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  • 1.
    Abrahamsson, Fredrik
    Jönköping University, School of Engineering, JTH, Mathematics.
    Strong L1 convergence to equilibrium without entropy conditions for the Boltzmann equation1999In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 24, no 7-8, p. 1501-1535Article in journal (Refereed)
    Abstract [en]

    The main result of this paper is that for the har dsphere kernel, the solution of the spatially homogenous Boltzmann equation converges strongly in L1 to equilibrium given that the initial data f0 belongs to L1(R3,(1+v^2)dv). This was previously known to be true with the additional assumption that f0logf0 belonged to L1(R3), which corresponds to bounded initial entropy.

  • 2.
    Abramsson, Matilda
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Elevers förståelse av likhetstecknet: En studie i årskurs 32016Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The aim of the study is to explore the understanding of the equal sign and how the teaching about the equal sign among third grade students can be varied to be as effective as possible.  The aim will be answered trough the questions: what patterns of variation can the studied students meet and what critical aspects have the students identified. Patterns of variation means that what is critical in the teaching should be varied to become visible. Critical aspects is what students need to identify to understand what should be learned. The foundation of the study is the Variation Theory, where patterns of variation and critical aspects are central concepts.

    The observations were accomplished during a third grade lesson and six students were selected for interviews about the equal sign. The result of the study shows that the students met six critical aspects during the lesson. For every critical aspect there were one or several patterns of variation that was exposed to the students. The result also states that the students who were interviewed have a relational and instrumental understanding of the equal sign. The students also have understanding of a critical aspect that they did not meet in the observed lesson, namely that all numbers have to enter in a task. Four out of six students have understanding of the critical aspect that there should be equivalence in a chain of similarities. The result also show that the students understanding of the equal sign is not dependent of that they meet patterns of variation in the teaching, but that they meet the critical aspects somehow.

  • 3.
    Akram, Muhammad Nauman
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Amin, Muhammad
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    A new Liu-type estimator for the Inverse Gaussian Regression Model2020In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, p. 1-20Article in journal (Refereed)
    Abstract [en]

    The Inverse Gaussian Regression Model (IGRM) is used when the response variable is positively skewed and follows the inverse Gaussian distribution. In this article, we propose a Liu-type estimator to combat multicollinearity in the IGRM. The variance of the Maximum Likelihood Estimator (MLE) is overstated due to the presence of severe multicollinearity. Moreover, some estimation methods are suggested to estimate the optimal value of the shrinkage parameter. The performance of the proposed estimator is compared with the MLE and some other existing estimators in the sense of mean squared error through Monte Carlo simulation and different real-life applications. Under certain conditions, it is concluded that the proposed estimator is superior to the MLE, ridge, and Liu estimator.

  • 4.
    Ali, A. A.
    et al.
    Linnaeus University, Växjö, Sweden.
    Månsson, Kristofer
    Jönköping University, Jönköping International Business School, JIBS, Statistics. Jönköping University, Jönköping International Business School, JIBS, Economics.
    Shukur, G.
    Linnaeus University, Växjö, Sweden.
    A wavelet-based variance ratio unit root test for a system of equations2019In: Studies in Nonlinear Dynamics and Econometrics, ISSN 1081-1826, E-ISSN 1558-3708, article id 20180005Article in journal (Refereed)
    Abstract [en]

    In this paper, we suggest a unit root test for a system of equations using a spectral variance decomposition method based on the Maximal Overlap Discrete Wavelet Transform. We obtain the limiting distribution of the test statistic and study its small sample properties using Monte Carlo simulations. We find that, for multiple time series of small lengths, the wavelet-based method is robust to size distortions in the presence of cross-sectional dependence. The wavelet-based test is also more powerful than the Cross-sectionally Augmented Im et al. unit root test (Pesaran, M. H. 2007. "A Simple Panel Unit Root Test in the Presence of Cross-section Dependence." Journal of Applied Econometrics 22 (2): 265-312.) for time series with between 20 and 100 observations, using systems of 5 and 10 equations. We demonstrate the usefulness of the test through an application on evaluating the Purchasing Power Parity theory for the Group of 7 countries and find support for the theory, whereas the test by Pesaran (Pesaran, M. H. 2007. "A Simple Panel Unit Root Test in the Presence of Cross-section Dependence." Journal of Applied Econometrics 22 (2): 265-312.) finds no such support. 

  • 5.
    Alka,
    et al.
    Department of Mathematics and Statistics, Banasthali University, Jaipur, Rajasthan, India.
    Rai, Piyush Kant
    Department of Statistics, Banaras Hindu University, Varanasi, Uttar Pradesh, India.
    Qasim, Muhammad
    Department of Statistics & Computer Science, University of Veterinary & Animal Sciences, Lahore, Pakistan.
    Two-step calibration of design weights under two auxiliary variables in sample survey2019In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 89, no 12, p. 2316-2327Article in journal (Refereed)
    Abstract [en]

    Calibration on the available auxiliary variables is widely used to increase the precision of the estimates of parameters. Singh and Sedory [Two-step calibration of design weights in survey sampling. Commun Stat Theory Methods. 2016;45(12):3510–3523.] considered the problem of calibration of design weights under two-step for single auxiliary variable. For a given sample, design weights and calibrated weights are set proportional to each other, in the first step. While, in the second step, the value of proportionality constant is determined on the basis of objectives of individual investigator/user for, for example, to get minimum mean squared error or reduction of bias. In this paper, we have suggested to use two auxiliary variables for two-step calibration of the design weights and compared the results with single auxiliary variable for different sample sizes based on simulated and real-life data set. The simulated and real-life application results show that two-auxiliary variables based two-step calibration estimator outperforms the estimator under single auxiliary variable in terms of minimum mean squared error. 

  • 6.
    Almasri, Abdullah
    et al.
    Department of Economics and Statistics, Karlstad University, Karlstad, Sweden.
    Månsson, Kristofer
    Jönköping University, Jönköping International Business School, JIBS, Statistics. Department of Economics and Statistics, Göteborg University, Göteborg, Sweden.
    Sjölander, Pär
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Statistics. Department of Economics and Statistics, Linnaeus University, Växjö, Sweden.
    A wavelet-based panel unit-root test in the presence of an unknown structural break and cross-sectional dependency, with an application of purchasing power parity theory in developing countries2017In: Applied Economics, ISSN 0003-6846, E-ISSN 1466-4283, Vol. 49, no 21, p. 2096-2105Article in journal (Refereed)
    Abstract [en]

    This article introduces two different non-parametric wavelet-based panel unit-root tests in the presence of unknown structural breaks and cross-sectional dependencies in the data. These tests are compared with a previously suggested non-parametric wavelet test, the parameteric Im-Pesaran and Shin (IPS) test and a Wald type of test. The results from the Monte Carlo simulations clearly show that the new wavelet-ratio tests are superior to the traditional tests both in terms of size and power in panel unit-root tests because of its robustness to cross-section dependency and structural breaks. Based on an empirical Central American panel application, we can, in contrast to previous research (where bias due to structural breaks is simply disregarded), find strong, clear-cut support for purchasing power parity (PPP) in this developing region.

  • 7.
    Almén, Oscar
    et al.
    Jönköping University, School of Education and Communication.
    Thörnow, Johan
    Jönköping University, School of Education and Communication.
    Interaktiva skrivtavlor: Erfarenheter från matematiklärare i Jönköping med omnejd.2010Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Studien har  undersökt matematiklärare på gymnasiet och deras erfarenheter från att använda interaktiva skrivtavlor (Smartboard, Activboard & Teamboard). Åtta lärare har blivit intervjuade i en kvalitativ undersökning med fenomenografiskt fokus.

    Det blir idag allt mer populärt med interaktiva skrivtavlor i svenska skolor. Många skolor har valt att satsa mycket pengar på att installera interaktiva skrivtavlor, trots att det råder delade meningar om huruvida det finns något samband mellan tavlorna och förhöjda elevprestationer. Skolan har under många år haft en hög förväntan på IT. Trots att flera av de undersökta lärarna i studien är positiva så finns det också många negativa erfarenheter att ta lärdom av. Inte minst ifrågasätts hur man infört tekniken på de olika skolorna och vilka intressen som ligger bakom. I studien kan du läsa om goda användningsexempel i matematikundervisningen. Du kan också ta del av de begränsningar som lärare upplever att tavlan har då den används i matematiken. Lärare diskuterar bland annat följande teman; förberedelse, spara och publicera, motivation och skriv- och rithjälp.

  • 8.
    Amin, Muhammad
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Amanullah, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Aslam, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Qasim, Muhammad
    Department of Statistics and Computer Science, University of Veterinary and Animal Sciences, Lahore, Pakistan.
    Influence diagnostics in gamma ridge regression model2019In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 89, no 3, p. 536-556Article in journal (Refereed)
    Abstract [en]

    In this article, we proposed some influence diagnostics for the gamma regression model (GRM) and the gamma ridge regression model (GRRM). We assess the impact of influential observations on the GRM and GRRM estimates by extending the work of Pregibon [Logistic regression diagnostics. Ann Stat. 1981;9:705–724] and Walker and Birch [Influence measures in ridge regression. Technometrics. 1988;30:221–227]. Comparison of both models is made and demonstrated with the help of a simulation study and a real data set. We report some momentous results in detecting the influential observations and their effects on the GRM and GRRM estimates. 

  • 9.
    Amin, Muhammad
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Statistics. Department of Statistics and Computer Science, University of Veterinary and Animal Sciences, Lahore, Pakistan.
    Amanullah, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Performance of Asar and Genç and Huang and Yang’s Two-Parameter Estimation Methods for the Gamma Regression Model2019In: Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, Vol. 43, no 6, p. 2951-2963Article in journal (Refereed)
    Abstract [en]

    This study assesses the performance of two-parameter estimation methods to combat multicollinearity in the Gamma regression model. We derived optimal values for two-parameter estimation methods in the Gamma regression model. Furthermore, we proposed some estimation methods to estimate the shrinkage parameters and these methods improve the efficiency of the two-parameter estimator. We compare the performance of these estimators by means of Monte Carlo simulation study where the mean squared error (MSE) is considered as a performance criterion. Finally, consider a reaction rate data to evaluate the performance of the estimators. The simulation and numerical example results showed that the two-parameter biased estimators have smaller MSE than the maximum likelihood estimator under certain conditions.

  • 10.
    Amin, Muhammad
    et al.
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Qasim, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Amanullah, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Afzal, Saima
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Performance of some ridge estimators for the gamma regression model2017In: Statistical papers, ISSN 0932-5026, E-ISSN 1613-9798Article in journal (Refereed)
    Abstract [en]

    In this study, we proposed some ridge estimators by considering the work of Månsson (Econ Model 29(2):178–184, 2012), Dorugade (J Assoc Arab Univ Basic Appl Sci 15:94–99, 2014) and some others for the gamma regression model (GRM). The GRM is a special form of the generalized linear model (GLM), where the response variable is positively skewed and well fitted to the gamma distribution. The commonly used method for estimation of the GRM coefficients is the maximum likelihood (ML) estimation method. The ML estimation method perform better, if the explanatory variables are uncorrelated. There are the situations, where the explanatory variables are correlated, then the ML estimation method is incapable to estimate the GRM coefficients. In this situation, some biased estimation methods are proposed and the most popular one is the ridge estimation method. The ridge estimators for the GRM are proposed and compared on the basis of mean squared error (MSE). Moreover, the outperforms of proposed ridge estimators are also calculated. The comparison has done using a Monte Carlo simulation study and two real data sets. Results show that Kibria’s and Månsson and Shukur’s methods are preferred over the ML method. 

  • 11.
    Amin, Muhammad
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Yasin, Ahad
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Amanullah, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Almost unbiased ridge estimator in the gamma regression model2020In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, p. 1-21Article in journal (Refereed)
    Abstract [en]

    This article introduces the almost unbiased gamma ridge regression estimator (AUGRRE) estimator based on the gamma ridge regression estimator (GRRE). Furthermore, some shrinkage parameters are proposed for the AUGRRE. The performance of the AUGRRE by using different shrinkage parameters is compared with the existing GRRE and maximum likelihood estimator. A Monte Carlo simulation is carried out to assess the performance of the estimators where the bias and mean squared error performance criteria are used. We also used a real-life dataset to demonstrate the benefit of the proposed estimators. The simulation and real-life example results show the superiority of AUGRRE over the GRRE and the maximum likelihood estimator for the gamma regression model with collinear explanatory variables.

  • 12.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    A modified Schwarz-Christoffel mapping for regions with piecewise smooth boundaries2008In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 213, no 1, p. 56-70Article in journal (Refereed)
    Abstract [en]

    A method where polygon corners in Schwarz-Christoffel mappings are rounded, is used to construct mappings from the upper half-plane to regions bounded by arbitrary piecewise smooth curves. From a given curve, a polygon is constructed by taking tangents to the curve in a number of carefully chosen so called tangent points. The Schwarz-Christoffel mapping for that polygon is then constructed and modified to round the corners.Since such a modification causes effects on the polygon outside the rounded corners, the parameters in the mapping have to be re-determined. This is done by comparing side-lengths in tangent polygons to the given curve and the curve produced by the modified Schwarz-Christoffel mapping. The set of equations that this comparison gives, can normally be solved using a quasi--Newton method.The resulting function maps the upper half--plane on a region bounded by a curve that apart from possible vertices is smooth, i.e., one time continuously differentiable, that passes through the tangent points on the given curve, has the same direction as the given curve in these points and changes direction monotonically between them. Furthermore, where the original curve has a vertex, the constructed curve has a vertex with the same inner angle.The method is especially useful for unbounded regions with smooth boundary curves that pass infinity as straight lines, such as channels with parallel walls at the ends. These properties are kept in the region produced by the constructed mapping.

  • 13.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Modified Schwarz-Christoffel mappings using approximate curve factors2009In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 233, no 4, p. 1117-1127Article in journal (Refereed)
    Abstract [en]

    The Schwarz–Christoffel mapping from the upper half-plane to a polygonal region in the complex plane is an integral of a product with several factors, where each factor corresponds to a certain vertex in the polygon. Different modifications of the Schwarz–Christoffel mapping in which factors are replaced with the so-called curve factors to achieve polygons with rounded corners are known since long times. Among other requisites, the arguments of a curve factor and its correspondent scl factor must be equal outside some closed interval on the real axis.

    In this paper, the term approximate curve factor is defined such that many of the already known curve factors are included as special cases. Additionally, by alleviating the requisite on the argument from exact to asymptotic equality, new types of curve factors are introduced. While traditional curve factors have a C1 regularity, C regular approximate curve factors can be constructed, resulting in smooth boundary curves when used in conformal mappings.

    Applications include modelling of wave scattering in waveguides. When using approximate curve factors in modified Schwarz–Christoffel mappings, numerical conformal mappings can be constructed that preserve two important properties in the waveguides. First, the direction of the boundary curve can be well controlled, especially towards infinity, where the application requires two straight parallel walls. Second, a smooth (C) boundary curve can be achieved.

  • 14.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Numerical Conformal Mappings for Regions Bounded by Smooth Curves2006Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In many applications, conformal mappings are used to transform twodimensional regions into simpler ones. One such region for which conformal mappings are needed is a channel bounded by continuously differentiable curves. In the applications that have motivated this work, it is important that the region an approximate conformal mapping produces, has this property, but also that the direction of the curve can be controlled, especially in the ends of the channel.

    This thesis treats three different methods for numerically constructing conformal mappings between the upper half–plane or unit circle and a region bounded by a continuously differentiable curve, where the direction of the curve in a number of control points is controlled, exact or approximately.

    The first method is built on an idea by Peter Henrici, where a modified Schwarz–Christoffel mapping maps the upper half–plane conformally on a polygon with rounded corners. His idea is used in an algorithm by which mappings for arbitrary regions, bounded by smooth curves are constructed.

    The second method uses the fact that a Schwarz–Christoffel mapping from the upper half–plane or unit circle to a polygon maps a region Q inside the half–plane or circle, for example a circle with radius less than 1 or a sector in the half–plane, on a region Ω inside the polygon bounded by a smooth curve. Given such a region Ω, we develop methods to find a suitable outer polygon and corresponding Schwarz–Christoffel mapping that gives a mapping from Q to Ω.

    Both these methods use the concept of tangent polygons to numerically determine the coefficients in the mappings.

    Finally, we use one of Don Marshall’s zipper algorithms to construct conformal mappings from the upper half–plane to channels bounded by arbitrary smooth curves, with the additional property that they are parallel straight lines when approaching infinity.

  • 15.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Numerical conformal mappings for waveguides2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Acoustic or electro-magnetic scattering in a waveguide with varying direction and cross-section can be re-formulated as a two-dimensional scattering problem, provided that the variations take place in only one dimension at a time. By using the so-called Building Block Method, it is possible to construct the scattering properties of a combination of scatterers when the properties of each scatterer are known. Hence, variations in the waveguide geometry or in the boundary conditions can be treated one at a time.

    Using the Building Block Method, the problem takes the form of the Helmholtz equation for stationary waves in a waveguide of infinite length and with smoothly varying geometry and boundary conditions. A conformal mapping is used to transform the problem into a corresponding problem in a straight horizontal waveguide, and by expanding the field in Fourier trigonometric series, the problem can be reformulated as an infinite-dimensional ordinary differential equation. From this, numerically solvable differential equations for the reflection and transmission operators are derived.

    To be applicable in the Building Block Method, the numerical conformal mapping must be constructed such that the direction of the boundary curve can be controlled. At the channel ends, it is an indispensable requirement, that the two boundary curves are (at least) asymptotically parallel and straight. Furthermore, to achieve bounded operators in the differential equations, the boundary curves must satisfy different regularity conditions, depending on the boundary conditions.

    In this work, several methods to accomplish such conformal mappings are presented. The Schwarz–Christoffel mapping, which is a natural starting point and for which also efficient numerical software exists, can be modified in different ways in order to achieve polygons with rounded corners. We present algorithms by which the parameters in the mappings can be determined after such modifications. We show also how the unmodified Schwarz–Christoffel mapping can be used for regions with a smooth boundary. This is done by constructing an appropriate outer polygon to the considered region.

    Finally, we introduce one method that is not Schwarz–Christoffel-related, by showing how one of the so-called zipper algorithms can be used for waveguides.

  • 16.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Numerical Conformal Mappings for Waveguides2010In: Computational Mathematics: Theory, Methods and Applications, Hauppauge NY, USA: Nova Science Publishers , 2010Chapter in book (Other (popular science, discussion, etc.))
    Abstract [en]

    Acoustic or electro-magnetic scattering in a waveguide with  varying direction and cross-section can, if the variations takes  place in only one dimension at a time be re-formulated as a  two-dimensional scattering problem. By using the so-called  Building Block Method, it is possible to construct the  scattering properties of a combination of scatterers when the  properties of each scatterer are known. Hence, variations in the  waveguide geometry or in the boundary conditions can be treated   one at a time.  We consider in this work acoustic scattering, but the same  techniques can be used for both electro-magnetic and some quantum  scattering problems.  By suppressing the time dependence and by using the Building Block  Method, the problem takes the form of the Helmholtz equation in a  waveguide of infinite length and with smoothly varying geometry and  boundary conditions.  A conformal mapping is used to transform the  problem into a corresponding problem in a straight horizontal  channel, and by expanding the field in Fourier trigonometric series,  the problem can be reformulated as an infinite-dimensional ordinary  differential equation. From this, numerically solvable differential  equations for the reflection and transmission operators are  derived.  To be applicable in the Building Block Method, the numerical  conformal mapping must be constructed such that the direction of the  boundary curve can be controlled. At the channel ends, it is an  indispensable requirement, that the two boundary curves are (at least)  asymptotically parallel and straight. Furthermore, to achieve  bounded operators in the differential equations, the boundary curves  must satisfy different regularity conditions, depending on the  properties of the boundary.  Several methods to accomplish such conformal mappings are  presented. The Schwarz-Christoffel mapping, which is a natural starting point and for which  also efficient numerical software exists, can be modified in  different ways to round the polygon corners, and we show algorithms  by which the parameter problem can be solved after such  modifications. It is also possible to use the unmodified Schwarz-Christoffel mapping for  regions with smooth boundary, by constructing an appropriate outer  polygon to the considered region.  Finally, we show how a so-called  zipper algorithm can be used for waveguides.

  • 17.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    On the curvature of an inner curve in a Schwarz--Christoffel mapping2009In: Further Progress in Analysis: Proceedings of the 6th International ISAAC Congress, Ankara, Turkey, 2007, World Scientific , 2009, p. 281-290Conference paper (Refereed)
    Abstract [en]

    In the so called outer polygon method, an approximative conformal mapping for a given simply connected region Ω is constructed using a Schwarz–Christoffel mapping for an outer polygon, a polygonal region of which Ω is a subset. The resulting region is then bounded by a C-curve, which among other things means that its curvature is bounded.In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz–Christoffel mapping from R, the unit disk or upper half–plane, to a polygonal region P of a curve inside R. From the Schwarz–Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.

  • 18.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Schwarz-Christoffel Mappings for Nonpolygonal Regions2008In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 31, no 1, p. 94-111Article in journal (Refereed)
    Abstract [en]

    An approximate conformal mapping for an arbitrary region Ω bounded by a smooth curve Γ is constructed using the Schwarz–Christoffel mapping for a polygonal region in which Ω is embedded. An algorithm for finding this so-called outer polygon is presented. The resulting function is a conformal mapping from the upper half-plane or the unit disk to a region R, approximately equal to Ω. R is bounded by a C∞ curve, and since the mapping function originates from the Schwarz–Christoffel mapping and tangent polygons are used to determine it, important properties of Γ such as direction, linear asymptotes, and inflexion points are preserved in the boundary of R. The method makes extensive use of existing Schwarz–Christoffel software in both the determination of outer polygons and the calculation of function values. By the use suggested here, the capabilities of such well-written software are extended.

  • 19.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Using a zipper algorithm to find a conformal map for a channel with smooth boundary2006In: Mathematical Modeling of Wave Phenomena: 2nd Conference, 2006, p. 378-Conference paper (Refereed)
    Abstract [en]

    The so called geodesic algorithm, which is one of the zipper algorithms for conformal mappings, is combined with a Schwarz–Christoffel mapping, in its original or in a modified form, to produce a conformal mapping function between the upper half-plane and an arbitrary channel with smooth boundary and parallel walls at the end.

  • 20.
    Andersson, Anders
    et al.
    Jönköping University, School of Engineering, JTH, Mathematics.
    Nilsson, Börje
    International Centre for Mathematical modelling, Växjö University.
    Acoustic Transmission in Ducts of Various Shapes with an Impedance Condition2008In: International Conference on Numerical Analysis and Applied Mathematics 2008, Melville: American Institute of Physics , 2008, p. 33-36Conference paper (Refereed)
    Abstract [en]

    Propagation of acoustic waves in a two-dimensional duct with an impedance condition at the boundary, is studied. The duct is assumed to have two ends at infinity being asymptotically straight, but otherwise to be arbitrarily shaped.The so called Building Block Method allows us to synthesize propagation properties for ducts with complicated geometries from results for simpler ducts. Conformal mappings can be used to transform these simple ducts to straight ducts with constant cross-sections.By using recently developed techniques for numerical conformal mappings, it is possible to construct a transformation between an infinite strip and an arbitrarily shaped duct with smooth or piecewise smooth boundary, keeping both smoothness and the well controlled boundary direction towards infinity that the above mentioned method requires.To accomplish a stable formulation of the problem, we express it in terms of scattering operators. The resulting differential equation is solved using wave splitting and invariant embedding techniques. We expand the involved functions in Fourier series, and hence, it is possible to give the operators a matrix representation. Numerical results are produced using truncated matrices.

  • 21.
    Andersson, Anders
    et al.
    Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.
    Nilsson, Börje
    Linnaeus university, Vaxjö, Sweden.
    Biro, Thomas
    Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.
    Fourier methods for harmonic scalar waves in general waveguides2016In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 98, no 1, p. 21-38Article in journal (Refereed)
    Abstract [en]

    A set of semi-analytic techniques based on Fourier analysis is used to solve wave-scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are the newly developed conformal mapping methods, wave splitting, Fourier series expansions in eigenfunctions to non-normal operators, the building block method or the cascade technique, Dirichlet-to-Neumann operators, and reformulation in terms of stable differential equations for reflection and transmission matrices. For an example, the results show good correspondence with a finite element method solution to the same problem in the low- and medium-frequency domains. The Fourier method complements finite element analysis as a waveguide simulation tool. For inverse engineering involving tuning of straight waveguide parts joining complicated waveguide elements, the Fourier method is an attractive alternative including time aspects. The prime motivation for the Fourier method is its added physical understanding primarily at low frequencies.

  • 22.
    Andersson, Frida
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Hur matematikläroböcker presenterar räknelagar och räkneregler2016Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In mathematics education textbooks to a large extent determine what is offered for students to be learnt. With this in mind, in this study, five Swedish textbooks series is reviewed in a latent and manifest content analysis approach where both quantitative and qualitative data is presented. The result of the quantitative data indicate that only a few textbooks series mentions the associative and distributive law in explicit manners. The result of the qualitative data shows that the basic laws of arithmetic is often described in other contexts. Many examples in the textbooks makes generalizations that may lead to limited understanding of the basic laws and rules of arithmetic.

  • 23.
    Andersson, Frida
    et al.
    Jönköping University, School of Education and Communication.
    Englund Eriksson, Cathrine
    Jönköping University, School of Education and Communication.
    Associativa lagen i matematikdidaktisk forskning2015Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Matematiken är en vetenskap som är indelad i flera områden. Ett av dessa områden är aritmetik som betyder räknelära. Tillhörande aritmetiken finns ett antal egenskaper, räkneregler och räknelagar. Syftet med studien var att undersöka hur den associativa lagen beskrivs och uppfattas enligt matematikdidaktisk forskning. Arbetet är en litteraturstudie av matematikdidaktiska forskningspublikationer. Alla analyserade publikationer i studien är internationella och berör studiens forskningsområde inom en skolkontext. Materialet har med ett hermeneutiskt synsätt analyserats genom närläsning och med en komparativ metod. Det analyserade materialet består av nio vetenskapliga tidskriftsartiklar, två konferensbidrag samt ett kapitel ur en antologi.

    Den associativa lagen beskrivs inom flera olika områden och sammanhang i matematikdidaktisk forskning. Lagen beskrivs förutom som en egenskap med direkt tillhörighet i aritmetiken, dessutom som en del i ett relationellt tänkande och som en komponent i medvetenhet för matematisk struktur. Förståelse för lagen och dess egenskaper utgör ett viktigt element för elevers övergång från aritmetik till algebra. Den associativa lagen missuppfattas ofta och används på ett felaktigt sätt av såväl elever, lärarstudenter som lärare. Bristande förståelse för lagen och dess egenskaper leder till svårigheter i att generalisera de aritmetiska egenskaperna till att gälla även för algebra. 

  • 24.
    Andersson, Sven
    et al.
    Jönköping University, School of Education and Communication, HLK, Disciplinary Research.
    Larsson, Peter
    Jönköping University, School of Education and Communication, HLK, Disciplinary Research.
    Läromedlets funktion i klassrummet, i matematik.2007Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis
    Abstract [sv]

    Syftet med detta arbete var att undersöka och få grepp om de faktorer, som verkar mellan läromedlen och eleverna, respektive läromedlen och lärarna. Frågeställningarna var följande:

    - Vilka faktorer påverkar läromedlets funktion?

    - Vad kommunicerar dessa faktorer till lärare, respektive elever?

    För att få svar på dessa frågor, genomfördes kvalitativa intervjuer bland lärare och elever i gymnasiet, i ämnet matematik.

    I vårt arbete såg vi en röd tråd som löpte genom litteratur och artiklar. Tråden var vikten av det matematiska språket, och hur viktig den var för ett utvecklande av den matematiska förståelsen. Vi har skärskådat olika faktorer som vi fått fram genom en amerikansk utvärderingsprocedur. Faktorerna har undersökts och vi har tagit reda på vad dessa innebär. I intervjuerna med elever och lärare i gymnasieskolan har vi sett att våra antaganden blivit bekräftade.

    Det som har framhållits i debatten, är att man skall ta bort läroböckerna, men med detta menar man inte alltid att de skall tas bort helt, utan att deras dominans skall minska. Detta bör ske till förmån för en dialog i klassrummen, i grupparbeten eller i dialoger mellan eleverna och lärarna. I vårt arbete har åsikter kommit fram som stödjer dessa tankar, att kommunikationen är viktig för att bygga upp den matematiska förståelsen.

  • 25.
    Askew, Mike
    et al.
    Univ Witwatersrand, Wits Sch Educ, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Univ Witwatersrand, Wits Sch Educ, Johannesburg, South Africa.
    Deconstructing South African Grade 1 learners’ awareness of number in terms of cardinality, ordinality and relational understandings2020In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704Article in journal (Refereed)
    Abstract [en]

    The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children’s understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also additive and multiplicative relations have been theorized. We examine how the connections between these can be considered through a focus on number line representations and children positioning and comparing numbers. The responses of a cohort of South African Grade 1 learners’ (6- and 7-year-olds) to a numerical magnitude estimation task and to a numerical comparison task are analysed and the findings compared to those in the international literature, some of which argue that children’s early, informal, understandings of cardinality and ordinality are underpinned by an intuitive logarithmic model relating number order and size. A main finding presented here is that the responses from learners in this study exhibited a better fit with an exponential model of the relationship between cardinality and ordinality. These findings raise questions about whether some of the findings in previous research are as universal as sometimes claimed.

  • 26.
    Askew, Mike
    et al.
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Abdulhamid, Lawan
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Mathews, Corin
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Morrison, Samantha
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Ramdhany, Viren
    University of Johannesburg, South Africa.
    Tshesane, Herman
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Teaching for structure and generality: Assessing changes in teachers mediating primary mathematics2019In: Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7-12 July 2019: Volume 2, Research reports (A-K) / [ed] M. Graven, H. Venkat, A. A. Essien & P. Vale, Pretoria, South Africa: PME , 2019, p. 41-48Conference paper (Refereed)
    Abstract [en]

    From a sociocultural perspective that a teacher’s use of mediational means is central to student learning, this paper presents an analysis of six teachers and their mediating, across a two-three year time gap. Drawing on the Mediating Primary Mathematics framework – developed to examine the type and quality of mediational means – we propose two composite assessments of quality of mediation – extent and depth – that indicate the extent to which teaching addresses mathematical structure and generality. The findings reveal a range of differences in these two assessments for each of the six teachers, but that all six teachers were more coherent in their use of mediational means in the later lesson than in the earlier one. These findings have implications for other schooling systems and researchers seeking to improve the quality of mathematics instruction.

  • 27.
    Avery, Helen
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Centre for Middle Eastern Studies, Lund University, Sweden.
    Acquérir les gestes qu’il faut: les mathématiques scolaires comme interaction et savoir-faire2019In: AREF 2019: Livret des résumés, 2019, p. 286-287Conference paper (Refereed)
    Abstract [en]

    The paper presents the synthesis of a series of studies on support measures for pupils with additional languages in Sweden, with a particular focus on the consequences of language support measures for teaching and learning school mathematics. The analysis identifies several critical aspects in mathematics teaching when the pupils transition from one school system to another, and particularly when they do not yet have a shared language to communicate among each other or with their teachers. Three aspects with relevance to language support will be discussed and illustrated with examples from the studies: the notion of mathematics as a formal language; the notion of levels and absolute progression in mathematics; the notion that learning mathematics means understanding "concepts".

  • 28.
    Axelsson, Johanna
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Geometriska mönster i Favorit matematik: En läromedelsgranskning av Favorit matematik i årskurserna 1-32017Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Algebra in mathematics is so much more than just equations and calculations. Through the primary grades in school, geometric patterns are a part of the Swedish curriculum. By working with patterns we prepare the students for the more difficult algebra to come, and they learn to express themselves generally. Many studies show the benefits with the work with patterns in the primary grades, for example students learn how to see connections and how to generalise.

     

    This study is a teaching material study of the material Favorit matematik in the primary grades. The aim is to contribute knowledge about which mathematical abilities students are given chance to develop by working with patterns in Favorit matematik. Focus is also to study what type of pattern, of repeating patterns and growing patterns, that are more processed in the material. The method that has been used is a chart where the patterns and the abilities were written into.

     

    The result shows flaws when it comes to patterns in Favorit matematik. The teacher has to work with this along with the material to give the students chance to explore every mathematical ability. Nor is it shown that patterns are something within the algebra, it is mostly linked to other areas from the curriculum. Mostly the exercises were about completing a pattern that was repeating, and therefore the majority of the exercises was connected to the first ability, which is about solving problems and evaluate your strategies and methods. The result also shows that growing geometric patterns is not presented as much as repeating patterns.

  • 29.
    Axelsson, Johanna
    et al.
    Jönköping University.
    Debreceni, Hanna
    Jönköping University.
    Mönster inom algebra: Med inriktning mot årskurs F-32016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Mönsterarbete i lågstadiet är en bra start för inlärning av algebra, detta ger en grund för den kommande mer avancerade algebraundervisningen. Studiens övergripande syfte är att undersöka hur arbetet med mönster inom åldrarna 6-10 år kan se ut, och vilka fördelar mönsterarbetet har för elevers kommande lärande inom matematik. Uppsatsen är baserad på nationell och internationell vetenskapligt granskad forskning. Olika undervisningsexempel, som kan tillämpas i lågstadiet, belyses och vikten av mönsterarbetet tas upp. Studien berör arbete med tre typer av mönster: upprepade mönster, växande mönster och talföljder. Vår analys av forskning visar att mönsterarbete är en viktig del i matematiken och att det kan komma till nytta i elevers fortsatta matematikinlärning. Den visar också att upprepade mönster är den vanligaste sorten av mönster att arbeta med i de yngre åldrarna, men forskarna menar att lärarna bör vidga undervisningen och även arbeta med andra mönster. Studien riktar sig främst till lärare som undervisar i F-3 men även till andra som är intresserade av hur arbetet med mönster kan se ut i de lägre åldrarna. Exemplen som tas upp i uppsatsen kan lärare använda i sin undervisning.

  • 30.
    Belov, I.
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology.
    Alavizadeh, Z.
    Lindgren, M.
    Application of engineering optimization to evaluate heating-based humidity management in electronics enclosures2011In: Electronic Environment Konferens & Mässa 2011, Stockholm Älvsjö,5-6 April 2011, Invited speech, 2011, p. 161-162Conference paper (Other academic)
  • 31.
    Belov, Ilja
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Anti-Moisture Methodology for Electronics Enclosures in Harsh Storage Environments2008Conference paper (Other academic)
  • 32.
    Belov, Ilja
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Evaluation of Anti-Moisture Measures in Electronics Enclosure: Application of CFD Modelling2009Conference paper (Other academic)
  • 33.
    Belov, Ilja
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Humidity Management in Electronics Enclosure under Severe Climatic Conditions2008Conference paper (Other academic)
  • 34.
    Belov, Ilja
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Optimization of PCB Heater Heating Profile for Power-efficient Humidity Management in Electronics Enclosures: OPTIMUS Worldwide User Meeting 2010, Antwerp, Belgium, November 22-23, 20102010Other (Other academic)
  • 35.
    Belov, Ilja
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Bespalov, Michail
    Klochkova, Ludmila
    Kuleshov, Alexander
    Suzan, Dmitriy
    Tishkin, Vladimir
    Транспортная модель распространения газообразных примесей в атмосфере города = Transport model of gas impurities spread processes in urban area2000In: Математическое моделирование: (Mathematical Modelling), ISSN 0234-0879, Vol. 12, no 11, p. 38-46Article in journal (Refereed)
  • 36.
    Belov, Ilja
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Bespalov, Michail
    Klochkova, Ludmila
    Pavlova, Natalya
    Suzan, Dmitriy
    Tishkin, Vladimir
    Сравнение моделей распространения загрязнений в атмосфере = Comparative Analysis of models of pollutions spreading in atmosphere1999In: Математическое моделирование: (Mathematical Modelling), ISSN 0234-0879, Vol. 11, no 8, p. 52-64Article in journal (Refereed)
  • 37.
    Belov, Ilja
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Lindgren, Mats
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Leisner, Peter
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Bergner, Fredrik
    Bornoff, Robin
    CFD aided reflow oven profiling for PCB preheating in a soldering process2007In: Proceedings of the 8th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Micro-Electronics and Micro-Systems: EuroSimE 2007, Piscataway, NJ.: IEEE , 2007, p. 535-542Conference paper (Refereed)
    Abstract [en]

    A CFD-aided reflow oven profile prediction algorithm has been developed and applied to modelling of preheating of a PCB with non-uniform distribution of component thermal mass in a forced air convection solder reflow oven. The iterative algorithm combines an analytic approach with CFD modelling. It requires an experimentally validated CFD model of the solder reflow oven and a CFD model of the PCB as main inputs. Results of computational experiments have been presented to reveal good agreement between predicted PCB profiles and corresponding CFD calculations. Application guidelines contained in the description of the algorithm will assist potential users both during the virtual prototyping phase of a PCB including designing for assembly and in the phase of reflow oven profiling.

  • 38.
    Belov, Ilja
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Lindgren, Mats
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Leisner, Peter
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Bergner, Fredrik
    Bornoff, Robin
    CFD aided reflow oven profiling for PCB preheating in a soldering process: Part 1(2)2007In: Electronic Environment, no 3, p. 25-28Article in journal (Other academic)
  • 39.
    Belov, Ilja
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Lindgren, Mats
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Leisner, Peter
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Bergner, Fredrik
    Bornoff, Robin
    CFD aided reflow oven profiling for PCB preheating in a soldering process: Part 2(2)2007In: Electronic Environment, no 4, p. 25-27Article in journal (Other academic)
  • 40.
    Belov, Ilja
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Lindgren, Mats
    Ryden, Jan
    Alavizadeh, Zahra
    Leisner, Peter
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    CFD Assisted Design Evaluation and Experimental Verification of a Logic-Controlled Local PCB Heater for Humidity Management in Electronics Enclosure2010In: IEEE EuroSimE 2010, 26-28 April, Bordeaux, France, 2010Conference paper (Refereed)
    Abstract [en]

    Humidity management of commercial-of-the-shelf electronic components in non-controlled climatic environments can be realized e.g. by introducing a local printed circuit board heater. By choosing appropriate size and location of the heater plate in the vicinity of the critical electronic packages, and utilizing logic control function, it is possible to improve the quality of local humidity management and reduce power consumption of the heater, which is important especially in case of battery driven portable or vehicle mounted devices. A computational fluid dynamics assisted methodology has been developed to determine the best feasible design of the heater, followed by experimental verification of the constructed logic controlled heater. The experiment has been performed in a harsh climatic environment including temperature variation from +33°C to +40°C, and relative humidity variation from 54% to 80%. Analysis of the experimental %RH and temperature curves as well as power profile of the heater has confirmed the feasibility of the chosen approach to maintain greater than 9°C difference between the electronics package surface temperature and the local dew point temperature, by applying discrete power pulses with the amplitude less than 6 W.

  • 41.
    Belov, Ilja
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Rydén, Jan
    Lindblom, Joakim
    Zhang, Yafan
    Hansson, T
    Bergner, Fredrik
    Leisner, Peter
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Application of CFD Modelling for Energy Efficient Humidity Mangement of an Electronics Enclosure in Storage under Severe Climatic Conditions2008In: International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Micro-Systems, 2008: EuroSimE 2008., IEEE , 2008, p. 430-437Conference paper (Refereed)
    Abstract [en]

    A CFD modelling methodology including experimental validation has been developed and applied for investigation of anti-moisture measures in a non- hermetic electronics enclosure containing a number of printed circuit boards, and placed in a severe storage environment. In the climatic test the temperature and the relative humidity have been varried from +33degC to +71degC and from 14% to 80%, respectively. Enclosure heater solutions have been parametrically studied by simulation. A heating strategy involving various power levels has been determined, which is just sufficient to maintain the internal relative humidity below 60%, thereby reducing the risk for dew formation on the electronics assembly.

  • 42.
    Belov, Ilja
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Wingbrant, Helena
    Spetz, Anita-Lloyd
    Sundgren, Hans
    Thuner, Bo
    Svenningstorp, Henrick
    Leisner, Peter
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Thermal and flow analysis of SiC-based gas sensors for automotive applications2004In: Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems, 2004: EuroSimE 2004., IEEE , 2004, p. 475-482Conference paper (Refereed)
    Abstract [en]

    Different block and tube mounting alternatives for SiC-based gas sensors were studied by means of temperature measurements and simulation of heat transfer and gas flow for steady state conditions. The most preferable tube mounting design was determined. Simulation-based guidelines were developed for designing tube-mounted gas sensors in the exhaust pipes of diesel and petrol engines, taking into account thermal constraints and flow conditions.

  • 43.
    Belov, Ilja
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Wingbrant, Helena
    Spetz, Anita-Lloyd
    Sundgren, Hans
    Thuner, Bo
    Svenningstorp, Henrik
    Leisner, Peter
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    CFD analysis of packaging and mounting solutions for SiC-based gas sensors in automotive applications2006In: Sensor Letters, ISSN 1546-198X, Vol. 4, no 1, p. 29-37Article in journal (Refereed)
    Abstract [en]

    Simulation-based guidelines were developed for designing tube-mounted gas sensors in the exhaust pipes of diesel and petrol engines, taking into account thermal constraints and gas flow conditions. Different block and tube mounting alternatives for SiC-based gas sensors were studied by means of temperature measurements and simulation of steady state heat transfer and gas flow. Design variables included the number of fins in the heat sink mounted on the inlet tube, the inlet construction, the mounting tube orientation, and the micro-heater substrate placement inside the mounting tube. The most preferable tube mounting design was determined with respect to the thermal performance of the sensor structure and with respect to the gas flow parameters, which are important for the sensor's selectivity, sensitivity and response time.

  • 44. Berggren, Martin
    Undervisning om problemlösning med dess didaktiska utformningar, utmaningar och anknytningar till matematikdidaktisk forskning: En studie om hur lärare i årskuserna 1-3 didaktiskt strukturerar och motiverar sin problemlösningsundervisning2016Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
  • 45.
    Bergqvist, Tomas
    et al.
    Umeå universitet, Institutionen för tillämpad utbildningsvetenskap.
    Boesen, Jesper
    NCM, Göteborg.
    Nyroos, Mikaela
    Umeå universitet, Pedagogiska institutionen.
    Vad vet vi om hur matematiklärare arbetar för att utveckla elevers matematikkunskaper?2010Report (Other academic)
  • 46. Billing, Elin
    Matematikundervisning för alla: En kvalitativ studie om lärares uppfattningar av individualiserad matematikundervisning2019Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med studien är att bilda kunskap om lärares uppfattningar av vad individualisering i matematikundervisningen kan innebära. Utifrån syftet har frågeställningar formulerats som avser att ta reda på lärares uppfattning av vad individualisering är och hur de uppfattar att de arbetar individualiserat i matematikundervisningen. Det är en kvalitativ studie som grundar sig på semistrukturerade intervjuer med fem verksamma grundskollärare. Det teoretiska och metodologiska tillvägagångssättet i studien är fenomenografiskt.

    Resultatet visar att det finns olika uppfattningar av vad individualiserad undervisning innebär. Det övergripande är att en individualiserad undervisning krävs i skolan för att alla elever har olika bakgrund, erfarenheter och behov. En individualiserad matematikundervisning kan möjliggöra att alla elever får utvecklas utifrån sina kunskaper. Precis som forskning visar framgår det i studien att hastighetsindividualisering genomsyrar matematikundervisningen. Lärare visar en tendens till att matematikundervisningen är läroboksbunden men resultatet visar att lärare till viss del är medvetna om dess negativa effekter och att de därför försöker variera matematikundervisningen. Det finns en önskan om att individualisera mer men det finns faktorer som påverkar möjligheten till individualisering, främsta faktorn är tiden. Om lärare har de förutsättningar som krävs för att kunna individualisera matematikundervisningen så kan uppfattningen av vad individualisering är förändras och därmed sättet att undervisa.

  • 47.
    Billing, Elin
    et al.
    Jönköping University, School of Education and Communication.
    Engsund, Maja
    Jönköping University, School of Education and Communication.
    Effekter av nivågruppering: En litteraturöversikt om nivågruppering i matematik2018Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Lärare ansvarar för att möta alla elevers olika förutsättningar och behov i matematikundervisningen därför bör det finnas flera vägar att nå målen. Att differentiera undervisningen genom nivågruppering är en väg att gå för att möta alla elevers olikheter. Syftet med denna studie är att belysa hur begreppet nivågruppering berörs i matematikdidaktisk forskning. Arbetet är en litteraturstudie som baseras på elva forskningsstudier. Varav tio är internationella och en är nationell. Materialet som valts ut har granskats genom närläsning och en komparativ analys.

    I litteraturstudien har det framkommit att nivågruppering används för att skapa grupper med mindre elevvariation. Högpresterande elever är de som gynnas mest av nivågrupperingar i matematik och de presterar överlag bättre i en homogen grupp där alla elever har liknande kunskaper. Däremot missgynnas lågpresterande elever av nivågruppering och det medför att skillnaderna mellan elevers förmågor ökar. Att dela in elever i grupper kan påverka dem negativt om de kunskapsmässigt placeras i “fel” grupp och det kan leda till att de får en negativ inställning till matematik. Vår slutsats är att lärare bör utgå från flera olika aspekter vid arbete med nivågruppering och de bör grunda grupplacering på både provresultat och sina tidigare bedömningar för att skapa en god lärandemiljö för alla elever.

  • 48. Bjellerup, Mårten
    et al.
    Holgersson, Thomas
    Jönköping University, Jönköping International Business School, JIBS, Economics.
    A simple multivariate test for asymmetry2009In: Applied Economics, ISSN 0003-6846, E-ISSN 1466-4283, Vol. 41, no 11, p. 1405-1416Article in journal (Refereed)
  • 49.
    Bjenning, Caroline
    Jönköping University, School of Education and Communication.
    Tänker vi lika om vad som sker i ett matematikklassrum och om sociomatematiska normer?: En fallstudie i en klass i årskurs 5, ur ett lärar- och elevperspektiv.2017Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In every classroom and group of students it occurs norms and expectations (Skott, Jess, Hansen & Lundin, 2010). Norms creates in interaction between the teacher and students, which conduce to that norms establish in the classroom (Cobb & Yackel, 1996). If the knowledge and consensus about norms is missing there is a risk that the students mathematical learning will be inhibit. The aim of the study is to describe which sociomathematical norms that shows in one classroom, in 5th grade. The theoretical basis of the study is social constructionism. 40 students from a school in Sweden was observed and eight of them and one of the teacher was interviewed in order to emphasize which sociomathematical norms that occurs during the observed lesson. Subsequently the teacher and eight students got to express the norms. The result showed that it’s not prevail a consensus between the teacher and students about the three norms: 1) discussion as a way to work 2) an acceptable mathematic answer and at last 3) the mathematic language and its meaning in the education. There was a consensus between some of the sociomathematical norms differences were founded though, which influences the teacher and the student view of what the mathematical education implicates. The conclusion of the study is that in some cases there is a gap between the teacher and the students’ knowledge about norms. The norm has accordingly been created unknowingly, which in turn can influence the teacher and the students acting and where they put their focus in their mathematical education.

  • 50. Björklund, C.
    et al.
    Ekdahl, Anna-Lena
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Runesson Kempe, Ulla
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research.
    Implementing a structural approach in preschool number activities: Effects of an intervention programManuscript (preprint) (Other academic)
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