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  1. 1. Skolans matematik : En kritisk analys av den svenska skolmatematikens förhistoria, uppkomst och utveckling

    Författare :Sverker Lundin; Donald Broady; Sten Kaijser; Göteborgs universitet; []
    Nyckelord :HUMANIORA; HUMANITIES; NATURVETENSKAP; NATURAL SCIENCES; matematik; skolmatematik; historia; Matematik;

    Sammanfattning : I argue that common beliefs regarding mathematics originate in the practices of elementary mathematics instruction rather than in science. While learning how to solve mathematical problems in school, we come to believe that mathematics has a set of properties in itself, for instance that it is useful in everyday life, even though this is not necessarily so. LÄS MER

  3. 2. Harmonic measures

    Författare :Jonatan Vasilis; Göteborgs universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; harmonic measure; square root of the Poisson kernel; Hardy space; p-Laplace operator; random walk; regular tree; discrete minimal thinness; Hardy space;

    Sammanfattning : This thesis uses both analytic and probabilistic methods to study continuous and discrete problems. The main areas of study are the asymptotic properties of p-harmonic measure, and various aspects of the square root of the Poisson kernel. Fix a domain and a boundary point, subject to certain regularity conditions. LÄS MER

  4. 3. Duality-based adaptive finite element methods with application to time-dependent problems

    Författare :August Johansson; Mats G. Larson; Paul Houston; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; finite element methods; dual-weighted residual method; multiphysics; a posteriori error estimation; adaptive algorithms; discontinuous Galerkin; MATHEMATICS; MATEMATIK; Mathematics; matematik;

    Sammanfattning : To simulate real world problems modeled by differential equations, it is often not sufficient to  consider and tackle a single equation. Rather, complex phenomena are modeled by several partial dierential equations that are coupled to each other. LÄS MER

  5. 4. Classification of Normal Discrete Kinetic Models

    Författare :Mirela Christina Vinerean; Alexander Bobylev; Mirela Vinerean-Bernhoff; Karlstads universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Kinetic theory; discrete kinetic velocity models; conservation laws; MATHEMATICS; MATEMATIK; Matematik; Mathematics;

    Sammanfattning : “In many interesting papers on discrete velocity models (DVMs), authors postulate from the beginning that the finite velocity space with "good" properties is given and only after this step they study the Discrete Boltzmann Equation. Contrary to this approach, our aim is not to study the equation, but to discuss all possible choices of finite phase spaces (sets) satisfying this type of "good" restrictions. LÄS MER

  7. 5. Discrete Kinetic Models and Conservation Laws

    Författare :Mirela Cristina Vinerean; Alexander Bobylev; Giampiero Spiga; Karlstads universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Kinetic theory; discrete kinetic velocity models; conservation laws; MATHEMATICS; MATEMATIK; Matematik; Mathematics;

    Sammanfattning : Classical kinetic theory of gases is based on the Boltzmann equation (BE) which describes the evolution of a system of particles undergoing collisions preserving mass, momentum and energy. Discretization methods have been developed on the idea of replacing the original BE by a finite set of nonlinear hyperbolic PDEs corresponding to the densities linked to a suitable finite set of velocities. LÄS MER