2016Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Over 20,000 Swedish lower high school students are currently learning mathematics in English but little research has been conducted in this area. This study looks into the question of how much second language learner training teachers teaching mathematics in English to Swedish speaking students have acquired and how many of those teachers are using effective teaching practices for second language learners. The study confirms earlier findings that report few teachers receive training in second language learning but indicates that some of the teaching practices shown to be effective with second language learners are being used in some Swedish schools

  • 25. Bring, Johan
    et al.
    Rönnegård, Lars
    Dalarna University, School of Technology and Business Studies, Statistics.
    Åldersbedömningar - en statistisk utmaning2018In: Folkvett, ISSN 0283-0795, no 1, p. 7-13Article in journal (Other (popular science, discussion, etc.))
  • 26.
    Carling, Kenneth
    Dalarna University, School of Technology and Business Studies, Microdata Analysis.
    A comment on outlier detection and skewed distributions2017Report (Other academic)
    Abstract [en]

    It seems that a paper of mine appearing in Computational Statistics & Data Analysis (Carling, 2000) has prompted the development of outlier detection methods for highly skewed data. However, I wrote the paper in the spirit of Exploratory Data Analysis (Tukey, 1977) and I shared Tukey’s opinion, and I still hold it, that skewed data are better to be transformed for approximate symmetry prior to detection of outliers (or other data analyses).

  • 27.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Han, Mengjie
    Dalarna University, School of Technology and Business Studies, Statistics.
    GRASP and statistical bounds for heuristic solutions to combinatorial problems2016Report (Other academic)
    Abstract [en]

    The quality of a heuristic solution to a NP-hard combinatorial problem is hard to assess. A few studies have advocated and tested statistical bounds as a method for assessment. These studies indicate that statistical bounds are superior to the more widely known and used deterministic bounds. However, the previous studies have been limited to a few metaheuristics and combinatorial problems and, hence, the general performance of statistical bounds in combinatorial optimization remains an open question. This work complements the existing literature on statistical bounds by testing them on the metaheuristic Greedy Randomized Adaptive Search Procedures (GRASP) and four combinatorial problems. Our findings confirm previous results that statistical bounds are reliable for the p-median problem, while we note that they also seem reliable for the set covering problem. For the quadratic assignment problem, the statistical bounds has previously been found reliable when obtained from the Genetic algorithm whereas in this work they found less reliable. Finally, we provide statistical bounds to four 2-path network design problem instances for which the optimum is currently unknown.

  • 28.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Han, Mengjie
    Dalarna University, School of Technology and Business Studies, Statistics.
    Håkansson, Johan
    Dalarna University, School of Technology and Business Studies, Information Systems.
    Rebreyend, Pascal
    Dalarna University, School of Technology and Business Studies, Computer Engineering.
    Testing the gravity p-median model empirically2015In: Operations Research Perspectives, ISSN 2214-7160, Vol. 2, no 124, article id 132Article in journal (Refereed)
    Abstract [en]

    Regarding the location of a facility, the presumption in the widely used p-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity p-median model offers an extension to the p-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the p-median model. We found, however, the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

  • 29.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Microdata Analysis.
    Li, Yujiao
    Dalarna University, School of Technology and Business Studies, Microdata Analysis.
    The Power of the Synthetic Control Method2016Report (Other academic)
    Abstract [en]

    The synthetic control method (SCM) is a new, popular method developed for the purpose of estimating the effect of an intervention when only one single unit has been exposed. Other similar, unexposed units are combined into a synthetic control unit intended to mimic the evolution in the exposed unit, had it not been subject to exposure. As the inference relies on only a single observational unit, the statistical inferential issue is a challenge. In this paper, we examine the statistical properties of the estimator, study a number of features potentially yielding uncertainty in the estimator, discuss the rationale for statistical inference in relation to SCM, and provide a Web-app for researchers to aid in their decision of whether SCM is powerful for a specific case study. We conclude that SCM is powerful with a limited number of controls in the donor pool and a fairly short pre-intervention time period. This holds as long as the parameter of interest is a parametric specification of the intervention effect, and the duration of post-intervention period is reasonably long, and the fit of the synthetic control unit to the exposed unit in the pre-intervention period is good.

  • 30.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Meng, Xiangli
    Dalarna University, School of Technology and Business Studies, Statistics.
    Confidence in heuristic solutions?2014Report (Other academic)
    Abstract [en]

    Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

  • 31.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Meng, Xiangli
    Dalarna University, School of Technology and Business Studies, Statistics.
    Confidence in heuristic solutions?2015In: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 63, no 2, p. 381-399Article in journal (Refereed)
    Abstract [en]

    Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

  • 32.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Meng, Xiangli
    Dalarna University, School of Technology and Business Studies, Statistics.
    On statistical bounds of heuristic solutions to location problems2016In: Journal of combinatorial optimization, ISSN 1382-6905, E-ISSN 1573-2886, Vol. 31, no 4, p. 1518-1549Article in journal (Refereed)
    Abstract [en]

    Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region.

  • 33.
    Carling, Kenneth
    et al.
    Dalarna University, School of Technology and Business Studies, Statistics.
    Meng, Xiangli
    Dalarna University, School of Technology and Business Studies, Statistics.
    On statistical bounds of heuristic solutions to location problems2014Report (Other academic)
    Abstract [en]

    Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

  • 34. Casals, M.
    et al.
    Langohr, K.
    Carrasco, J. L.
    Rönnegård, Lars
    Dalarna University, School of Technology and Business Studies, Statistics.
    Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles: a simulation study2015In: SORT - Statistics and Operations Research Transactions, ISSN 1696-2281, E-ISSN 2013-8830, Vol. 39, no 2, p. 281-308Article in journal (Refereed)
    Abstract [en]

    Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles - marginal likelihood, extended likelihood, Bayesian analysis-via simulation studies. Real data on contact wrestling are used for illustration.

  • 35.
    Charrière, Lionel
    Dalarna University, School of Education, Health and Social Studies, Mathematics Education.
    Det vet man inte, men så tror jag!: Om hur elever i årskurs 9 löser sannolikhetsuppgifter2014Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
  • 36.
    Cortas Nordlander, Maria
    Université de Reims Champagne Ardenne, Ecole Doctorale Sciences Exactes et Biologie, France.
    Calcul par tranches pour les équations différentielles à variable temps à caractère explosif2005Doctoral thesis, monograph (Other academic)
    Abstract [en]

    The aim of this work is to propose a numerical method for solving different types of partial and ordinary differential equations. The equations share the same common property for their solutions to become infinite (blow up behaviour) or to become null (extinction behaviour) in finite time. This type of equations is solved using a sliced time computing technique, combined with rescaling both the variable time and the solution of the differential system. The main criterion under which the slice of time is defined, consists in imposing that the rescaled solution should not be greater than a preset cut off value. Another selection criterion for the method is based on the invariance and similarity conditions, enforced on the rescaled model in each of the time slices

  • 37.
    Cortas Nordlander, Maria
    Dalarna University, School of Education, Health and Social Studies, Mathematics Education.
    Dissection of text-based mathematical tasks in the multilingual classroom: A pilot study2019Conference paper (Refereed)
  • 38.
    Cortas Nordlander, Maria
    et al.
    Vasaskolan, Gävle.
    Nordlander, Edvard
    Högskolan i Gävle, Ämnesavdelningen för elektronik.
    A Study of Students’ Ability to Solve Text-Based Mathematical Problems with Irrelevant or Superfluous Information2008In: Mathematical Views, MAVI 14: Strobl/Salzburg, Austria, May 2008, 2008Conference paper (Refereed)
    Abstract [en]

    A limited quantitative survey has been performed in order to study the capability of students to solve text-based mathematical problems containing irrelevant or superfluous information, as well as their ability to scrutinize text and sort out the relevant information. The students took a written test with text-based problems of different amount of irrelevant or superfluous information. The capability of understanding such problems was investigated versus degree of maturity and gender. Obtained results indicate a noticeable correlation between the occurrence of irrelevant or superfluous information and ability of solving the problems. Furthermore, the results show that the degree of maturity, expressed in terms of age, has a clear influence on the results. This study has not revealed any significant difference between genders as regards ability of sorting out the relevant information.

  • 39.
    Cortas Nordlander, Maria
    et al.
    Vasaskolan, Gävle.
    Nordlander, Edvard
    Högskolan i Gävle, Ämnesavdelningen för elektronik.
    Influence of Student’s Attitudes and Beliefs on the Ability of Solving Mathematical Problems with Irrelevant Information2009In: Beliefs and attitudes in mathematics education: new research results / [ed] Jürgen Maasz and Wolfgang Schlöglmann, Rotterdam: Sense Publishers , 2009, p. 165-178Chapter in book (Other academic)
    Abstract [en]

    A limited quantitative survey has been performed in order to study how attitudes, beliefs and feelings of students may influence the ability of solving text-based mathematical problems containing irrelevant information. The survey is also analyzing their capability of scrutinizing texts and sorting out relevant information.

    The students took a written test with text-based problems of different amount of irrelevant information. The capability of understanding such problems was investigated versus degree of mathematical maturity and gender. Obtained results indicate a noticeable correlation between the occurrence of irrelevant information and the ability of solving the problems. Furthermore, attitudes, beliefs, and the degree of mathematical maturity, expressed in terms of age, have a clear influence on the results. On the other hand, this study has not revealed any significant difference between genders as regards the capability of solving text-based problems with irrelevant information.

     

  • 40.
    Cortas Nordlander, Maria
    et al.
    Vasaskolan, Gävle.
    Nordlander, Edvard
    Högskolan i Gävle, Elektronik.
    Komplexa tal är inte så komplexa!2010Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    Abstraktion kan ofta utgöra ett hinder för lärande i matematik. Momentet med komplexa tal är inte något undantag. Varför ska man acceptera att i2=-1? Hur kan lärare introducera det på ett pedagogiskt sätt? Visualisering kan vara ett väsentligt led i att underlätta studenters lärande, ge dem en känsla av lägre abstraktion och härigenom vara nyckeln till djupare förståelse. Artikeln beskriver en visuell ansats som uppfyller kravet på lättillgänglighet. Metoden bygger på upprepade rotationer i det komplexa talplanet, vilket åskådliggör och konkretiserar komplexa tal genom visualisering.

  • 41.
    Danielsson, Stina
    Dalarna University, School of Education and Humanities, Mathematics Education.
    Håller din lärobok i matematik måttet?: En modell för granskning av hur läroböcker i matematik förhåller sig till rådande styrdokuments centrala innehåll2012Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
  • 42.
    Eklund, Karin
    Dalarna University, School of Education and Humanities, Educational Work.
    Andraspråkselever och matematik - språksvårigheter är bara halva sanningen: En studie i åk 6-92012Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Ett större antal andraspråkelever i den svenska skolan ställer nya krav på undervisningen och på lärarna. Svårigheter uppstår när elever ska lära ett nytt språk samtidigt som de ska inhämta kunskaper på det nya språket. Inom matematiken ger de matematiska textuppgifterna eleverna en extra utmaning där ett enda missat ord kan omintetgöra hela förståelsen. Det matematiska språket har sin egen speciella utformning och avviker ifrån vardagligt språk. Det kan därför vara ord i textuppgifterna som är nya och främmande för elever som inte har kommit så långt i sin svenska språkutveckling. Många av de begrepp som vi har i matematiken har dessutom flera betydelser som tex. volym, rymmer, axel, udda och så vidare och när eleverna inte förstår innebörden i texten så vet de inte heller vad de ska göra och kan därför inte göra den matematiska beräkning som uppgiften efterfrågar.Huvudsyftet med denna undersökning är därför att få kunskap om vilka svårigheter som möter andraspråkselever i matematikundervisningen. Svårigheter som lärare i matematik behöver känna till för att kunna ta hänsyn till dessa och på bästa sätt kunna stödja och hjälpa andraspråkelever till en god inlärning med de resurser som finns tillgängliga på skolan idag.Uppsatsen presenterar resultatet av ett språktest med matematiska textuppgifter. Detta resultat kompletteras sedan med intervjuer av lärare, elever och elevernas studiehandledare.Matematikundervisningen behöver utformas med en större kunskap om språk och språkinlärning. För att kunna bilda sig en uppfattning om ett nytt ords betydelse måste ordet få användas i olika sammanhang, ordet måste behövas. Mer muntliga övningar och mer träning i att beskriva tankar och begrepp skulle gynna inte bara andraspråkeleverna utan alla elever i klassen.Lärare i matematik kan känna att de har för lite tid och resurser för att kunna hjälpa andraspråkelever till goda matematikkunskaper. Det saknas även kunskaper om vad som är svårt inom matematiken och i texten till matematiska läsuppgifter. Till en del saknas också kunskaper i vad det innebär att lära sig ett språk och hur det är att studera på ett språk som man inte behärskar. De elever som jag har talat med är nöjda med sin matematikundervisning, sin lärare och sin studiehandledare. Två av dem är entusiastiska och mycket motiverade och har bra resultat. De andra två tycker att matematiken är svår och tråkig och har trots ansträngningar jobbigt med förståelsen. Lärare skulle behöva mer kunskaper om matematikundervisning för andraspråkelever. De behöver också ta ett större övergripande ansvar för varje enskild elevs kunskapsinhämtning. Som det är idag läggs ofta ansvaret för andraspråkeleven på någon annan, det kan vara studiehandledaren, läraren i svenska som andraspråk, modersmålsläraren eller speciallärare. Självklart ska alla dessa lärare samarbeta för att skapa en bra studiesituation för eleven men någon måste ha huvudansvaret. Det mest naturliga är att ansvaret innehas av den ordinarie läraren som känner till de mål och kursplaner som finns för ämnet.

  • 43.
    Fahlström, Magnus
    et al.
    Dalarna University, School of Technology and Business Studies, Microdata Analysis.
    Teledahl, Anna
    Dalarna University, School of Education, Health and Social Studies, Mathematics Education.
    Students’ use of images for documenting their problem solving2017Conference paper (Other academic)
  • 44.
    Fan, Ming
    Dalarna University, School of Technology and Business Studies, Mathematics.
    A queueing model for mixed loss-delay systems with general interarrival processes for wide-band calls2007In: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 180, no 3, p. 1201-1220Article in journal (Refereed)
    Abstract [en]

    We investigate the single link mixed loss-delay FIFO system with the exponential holding time distribution, the Markovian interarrival process for the narrow-band calls, and the general independently and identically distributed interarrival process for the wide-band calls. This is achieved by combining the embedded Markov chain method and the matrix-analytic technique.

  • 45.
    Fan, Ming
    Dalarna University, School of Technology and Business Studies, Mathematics.
    Commutator estimates for interpolation scales with holomorphic structure2010In: Complex Analysis and Operator Theory, ISSN 1661-8254, E-ISSN 1661-8262, Vol. 4, no 2, p. 159-178Article in journal (Refereed)
    Abstract [en]

    The main result of this paper is some quantitative estimates for nonlinear commutators under the complex interpolation methods and more general interpolation scales with holomorphic structures. We also investigate the spectral behaviour of bounded linear operators under this kind of interpolation methods.

  • 46.
    Fan, Ming
    Dalarna University, School of Technology and Business Studies, Mathematics.
    Interpolation of vector-valued Banach lattices and Calderón-Lozanovskii construction2001In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 227, no 1, p. 63-80Article in journal (Refereed)
    Abstract [en]

    We establish the connection between the variants of Schechter's complex interpolation methods, Peetre-Gustavsson's interpolation methods, and the Calderon-Lozanovskii construction on vector-valued Banach lattices. As applications, we show that the uniform convexity and the UMD property are stable byinterpolation.

  • 47.
    Fan, Ming
    Dalarna University, School of Technology and Business Studies, Mathematics.
    Lions-Peetre’s interpolation methods associated with quasi-power functions and some applications2006In: Rocky Mountain Journal of Mathematics, ISSN 0035-7596, E-ISSN 1945-3795, Vol. 36, no 5, p. 1487-1510Article in journal (Refereed)
    Abstract [en]

    This paper concerns some properties of Lions-Peetre's interpolation methods of constants and means associated with quasi-power functions, and their applications in harmonic analysis, martingale inequalities, and geometric properties of Banach spaces. We describe Besov-Orlicz spaces and Triebel-Lizorkin-Orlicz spaces in terms of interpolation and wavelet bases. We study the commutators of quasi-logarithmic operators and singular integral operators, Hankel operators in Schatten-Orlicz classes, martingale inequalities for the partial derivative-variation, and the stability of multi-dimensional uniform rotundity under interpolation.

  • 48.
    Fan, Ming
    Dalarna University, School of Technology and Business Studies, Mathematics.
    Lions-Schechter’s methods of complex interpolation and some quantitative estimates2006In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 140, no 1, p. 46-60Article in journal (Refereed)
    Abstract [en]

    Some quantitative estimates concerning multi-dimensional rotundity, weak noncompactness, and certain spectral inequalities are formulated for Lions-Schechter's complex methods of interpolation with derivatives.

  • 49.
    Fan, Ming
    Dalarna University, School of Technology and Business Studies, Mathematics.
    Quadratic interpolation and some operator inequalities2011In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 5, no 3, p. 413-427Article in journal (Refereed)
    Abstract [en]

    We investigate some properties of Hilbert spaces and bounded linear operators under quadratic interpolation in both qualitative and quantitative ways. Interpolation type, reiteration, interpolation methods associated with quasi-power function parameters, nonlinear commutator estimates, and interpolation of certain operators and spectral properties are under consideration.

  • 50.
    Fan, Ming
    Dalarna University, School of Technology and Business Studies, Mathematics.
    Some quantitative interpolation theorems under Lions-Peetre’s methods2009In: Journal of Convex Analysis, ISSN 0944-6532, Vol. 16, no 2, p. 487-499Article in journal (Refereed)
    Abstract [en]

    We formulate the quantitative version of interpolation theorems on compactness and weak compactness, the improved estimate for the k-uniform rotundity, and even the stability of the nearly uniform convexity under Lions-Peetre's interpolation methods of constants and means associated with quasi-power function parameters.

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