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1. 1. “Count on me!” : Mathematical development, developmental dyscalculia and computer-based intervention

   Författare :Linda Olsson; Ulf Träff; Joakim Samuelsson; Lisa Thorell; Linköpings universitet; []
   Nyckelord :SAMHÄLLSVETENSKAP; SOCIAL SCIENCES; mathematical development; symbolic number processing; Approximate number system; developmental dyscalculia; computer-based intervention; matematisk utveckling; symboliskt nummerprocessande; Approximativa nummersystemet; dyskalkyli; datorbaserad intervention;

   Sammanfattning : A “sense” of number can be found across species, yet only humans supplement it with exact and symbolic number, such as number words and digits. However, what abilities leads to successful or unsuccessful arithmetic proficiency is still debated. LÄS MER

3. 2. G-Convergence and Homogenization of some Sequences of Monotone Differential Operators

   Författare :Liselott Flodén; Anders Holmbom; Nils Svanstedt; Mårten Gulliksson; Björn Birnir; Mittuniversitetet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; G-convergence; Homogenization; Multiscale convergence; Two-scale convergence; Monotone opertors; Functional analysis; Partial differential equations; Mathematical analysis; Analys;

   Sammanfattning : This thesis mainly deals with questions concerning the convergence of some sequences of elliptic and parabolic linear and non-linear operators by means of G-convergence and homogenization. In particular, we study operators with oscillations in several spatial and temporal scales. LÄS MER

4. 3. Homogenization of Some Selected Elliptic and Parabolic Problems Employing Suitable Generalized Modes of Two-Scale Convergence

   Författare :Jens Persson; Anders Holmbom; Liselott Flodén; Marianne Lindberg; Mårten Gulliksson; Peter Wall; Mittuniversitetet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; H-convergence; G-convergence; homogenization; multiscale analysis; two-scale convergence; multiscale convergence; elliptic partial differential equations; parabolic partial differential equations; monotone operators; heterogeneous media; non-periodic media; Mathematical analysis; Analys;

   Sammanfattning : The present thesis is devoted to the homogenization of certain elliptic and parabolic partial differential equations by means of appropriate generalizations of the notion of two-scale convergence. Since homogenization is defined in terms of H-convergence, we desire to find the H-limits of sequences of periodic monotone parabolic operators with two spatial scales and an arbitrary number of temporal scales and the H-limits of sequences of two-dimensional possibly non-periodic linear elliptic operators by utilizing the theories for evolution-multiscale convergence and λ-scale convergence, respectively, which are generalizations of the classical two-scale convergence mode and custom-made to treat homogenization problems of the prescribed kinds. LÄS MER

5. 4. Selected Topics in Homogenization

   Författare :Jens Persson; Anders Holmbom; Liselott Flodén; Marianne Olsson Lindberg; Mårten Gulliksson; Peter Wall; Mittuniversitetet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; homogenization theory; H-convergence; two-scale convergence; very weak two-scale convergence; multiscale convergence; very weak multiscale convergence; evolution-multiscale convergence; very weak evolution-multiscale convergence; λ-scale convergence; non-periodic linear elliptic problems; evolution-multiscale linear parabolic problems; evolution-multiscale monotone parabolic problems; detection of scales of heterogeneity;

   Sammanfattning : The main focus of the present thesis is on the homogenization of some selected elliptic and parabolic problems. More precisely, we homogenize: non-periodic linear elliptic problems in two dimensions exhibiting a homothetic scaling property; two types of evolution-multiscale linear parabolic problems, one having two spatial and two temporal microscopic scales where the latter ones are given in terms of a two-parameter family, and one having two spatial and three temporal microscopic scales that are fixed power functions; and, finally, evolution-multiscale monotone parabolic problems with one spatial and an arbitrary number of temporal microscopic scales that are not restricted to be given in terms of power functions. LÄS MER

7. 5. Mathematical Learning Disability : Cognitive Conditions, Development and Predictions

   Författare :Rickard Östergren; Ulf Träff; Joakim Samuelsson; Örjan Dahlström; Åke Olofsson; Linköpings universitet; []
   Nyckelord :SAMHÄLLSVETENSKAP; SOCIAL SCIENCES; Mathematical learning disability; dyscalculia; mathematical cognition; number sense; Matematiska inlärningssvårigheter; dyskalkyli; matematisk kognition; antalsuppfattning;

   Sammanfattning : The purpose of the present thesis was to test and contrast hypotheses about the cognitive conditions that support the development of mathematical learning disability (MLD). Following hypotheses were tested in the thesis: a) domain general deficit, the deficit is primarily located in the domain general systems such as the working memory, b) number sense deficit, the deficit is located in the innate approximate number system (ANS), c) numerosity coding deficit, the deficit is located to a exact number representation system, d) access deficit, the deficit is in the mapping between symbols and the innate number representational system (e. LÄS MER