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• 19301.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Statistical Assessment of Estimated Transformations in Observed-Score Equating2016Inngår i: Journal of educational measurement, ISSN 0022-0655, E-ISSN 1745-3984, Vol. 53, nr 1, s. 106-125Artikkel i tidsskrift (Fagfellevurdert)

Equating methods make use of an appropriate transformation function to map the scores of one test form into the scale of another so that scores are comparable and can be used interchangeably. The equating literature shows that the ways of judging the success of an equating (i.e., the score transformation) might differ depending on the adopted framework. Rather than targeting different parts of the equating process and aiming to evaluate the process from different aspects, this article views the equating transformation as a standard statistical estimator and discusses how this estimator should be assessed in an equating framework. For the kernel equating framework, a numerical illustration shows the potentials of viewing the equating transformation as a statistical estimator as opposed to assessing it using equating-specific criteria. A discussion on how this approach can be used to compare other equating estimators from different frameworks is also included.

• 19302.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Statistical assessment of equating transformations2014Konferansepaper (Fagfellevurdert)
• 19303.
Umeå universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
Computerized achievement tests: sequential and fixed length tests2003Doktoravhandling, med artikler (Annet vitenskapelig)

The aim of this dissertation is to describe how a computerized achivement test can be constructed and used in practice. Throughout this dissertation the focus is on classifying the examinees into masters and non-masters depending on their ability. However, there has been no attempt to estimate their ability.

In paper I, a criterion-referenced computerized test with a fixed number of items is expressed as a statistical inference problem. The theory of optimal design is used to find the test that has the strongest power. A formal proof is provided showing that all items should have the same item characteristics, viz. high discrimination, low guessing and difficulty near the cutoff score, in order to give us the most powerful statistical test. An efficiency study shows how many times more non-optimal items are needed if we do not use optimal items in order to achieve the same power in the test.

In paper II, a computerized mastery sequential test is examined using sequential analysis. The focus is on examining the sequential probability ratio test and to minimize the number of items in a test, i.e. to minimize the average sample number function, abbreviated as the ASN function. Conditions under which the ASN function decreases are examined. Further, it is shown that the optimal values are the same for item discrimination and item guessing, but differ for item difficulty compared with tests with fixed number of items.

Paper III presents three simulation studies of sequential computerized mastery tests. Three cases are considered, viz. the examinees' responses are either identically distributed, not identically distributed, or not identically distributed together with estimation errors in the item characteristics. The simulations indicate that the observed results from the operating characteristic function differ significantly from the theoretical results. The mean number of items in a test, the distribution of test length and the variance depend on whether the true values of the item characteristics are known and whether they are iid or not.

In paper IV computerized tests with both pretested items with known item parameters, and try-out items with unknown item parameters are considered. The aim is to study how the item parameters for try-out items can be estimated in a computerized test. Although the unknown examinees' abilities may act as nuisance parameters, the asymptotic variance of the item parameter estimators can be calculated. Examples show that a more reliable variance estimator yields much larger estimates of the variance than commonly used variance estimators.

• 19304.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Optimal Scores as an Alternative to Sum Scores2018Inngår i: Quantitative Psychology: The 82nd Annual Meetingof the Psychometric Society, Zurich,Switzerland, 2017 / [ed] Marie Wiberg, Steven Culpepper, Rianne Janssen, Jorge González, & Dylan Molenaar, Cham, Switzerland: Springer , 2018, s. 1-10Kapittel i bok, del av antologi (Fagfellevurdert)

This paper discusses the use of optimal scores as an alternative to sum scores and expected sum scores when analyzing test data. Optimal scores are built on nonparametric methods and use the interaction between the test takers´ responses on each item and the impact of the corresponding items on the estimate of their performance. Both theoretical arguments for optimal score as well as arguments built upon simulation results are given. The paper claims that in order to achieve the same accuracy in terms of mean squared error and root mean squared error, an optimally scored test needs substantially fewer items than a sum scored test. The top-performing test takers and the bottom 5% test takers are by far the groups that benefit most from using optimal scores.

• 19305.
Umeå universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
Umeå universitet, Samhällsvetenskapliga fakulteten, Institutionen för tillämpad utbildningsvetenskap.
School-effectiveness in mathematics in Sweden compared with countries in Europe and Asia-Pacific2010Konferansepaper (Fagfellevurdert)

There is an increased focus on educational quality and learning outcomes in Sweden, especially since international comparative studies like TIMSS has put the limelight on declining study results in core subject like mathematics. School-effectiveness is therefore an urgent issue. The aim of this study is to identify factors that contribute to the explanation why some schools is effective but others are less effective in terms of the students’ academic achievement in mathematics on TIMSS. This is conducted by examining Sweden in contrast with school-effectiveness in some high achieving countries in Europe and Asia-Pacific. The framework of multilevel analysis was used, since it is important to separate the effect of school-level variables from the effect of home environment and to take care of the sampling design used in TIMSS 2007. The results show that different educational system identifies different school level factors when controlling for home background. Noteworthy is that very few school level factors were significant in the full models. The single most important factor for school- effectiveness appears to be student behavior in school. Offering enrichment or remedial in mathematic seem to have different effects in different countries. Professional development opportunities for the teachers and the use of different incentives do not seem to have any effect in any of the countries, except in Chinese-Taipei. Disappointingly, we were unable to detect any significant school level factors in Sweden. A possible reason for this is that we excluded variables that have been altered in any of the countries, since we do believe that such changes might be a threat to the validity. Hence, it is possible that important questions in the Swedish context were excluded.

• 19306.
Umeå universitet, Samhällsvetenskaplig fakultet, Statistik.
Umeå universitet, Samhällsvetenskaplig fakultet, Beteendevetenskapliga mätningar.
Implications of range restriction: a comparison of two approaches for correcting correlation in range restriction.2009Inngår i: Practical Assessment, Research & Evaluation, ISSN 1531-7714, E-ISSN 1531-7714, Vol. 14, nr 5, s. 1-9-Artikkel i tidsskrift (Fagfellevurdert)

A common problem in predictive validity studies in the educational and psychological fields, e.g. in educational and employment selection, is restriction in range of the predictor variables. There are several methods for correcting correlations for restriction of range. The aim of this paper was to examine the usefulness of two approaches to correcting for range restriction; Thorndike’s case 2 correction and ML estimates obtained from the EM algorithm, by comparing the corrected correlations with the correlation from an unrestricted sample. The unrestricted sample consisted of examinees who took the practical Swedish driving-license test regardless of their result on the theory test. Examinees that passed the theory test and took the practical test were regarded as a restricted sample. The result provided empirical support for the appropriateness of Thorndike’s case 2 correction method. Although using the EM algorithm yielded a good estimate of the correlation in the unrestricted sample, further studies are needed on this topic.

• 19307.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Local Observed-Score Kernel Equating2014Inngår i: Journal of educational measurement, ISSN 0022-0655, E-ISSN 1745-3984, Vol. 51, nr 1, s. 57-74Artikkel i tidsskrift (Fagfellevurdert)

Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as biasas defined by Lord's criterion of equityand percent relative error. The local kernel item response theory observed-score equating method, which can be used for any of the common equating designs, had a small amount of bias, a low percent relative error, and a relatively low kernel standard error of equating, even when the accuracy of the test was reduced. The local kernel equating methods for the nonequivalent groups with anchor test generally had low bias and were quite stable against changes in the accuracy or length of the anchor test. Although all proposed methods showed small percent relative errors, the local kernel equating methods for the nonequivalent groups with anchor test design had somewhat larger standard error of equating than their kernel method counterparts.

• 19308.
Umeå universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
Local linear observed-score equating2011Inngår i: Journal of educational measurement, ISSN 0022-0655, E-ISSN 1745-3984, Vol. 48, nr 3, s. 229-254Artikkel i tidsskrift (Fagfellevurdert)

Two methods of local linear observed-score equating for use with anchor-test and single-group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed-score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord’s (1980) definition of equity was used. The local method for the anchor-test design yielded minimum bias, even for considerable variation of the relative difficulties of the two test forms and the length of the anchor test. Among the traditional methods, the method of chain equating performed best. The local method for singlegroup designs yielded equated scores with bias comparable to the traditional methods. This method, however, appears to be of theoretical interest because it forces us to rethink the relationship between score equating and regression.

• 19309.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Ensuring Test Fairness Through Monitoring the Anchor Test and Covariates2016Konferansepaper (Fagfellevurdert)
• 19310.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Educational Testing Service.
Fairness in large testing programs over time through monitoring the anchor test and the covariates2015Konferansepaper (Fagfellevurdert)
• 19311.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Examining the Impact of Covariates on Anchor Tests to Ascertain Quality Over Time in a College Admissions Test2017Inngår i: International Journal of Testing, ISSN 1530-5058, E-ISSN 1532-7574, Vol. 17, nr 2, s. 105-126Artikkel i tidsskrift (Fagfellevurdert)

We propose a comprehensive procedure for the implementation of a quality control process of anchor tests for a college admissions test with multiple consecutive administrations. We propose to examine the anchor tests and their items in connection with covariates to investigate if there was any unusual behavior in the anchor test results over time and if the test results differed for different groups of test takers. Descriptive statistics, ANOVA, and linear mixed effect models were used to examine the impact of covariates on the anchor test over time. Descriptive statistics and logistic regression were used to examine the quality of each anchor item over time. It is concluded that examining the impact of the test takers' covariates at different administrations can help in the process of providing fair tests for all test takers. The results are discussed with recommendations how it can be used in other large testing programs.

• 19312.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
Terrain machine learning: A predictive method for estimating terrain model parameters using simulated sensors, vehicle and terrain2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave

Predicting terrain trafficability of deformable terrain is a difficult task with applications in e.g, forestry, agriculture, exploratory missions. The currently used techniques are neither practical, efficient, nor sufficiently accurate and inadequate for certain soil types. An online method which predicts terrain trafficability is of interest for any vehicle with purpose to reduce ground damage, improve steering and increase mobility. This thesis presents a novel approach for predicting the model parameters used in modelling a virtual terrain. The model parameters include particle stiffness, tangential friction, rolling resistance and two parameters related to particle plasticity and adhesion. Using multi-body dynamics, both vehicle and terrain can be simulated, which allows for an efficient exploration of a great variety of terrains. A vehicle with access to certain sensors can frequently gather sensor data providing information regarding vehicle-terrain interaction. The proposed method develops a statistical model which uses the sensor data in predicting the terrain model parameters. However, these parameters are specified at model particle level and do not directly explain bulk properties measurable on a real terrain. Simulations were carried out of a single tracked bogie constrained to move in one direction when traversing flat, homogeneous terrains. The statistical model with best prediction accuracy was ridge regression using polynomial features and interaction terms of second degree. The model proved capable of predicting particle stiffness, tangential friction and particle plasticity, with moderate accuracy. However, it was deduced that the current predictors and training scenarios were insufficient in estimating particle adhesion and rolling resistance. Nevertheless, this thesis indicates that it should be possible to develop a method which successfully predicts terrain model properties.

• 19313.
Högskolan i Jönköping, Högskolan för lärande och kommunikation.
Från situation till ekvation: En studie om hur gymnasieelever översätter textuppgifter till andragradsekvationer2013Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave

Eftersom tidigare undersökningar om översättningsfasen i den algebraiska cykeln handlat om översättning till uttryck eller förstagradsekvationer, är denna studies syfte att försöka klargöra och beskriva vilka olika uppfattningar som finns när elever på gymnasiet, som läser kursen matematik 2b, översätter textuppgifter till andragradsekvationer. Frågeställningarna handlar om hur elever översätter textproblem till andragradsekvationer samt vilka olika typer av svårigheter som finns i översättningsmomentet.

Studien har utförts med en metod inspirerad av fenomenografi, där ett individuellt skriftligt frågeformulär besvarades av 43 elever i två olika klasser. Resultatet visar, i stora drag, att vanliga svårigheter är att förstå den matematiska innebörden i texten samt att kunna representera de olika delarna med ett korrekt matematiskt symbolspråk. Svårigheter finns också att se problemets alla delar samt att relatera delarna rätt i det stora övergripande sammanhanget. Många elever har tecknat förstagradsekvationer i stället för andragradsekvationer.

Förhoppningen är att lärare, genom att ta del av de i studien framtagna kategorierna, kan få större insikt i och förståelse för de olika tankesätt som finns hos eleverna.

• 19314.
Högskolan i Halmstad, Sektionen för lärarutbildning (LUT).
Lust och motivation i matematikämnet: En kvalitativ intervjustudie om hur fem lärare i matematik för årskurs 1-2 uppfattar att lärare kan undervisa i matematik för att skapa lust och motivation för eleverna.2013Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave

Syftet med studien är att genom kvalitativa intervjustudier undersöka vad lärare uppfattar kan vara orsaken till att en del elever tappar lust och motivation till matematiken, om lärarens egen inställning påverkar eleverna, samt hur lärare uppfattar att lärare kan undervisa för att främja elevers lust och motivation till matematikämnet. Denna studie utgår från forskningsmetoden fenomenografi som går ut på att finna olika uppfattningar hos ett fenomen.

Genom resultatet av denna studie framkommer det att det handlar om att skapa ett varierande lärande för eleverna och att eleverna får konkreta mål att arbeta mot. Lärarna i studien är alla överens om att den inställning läraren har till matematikämnet med stor möjlighet kommer att spegla av sig på eleverna och menar att det är viktigt att läraren går in med attityden att matematik är roligt och viktigt.

De slutsatser som kan dras av detta resultat är att det är viktigt att läraren kontinuerligt granskar sin egen syn på ämnet och att läraren individanpassar undervisningen så att alla elever får möjlighet att känna lust och motivation för matematiken.

• 19315.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
Adaptive Dynamics for Spatially Structured Populations2013Independent thesis Advanced level (degree of Master (Two Years)), 40 poäng / 60 hpOppgave

The impact of spatial structure on evolutionary processes is examined by using partial differential equation models coupled with adaptive dynamics analysis. A brief introduction to adaptive dynamics is provided, where the central concepts of the framework are explained. The formalism of spatial adaptive dynamics is detailed, and perturbation methods for improving numerical calculations are introduced. Two example models are investigated, and the applicability of the framework is discussed.

• 19316.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
Jump-Diffusion Models and Implied Volatility2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
• 19317.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
Deep learning-based forecasting of financial assets2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave

Deep learning and neural networks has recently become a powerful tool to solve complex problem due to improvements in training algorithms. Examples of successful application can be found in speech recognition and machine translation. There exist relative few finance articles were deep learning have been applied, but existing articles indicate that deep learning can be successfully applied to problems in finance.

This thesis studies forecasting of financial price movements using two types of neural networks, namely; feedforward and recurrent networks. For the feedforward neural networks we considered non-deep networks with more neurons and deep networks with fewer neurons. In addition to the comparison between feedforward and recurrent networks, a comparison between deep and non-deep networks will be made. The recurrent architecture consists of a recurrent layer mapping into a feedforward layer followed by an output layer. The networks are trained with two different feature setups, one less complex and one more complex.

The findings for non-deep vs. deep feedforward neural networks imply that there does not exist any general pattern whether deep or non-deep networks are preferable. The findings for recurrent neural networks vs. feedforward neural networks imply that recurrent neural networks do not necessarily outperform feedforward neural networks even though financial data in general are time-dependent. In some cases, adding batch normalization can improve the accuracy for the feedforward neural networks. This can be preferable instead of using more complex models, such as a recurrent neural networks. Moreover, there are significant differences in accuracies between using the two different feature setups. The highest accuracy for all networks are 52.82%, which is significantly better than the simple benchmark.

• 19318.
Att arbeta med laborativ matematik2003Independent thesis Basic level (professional degree)Oppgave

Arbetet är en studie kring hur elevers attityder, lust och motivation samt resultat påverkas och förändras då man förändrar arbetssättet i matematikundervisningen. Undersökningen utfördes i samband med en praktikperiod i slutet av min lärarutbildning. Klassen i vilken jag utförde studien bestod av 28 elever år 7. Med hjälp av min handledare delades klassen i två likvärdiga grupper vardera med 14 elever. Handledaren undervisade ena halvan på ett traditionellt sätt och jag som hade andra halvan arbetade med laborativa uppgifter som eleverna fick lösa i smågrupper. Handledarens grupp, som fick vara referensgrupp, fortsatte att arbeta som de var vana d.v.s. med korta genomgångar på tavlan följt av individuellt räknande. För den grupp som jag ansvarade för förändrades undervisnings radikalt mot mer betoning på själva processen.

Två enkäter en före försöket och en i slutfasen samt en provräkning fick bilda underlag för utvärdering av försöket och analys av mina problemformuleringar.

Skillnaderna i resultat av denna undersökning blev mindre än jag hade förväntat mig och de slutsatser jag kunde dra var att traditionens makt är stor. Dessutom var den tid som stod till förfogande inte tillräcklig för att få eleverna att förändra sitt förhållningssätt till matematik och matematikundervisning. Dock kunde jag sammantaget märka en positiv inställning hos eleverna i försöksgruppen, till ett mera varierat problemorienterat arbetssätt.

Arbetet gav många nya erfarenheter som utgör en ny plattform att arbeta utifrån när jag startar upp som nyutbildad lärare med ansvar för matematikundervisningen i eget klassrum.

• 19319.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
Solvency Capital Requirement (SCR) for Market Risks: A quantitative assessment of the Standard formula and its adequacy for a Swedish insurance company2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave

The purpose of this project is to validate the adequacy of the Standard formula, used to calculate the Solvency Capital Requirement (SCR), with respect to a Swedish insurance company. The sub-modules evaluated are Equity risk (type 1) and Interest rate risk. The validation uses a quantitative assessment and the concept of Value at Risk (VaR). Additionally, investment strategies for risk free assets are evaluated through a scenario based analysis.

The findings support that the Equity shock of 39%, as proposed in the Standard formula, is appropriate for a diversified portfolio of global equities. Furthermore, to some extent; the Equity shock is also sufficient for a diversified global portfolio with an overweight of Swedish equities. Additionally, the findings shows that the Standard formula for Interest rate risks occasionally underestimates the true Interest rate risk. Furthermore, it’s shown that there are some advantage of selecting an investment strategy that stabilizes the Own fund of an insurance company rather than a strategy that minimizes the SCR.

• 19320.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
Valuation Practices of IFRS 172018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave

This research assesses the IFRS 17 Insurance Contracts standard from a mathematical and actuarial point of view. Specifically, a valuation model that complies with the standard is developed in order to investigate implications of the standard on financial statements of insurance companies. This includes a deep insight into the standard, construction a valuation model of a fictive traditional life insurance product and an investigation of the outcomes of the model.

The findings show firstly that an investment strategy favorable for valuing insurance contracts according to the standard may conflict with the Asset & Liability Management of the firm. Secondly, that a low risk adjustment increases the contractual service margin (CSM) and hence the possibility of smoothing profits over time. Thirdly, that the policy for releasing the CSM should take both risk-neutral and real assumptions into account.

• 19321.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
A note on unconditionally stable linear multistep methods1967Inngår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 7, s. 65-70Artikkel i tidsskrift (Fagfellevurdert)
• 19322.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
On difference methods for parabolic equations and alternating direction implicit methods for elliptic equations1967Inngår i: IBM Journal of Research and Development, ISSN 0018-8646, E-ISSN 2151-8556, Vol. 11, s. 239-243Artikkel i tidsskrift (Fagfellevurdert)
• 19323.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Från det imaginära till normala familjer: Analytiska konvergenser2010Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave

I komplex analys finns det ett antal olika konvergenser varav vi tittar närmare på några här. Bland annat hur likformig konvergens medför punktvis konvergens men att det omvända ej gäller. Vi tittar också på vad de har för samband med lokal likformig konvergens och normal konvergens dvs. likformig konvergens på kompakta delmängder. Slutligen kommer vi att se på vad som gäller för familjer och kommer då in på lokalt begränsad, ekvikontinuitet, Arzela/Ascoli, Montels och Runges satser. Vi kommer här även se exempel på hur stort fel det egentligen kan bli för punktvisa konvergenta följder. De får normalt inte en gränsfunktion som är analytisk men vi ser både i Exempel 3.19 och Korollarium 3.23 att dessa ger resultat som är analytiska nästan överallt.

• 19324.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Regression då data utgörs av urval av ranger2012Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave

För alpina skidåkare mäter man prestationer i så kallad FIS-ranking. Vi undersöker några metoder för hur man kan analysera data där responsen består av ranger som dessa. Vid situationer då responsdata utgörs av urval av ranger finns ingen självklar analysmetod. Det vi undersöker är skillnaderna vid användandet av olika regressionsanpassningar så som linjär, logistisk och ordinal logistisk regression för att analysera data av denna typ. Vidare används bootstrap för att bilda konfidensintervall. Det visar sig att för våra datamaterial ger metoderna liknande resultat när det gäller att hitta betydelsefulla förklarande variabler. Man kan därmed utgående från denna undersökning, inte se några skäl till varför man ska använda de mer avancerade modellerna.

• 19325.
Karlstads universitet, Institutionen för ingenjörsvetenskap, fysik och matematik.
Förståelse i undervisningssituationen: En grupp gymnasieelevers inställning till inlärningssituationen i matematik2006Independent thesis Basic level (professional degree), 5 poäng / 7,5 hpOppgave

Mitt syfte med det här arbetet var att undersöka en grupp gymnasieelevers tankar kring sin inlärningssituation i matematik och se under vilka förutsättningar de själva tror att de lär sig bäst. Studien genomfördes med hjälp av 175 enkäter som delades ut på en gymnasieskola i Västergötland. De svarande tillhörde olika program och olika årskurser, och enkäten hade dels frågor med fasta svarsalternativ och dels några ganska öppna frågor. Resultatet kan sammanfattas med bland annat:

- att de flesta elever tror att det är viktigt att öva många gånger på samma sorts uppgifter i matematik; framför allt flickornas svar betonar detta.

- att det finns en svag positiv korrelation mellan använd tid till läxläsning i matematik och betyg i matematik även om kausaliteten är oklar.

- att det finns en stark önskan hos många elever om förståelse av matematikstoffet.

• 19326.
Örebro universitet, Handelshögskolan vid Örebro universitet.
Ungdomsarbetslöshet: En deskriptiv undersökning av olika länder samt en multipelregressionsanalys2011Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
• 19327. Wiedermann, Marc
Stockholms universitet, Naturvetenskapliga fakulteten, Stockholm Resilience Centre.
Macroscopic description of complex adaptive networks coevolving with dynamic node states2015Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 91, nr 5, artikkel-id 052801Artikkel i tidsskrift (Fagfellevurdert)

In many real-world complex systems, the time evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here we study opinion formation and imitation on an adaptive complex network which is dependent on the individual dynamic state of each node and vice versa to model the coevolution of renewable resources with the dynamics of harvesting agents on a social network. The adaptive voter model is coupled to a set of identical logistic growth models and we mainly find that, in such systems, the rate of interactions between nodes as well as the adaptive rewiring probability are crucial parameters for controlling the sustainability of the system's equilibrium state. We derive a macroscopic description of the system in terms of ordinary differential equations which provides a general framework to model and quantify the influence of single node dynamics on the macroscopic state of the network. The thus obtained framework is applicable to many fields of study, such as epidemic spreading, opinion formation, or socioecological modeling.

• 19328. Wiedermann, Marc
Stockholms universitet, Naturvetenskapliga fakulteten, Stockholm Resilience Centre. Potsdam Institute for Climate Impact Research, Germany.
Mapping and discrimination of networks in the complexity-entropy plane2017Inngår i: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, nr 4, artikkel-id 042304Artikkel i tidsskrift (Fagfellevurdert)

Complex networks are usually characterized in terms of their topological, spatial, or information-theoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network's complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis. Here we explore the possibility to classify complex networks by means of a statistical complexity measure that has formerly been successfully applied to distinguish different types of chaotic and stochastic time series. It is composed of a network's averaged per-node entropic measure characterizing the network's information content and the associated Jenson-Shannon divergence as a measure of disequilibrium. We study 29 real-world networks and show that networks of the same category tend to cluster in distinct areas of the resulting complexity-entropy plane. We demonstrate that within our framework, connectome networks exhibit among the highest complexity while, e.g., transportation and infrastructure networks display significantly lower values. Furthermore, we demonstrate the utility of our framework by applying it to families of random scale-free and Watts-Strogatz model networks. We then show in a second application that the proposed framework is useful to objectively construct threshold-based networks, such as functional climate networks or recurrence networks, by choosing the threshold such that the statistical network complexity is maximized.

• 19329. Wiedermann, Marc
Stockholms universitet, Naturvetenskapliga fakulteten, Stockholm Resilience Centre. Potsdam Institute for Climate Impact Research, Germany.
Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes2016Inngår i: Physical Review E, ISSN 2470-0045, Vol. 93, nr 4, artikkel-id 042308Artikkel i tidsskrift (Fagfellevurdert)

Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve certain global and local statistics associated with the nodes' embedding in a metric space. Comparing the original network's and the resulting surrogates' global characteristics allows one to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes' spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling the underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology.

• 19330.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
On the Smoothness of the Quot Functor2013Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave

For a commutative ring k,we consider free k-modules E, endowing them with k[x_1,...,x_m]-module structuresthrough a ring homomorphism k[x_1,...,x_m] -> End_Z(E). These structures arethen inspected by encoding the actions of the unknowns x_i in matricesX_1,...,X_m. We further introduce the concepts of lifts and formal smoothnessfor functors, and define the Quot_{F/A/k}^n functor acting on the category ofk-algebras, taking some k-algebra B to the set of quotients of the form (F ⊗_k B)/N, which are locallyfree as B-modules. Lastly, we find concrete examples of modules showing thatthe functors Hilb_{k[x,y,z]/k}^4 and Quot_{⊕^2 k[x,y]/k[x,y]/k}^2 are not formally smooth

• 19331.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
A bivariate survival model with compound Poisson frailty2010Inngår i: Statistics in Medicine, ISSN 0277-6715, E-ISSN 1097-0258, Vol. 29, nr 2, s. 275-283Artikkel i tidsskrift (Fagfellevurdert)

A correlated frailty model is suggested for analysis of bivariate time-to-event data. The model is an extension of the correlated power variance function (PVF) frailty model (correlated three-parameter frailty model) (J. Epidemiol. Biostat. 1999; 4:53-60). It is based on a bivariate extension of the compound Poisson frailty model in univariate survival analysis (Ann. Appl. Probab. 1992; 4:951-972). It allows for a non-susceptible fraction (of zero frailty) in the population, overcoming the common assumption in survival analysis that all individuals are susceptible to the event under study. The model contains the correlated gamma frailty model and the correlated inverse Gaussian frailty model as special cases. A maximum likelihood estimation procedure for the parameters is presented and its properties are studied in a small simulation study. This model is applied to breast cancer incidence data of Swedish twins. The proportion of women susceptible to breast cancer is estimated to be 15 per cent.

• 19332.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Algebraic Hopf InvariantsManuskript (preprint) (Annet vitenskapelig)
• 19333.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Hopf invariants and differential formsManuskript (preprint) (Annet vitenskapelig)
• 19334.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
Hopf Invariants in Real and Rational Homotopy Theory2017Doktoravhandling, med artikler (Annet vitenskapelig)

In this thesis we use the theory of algebraic operads to define a complete invariant of real and rational homotopy classes of maps of topological spaces and manifolds. More precisely let f,g : M -> N be two smooth maps between manifolds M and N. To construct the invariant, we define a homotopy Lie structure on the space of linear maps between the homology of M and the homotopy groups of N, and a map mc from the set of based maps from M to N, to the set of Maurer-Cartan elements in the convolution algebra between the homology and homotopy. Then we show that the maps f and g are real (rational) homotopic if and only if mc(f) is gauge equivalent to mc(g), in this homotopy Lie convolution algebra. In the last part we show that in the real case, the map mc can be computed by integrating certain differential forms over certain subspaces of M. We also give a method to determine in certain cases, if the Maurer-Cartan elements mc(f) and mc(g) are gauge equivalent or not.

• 19335.
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
HOMOTOPY MORPHISMS BETWEEN CONVOLUTION HOMOTOPY LIE ALGEBRASManuskript (preprint) (Annet vitenskapelig)
• 19336.
Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
Stratification, Sampling and Estimation: Finding the best design for the Swedish Investment Survey2013Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave

In this thesis, different methods are used to investigate the best design for the Swedish Investment Survey. The methods used today are stratify on number of employees, Neyman-allocation, STSRS-sampling and HT-estimation. The alternative methods in this thesis are stratify on turnover, -sampling and GREG-estimation. These methods are combined into eight combinations and tested on the enterprises and their investments in the Swedish energy domains. The conclusion is that changing the design to stratify on turnover, -sampling and GREG-estimation will provide a smaller standard deviation in most of the energy domains.

• 19337.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Indikatorer för bedömning av effektiv elnätsdrift2016Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave

This Master thesis has been performed at the department Technical analysis at the Swedish Energy Markets Inspectorate (Ei). The thesis intends to explore possible indicators for assessing efficient power grid utilization.

Today there are two different types of efficiency incentives in the Swedish regulation of grid companies and these are a demand on streamlining current operating costs and an incentive scheme for an efficient grid utilization. To quantify to what extent the grid is utilized efficiently two indicators, a load factor and network losses, are used in an incentive scheme too incentivize an efficient grid utilization.  This thesis has been limited to examining other possible indicators for quantifying to what extent the grid is utilized efficiently and the analysis has been limited to an evaluation of indicators that treats load in the interconnection points between grid companies. The used load factor has also been further analysed and two possible changes to the load factor are suggested.

To analyse the indicators that treats load in the interconnection points between grid companies a simulation model has been created. A previously developed test network has stood as model for the customer mix and load patterns used in this developed model.  During this work, data from a medium-sized Swedish grid company has also been analysed. To do this, a syntax has been created which enables a further analysis of data from other companies if it is to be collected in the future. The created model treats three different scenarios and their impact on the analysed indicators. The scenarios are about demand response, an increased proportion of solar cells in the network as well as an increased amount of electric cars and their resulting load from home charging. The resulting model has been implemented in Matlab.

The results mainly show that a weighted average in relation to the amount of energy transmitted for the load factor can provide a greater signal as to what the indicator mainly aims to incentivize, i.e. to even out the load during times of high load.  At least this is what is the most important with today’s conditions for Swedish networks. The results also give an indication as to how the analysed indicators can change depending on the analysed scenarios, but an analysis on more networks is recommended since the results may differ for different networks. For the performed analysis the most important thing to consider is that an increase in solar power in a network may have a negative impact on the indicators, which should be taken into consideration when using the analysed indicators in a regulation for efficient utilization.

The recommendation I would like to give to Ei, based on the results, is to consider a weighted average for the load factor to further incentivize an even load at days with a higher load more than less congested days. If all days are to be considered as equally important to even out the load in the interconnection points, I would like to recommend to accounting for the distribution of the daily values that are used in calculating the load factor by using for example percentiles. Ei is also recommended to collect data from more Swedish grid companies to further investigate possible changes to the analysed indicators for the analysed scenarios. For future investigation I would also recommend an analysis of indicators that does not treat load in the interconnection points, if these are of interest in relation to the definition used for what can be considered an effective utilization of the power grid in Sweden.

• 19338.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
Fluctuations of the nodal length of random spherical harmonics2010Inngår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 298, nr 3, s. 787-831Artikkel i tidsskrift (Fagfellevurdert)

Using the multiplicities of the Laplace eigenspace on the sphere (the space of spherical harmonics) we endow the space with Gaussian probability measure. This induces a notion of random Gaussian spherical harmonics of degree n having Laplace eigenvalue E = n(n + 1). We study the length distribution of the nodal lines of random spherical harmonics. It is known that the expected length is of order n. It is natural to conjecture that the variance should be of order n, due to the natural scaling. Our principal result is that, due to an unexpected cancelation, the variance of the nodal length of random spherical harmonics is of order log n. This behaviour is consistent with the one predicted by Berry for nodal lines on chaotic billiards (Random Wave Model). In addition we find that a similar result is applicable for "generic" linear statistics of the nodal lines.

• 19339.
Karlstads universitet, Fakulteten för teknik- och naturvetenskap, Avdelningen för matematik.
The Cauchy-Schwarz inequality: Proofs and applications in various spaces2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave

We give some background information about the Cauchy-Schwarz inequality including its history. We then continue by providing a number of proofs for the inequality in its classical form using various proof techniques, including proofs without words. Next we build up the theory of inner product spaces from metric and normed spaces and show applications of the Cauchy-Schwarz inequality in each content, including the triangle inequality, Minkowski's inequality and Hölder's inequality. In the final part we present a few problems with solutions, some proved by the author and some by others.

• 19340.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för systemteknik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Reglerteknik.
MATLAB software for recursive identification and scaling using a structured nonlinear black-box model: Revision 12005Rapport (Annet vitenskapelig)
• 19341.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för systemteknik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Reglerteknik.
MATLAB software for recursive identification and scaling using a structured nonlinear black-box model: Revision 22005Rapport (Annet vitenskapelig)
• 19342.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för systemteknik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Reglerteknik.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för systemteknik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Reglerteknik.
MATLAB software for recursive identification and scaling using a structured nonlinear black-box model: Revision 32007Rapport (Annet vitenskapelig)
• 19343.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för systemteknik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Reglerteknik.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för systemteknik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Reglerteknik.
MATLAB software for recursive identification and scaling using a structured nonlinear black-box model: Revision 42008Rapport (Annet vitenskapelig)
• 19344.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för systemteknik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Reglerteknik.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för systemteknik. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Reglerteknik.
MATLAB software for recursive identification and scaling using a structured nonlinear black-box model: Revision 62010Rapport (Annet vitenskapelig)
• 19345.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
FE-modellering och simulering av tunna skal med tillämpning på korrugerade strukturer2008Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
• 19346.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
A geometric view on Pearson's correlation coefficient and a generalization of it to non-linear dependencies2016Inngår i: Ratio Mathematica, ISSN 1592-7415, Vol. 30, s. 3-21, artikkel-id 1Artikkel i tidsskrift (Fagfellevurdert)

Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson's correlation coefficient $\rho$ is an accurate measure of linear dependence. We show that $\rho$ is a normalized, Euclidean type distance between joint probability distribution of the two random variables and that when their independence is assumed while keeping their marginal distributions. And the normalizing constant is the geometric mean of two maximal  distances; each between the joint probability distribution when the full linear dependence is assumed while preserving respective marginal distribution and that when the independence is assumed. Usage of it  is  restricted to linear dependence because it is based on  Euclidean type distances that are generally not metrics and considered full dependence is linear. Therefore, we argue that if a suitable distance metric is used while considering all possible maximal dependences then it can measure any non-linear dependence.  But then, one must define all the full dependences.  Hellinger distance that is a metric can be used as the distance measure between probability distributions and obtain a generalization of $\rho$ for the discrete case.

• 19347.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Causal Effect Estimation Methods2014Inngår i: Journal of Statistical and Econometric Methods, ISSN 2241-0376, Vol. 3, nr 2, s. 153-170Artikkel i tidsskrift (Fagfellevurdert)

Relationship between two popular modeling frameworks of causalinference from observational data, namely, causal graphical model andpotential outcome causal model is discussed. How some popular causaleﬀect estimators found in applications of the potential outcome causalmodel, such as inverse probability of treatment weighted estimator anddoubly robust estimator can be obtained by using the causal graphicalmodel is shown. We conﬁne to the simple case of binary outcome andtreatment variables with discrete confounders and it is shown how togeneralize results to cases of continuous variables.

• 19348.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Data Deluge and Its Analysis Issues2016Inngår i: Proceedings of the 2nd International Conference in Accounting Researchers and Educators (ICARE 2016), Kelaniya, Sri Lanka: Priyantha Wijayatunga , 2016, s. 21-21, artikkel-id 21Konferansepaper (Fagfellevurdert)

Current availability of enormous amount of data is mainly due to technological advances. They are useful drawing inferences for creating new businesses, formulation of new policies or revising existing ones, etc. However, much of analyses are performed either by subject domain experts implementing mathematical and computational models incorrectly or by mathematical and computational professionals, purely on data driven basis without paying required attention to the subject domain knowledge. Both of these exercises often result in incorrect inferences and therefore they may harm the society, especially when their inferences are used in practice. We argue that, in order to get valid inferences these two parties should work together. Here we briefly discuss some of the issues that the large-scale data analyses should take into account, especially in open data and big data. We also briefly discuss our solutions that are rather simple to implement.

• 19349.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
Discussion on the paper by Caron and Fox2017Inngår i: Journal of The Royal Statistical Society Series B-statistical Methodology, ISSN 1369-7412, E-ISSN 1467-9868, Vol. 79, nr 5, s. 1359-1359Artikkel i tidsskrift (Annet vitenskapelig)

A measure of dependence for graph models

• 19350.
Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
On Associative Confounder Bias2015Inngår i: Thirteenth Scandinavian Conference on Artificial Intelligence / [ed] Sławomir Nowaczyk, 2015, Vol. 278, s. 157-166Konferansepaper (Fagfellevurdert)

Conditioning on some set of confounders that causally affect both treatmentand outcome variables can be sufficient for eliminating bias introduced by allsuch confounders when estimating causal effect of the treatment on the outcomefrom observational data. It is done by including them in propensity score modelin so-called potential outcome framework for causal inference whereas in causalgraphical modeling framework usual conditioning on them is done. However inthe former framework, it is confusing when modeler finds a variable that is noncausallyassociated with both the treatment and the outcome. Some argue that suchvariables should also be included in the analysis for removing bias. But others arguethat they introduce no bias so they should be excluded and conditioning onthem introduces spurious dependence between the treatment and the outcome, thusresulting extra bias in the estimation. We show that there may be errors in boththe arguments in different contexts. When such a variable is found neither of theactions may give the correct causal effect estimate. Selecting one action over theother is needed in order to be less wrong.We discuss how to select the better action.

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