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  • 101.
    Andren, Lina J.
    et al.
    Umeå University, Sweden .
    Casselgren, Carl Johan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Ohman, Lars-Daniel
    Umeå University, Sweden .
    Avoiding Arrays of Odd Order by Latin Squares2013In: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 22, no 2, p. 184-212Article in journal (Refereed)
    Abstract [en]

    We prove that there is a constant c such that, for each positive integer k, every (2k + 1) x (2k + 1) array A on the symbols 1, ... , 2k + 1 with at most c(2k + 1) symbols in every cell, and each symbol repeated at most c(2k + 1) times in every row and column is avoidable; that is, there is a (2k + 1) x (2k + 1) Latin square S on the symbols 1, ... , 2k + 1 such that, for each i, j is an element of {1, ... , 2k + 1}, the symbol in position (i, j) of S does not appear in the corresponding cell in Lambda. This settles the last open case of a conjecture by Haggkvist. Using this result, we also show that there is a constant rho, such that, for any positive integer n, if each cell in an n x n array B is assigned a set of m andlt;= rho n symbols, where each set is chosen independently and uniformly at random from {1, ... , n}, then the probability that B is avoidable tends to 1 as n -andgt; infinity.

  • 102.
    Andrushchenko, Zhanna
    et al.
    Department of Biometry and Engineering SLU.
    Ohlson, Martin
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    von Rosen, Dietrich
    Department of Biometry and Engineering SLU.
    Estimation of banded covariance matrices in a multivariate normal distribution2008Report (Other academic)
  • 103.
    Andrushchenko, Zhanna
    et al.
    Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden.
    von Rosen, Dietrich
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Asymptotic distribution of the estimators of a harmonic component in a multivariate time series under m-dependence2011Report (Other academic)
    Abstract [en]

    Multivariate time series with definite harmonic structure is considered, in the special case when the marginal univariate time series are independent and asymptotically stationary to second order. The asymptotic distribution of the estimators of a harmonic component under $m$-dependence is found

  • 104.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Jonsson, Peter
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Linusson, Svante
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Thapper, Johan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Determining the Number of Solutions to Binary CSP Instances2002In: Principles and Practice of Constraint Programming, 8th International Conference CP-2002,2002, Heidelberg: Springer Verlag , 2002, p. 327-Conference paper (Refereed)
    Abstract [en]

    Counting the number of solutions to CSP instances has applications in several areas, ranging from statistical physics to artificial intelligence. We give an algorithm for counting the number of solutions to binary CSPs, which works by transforming the problem into a number of 2-SAT instances, where the total number of solutions to these instances is the same as those of the original problem. The algorithm consists of two main cases, depending on whether the domain size d is even, in which case the algorithm runs in O(1.3247^n*(d/2)^n) time, or odd, in which case it runs in O(1.3247^n*((d^2+d+2)/4)^(n/2)) if d=4*k+1, and O(1.3247^n*((d^2+d)/4)^(n/2)) if d=4*k+3. We also give an algorithm for counting the number of possible 3-colourings of a given graph, which runs in O(1.8171^n), an improvement over our general algorithm gained by using problem specific knowledge. 

  • 105.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Thapper, Johan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    A Microstructure Based Approach to Constraint Satisfaction Optimisation Problems2005In: The 18th International FLAIRS Conference,2005, Menlo Park, CA, USA: AAAI Press , 2005, p. 155-Conference paper (Refereed)
    Abstract [en]

    We study two constraint satisfaction optimisation problems: The Max Value problem for CSPs, which, somewhat simplified, aims at maximising the sum of the (weighted) variable values in the solution, and the Max Ind problem, where the goal is to find a satisfiable subinstance of the original instance containing as many variables as possible. Both problems are NP-hard to approximate within n^(1-e), e>0, where n is the number of variables in the problems, which implies that it is of interest to find exact algorithms. By exploiting properties of the microstructure, we construct algorithms for solving instances of these problems with small domain sizes, and then, using a probabilistic reasoning, we show how to get algorithms for more general versions of the problems. The resulting algorithms have running times of O((0.585d)^n) for Max Value (d,2)-CSP, and O((0.503d)^n) for MaxInd (d,2)-CSP. Both algorithms represent the best known theoretical bounds for their respective problem, and, more importantly, the methods used are applicable to a wide range of optimisation problems. 

  • 106.
    Angelsmark, Ola
    et al.
    Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
    Thapper, Johan
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Algorithms for the Maximum Hamming Distance Problem2006In: Recent Advances in Constraints: Joint ERCIM/CoLogNet International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2004, Lausanne, Switzerland, June 23-25, 2004, Revised Selected and Invited Papers / [ed] Boi V. Faltings, Adrian Petcu, François Fages and Francesca Rossi, Springer Berlin/Heidelberg, 2006, p. 128-141Chapter in book (Refereed)
    Abstract [en]

    This book constitutes the thoroughly refereed and extended post-proceedings of the Joint ERCIM/CoLogNet International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2005, held in Uppsala, Sweden in June 2005.

    Besides papers taken from the workshop, others are submitted in response to an open call for papers after the workshop.

    The 12 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on global constraints, search and heuristics, language and implementation issues, and modeling.

  • 107.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Thapper, Johan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    New Algorithms for the Maximum Hamming Distance Problem2004In: Joint Annual Workshop of ERCIMCoLogNet on Constraint Solving and Constraint Logic Programming,2004, 2004, p. 271-285Conference paper (Refereed)
  • 108.
    Angelöv Petersson, Elina
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    Programmering som en problemlösningsmetod i ämnet matematik inom gymnasieskolan2018Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In 2017, the Swedish National Agency of Education introduced a new subject in the mathematics courses: Programming as a method of problem solving. Teachers have different opinions about the implementation of programming, because some teachers find it already difficult to catch up with the central content in the available time and fear that the introduction of this new subject will worsen the situation.The purpose of the study is to compile results from research literature on how programming as a problem solving method affects students’ ability to solve problems. The research question is ”How is the problem solving ability of students affected by the use of programming as a problem solving method in mathematics in upper secondary school?”.The method is a general literature study, where nine scientific articles are included in the sample.Teaching shall according to law be based on scientific research and proven experience. The literature study shows that research literature documents positive effects on problem solving ability programming as a problem solving method.

  • 109.
    Appleby, D.M.
    et al.
    Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada.
    Bengtsson, Ingemar
    Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden.
    Brierley, Stephen
    Heilbronn Institute for Mathematical Research, Department of Mathematics, University of Bristol, United Kingdom.
    Ericsson, Åsa
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Grassl, Markus
    Centre for Quantum Technologies, National University of Singapore, Singapore.
    Larsson, Jan-Åke
    Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, The Institute of Technology.
    Systems of Imprimitivity for the Clifford Group2014In: Quantum information & computation, ISSN 1533-7146, Vol. 14, no 3-4, p. 339-360Article in journal (Refereed)
    Abstract [en]

    It is known that if the dimension is a perfect square the Clifford group can be represented by monomial matrices. Another way of expressing this result is to say that when the dimension is a perfect square the standard representation of the Clifford group has a system of imprimitivity consisting of one dimensional subspaces. We generalize this result to the case of an arbitrary dimension. Let k be the square-free part of the dimension. Then we show that the standard representation of the Clifford group has a system of imprimitivity consisting of k-dimensional subspaces. To illustrate the use of this result we apply it to the calculation of SIC-POVMs (symmetric informationally complete positive operator valued measures), constructing exact solutions in dimensions 8 (hand-calculation) as well as 12 and 28 (machine-calculation).

  • 110.
    Arenas, FG
    et al.
    Univ Almeria, Fac Sci, Area Geometry & Topol, Almeria 04120, Spain Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    Chatyrko, VA
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Puertas, ML
    Univ Almeria, Fac Sci, Area Geometry & Topol, Almeria 04120, Spain Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    Transfinite extension of Steinke's dimension2000In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 88, no 1-2, p. 105-112Article in journal (Refereed)
    Abstract [en]

    We introduce a transfinite extension trt of dimension t from [10]. We extend all main theorems for t such as the sum theorems, the product theorem and the compactification theorem to the transfinite numbers. We also consider the class of all spaces X with trt (X) = omega(0), the so called finite-dimensional separated spaces [2], with respect to the usual classes of infinite-dimensional spaces.

  • 111.
    Arndt, Carl-Fredrik
    Linköping University, Department of Mathematics, Scientific Computing.
    Energy estimates and variance estimation for hyperbolic stochastic partial differentialequations2011Independent thesis Advanced level (professional degree), 30 credits / 45 HE creditsStudent thesis
    Abstract [en]

    In this thesis the connections between the boundary conditions and the vari- ance of the solution to a stochastic partial differential equation (PDE) are investigated. In particular a hyperbolical system of PDE’s with stochastic initial and boundary data are considered. The problem is shown to be well- posed on a class of boundary conditions through the energy method. Stability is shown by using summation-by-part operators coupled with simultaneous- approximation-terms. By using the energy estimates, the relative variance of the solutions for different boundary conditions are analyzed. It is concluded that some types of boundary conditions yields a lower variance than others. This is verified by numerical computations.

  • 112.
    Arnlind, Joakim
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Curvature and geometric modules of noncommutative spheres and tori2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 4, p. 041705-Article in journal (Refereed)
    Abstract [en]

    When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is the projection operator, projecting tangent vectors in the ambient space onto the tangent space of the submanifold. In this note, we point out that there exist noncommutative analogues of these projection operators, which implies a very natural definition of noncommutative tangent spaces as particular projective modules. These modules carry an induced connection from Euclidean space, and we compute its scalar curvature.

  • 113.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Al-Shujary, Ahmed
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Kahler-Poisson algebras2019In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 136, p. 156-172Article in journal (Refereed)
    Abstract [en]

    We introduce Kahler-Poisson algebras as analogues of algebras of smooth functions on Kahler manifolds, and prove that they share several properties with their classical counterparts on an algebraic level. For instance, the module of inner derivations of a Kahler-Poisson algebra is a finitely generated projective module, and allows for a unique metric and torsion-free connection whose curvature enjoys all the classical symmetries. Moreover, starting from a large class of Poisson algebras, we show that every algebra has an associated Kahler-Poisson algebra constructed as a localization. At the end, detailed examples are provided in order to illustrate the novel concepts. (C) 2018 Elsevier B.V. All rights reserved.

  • 114.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Anders
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces2016In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 134, p. 70-104Article in journal (Refereed)
    Abstract [en]

    We develop a framework for studying variational problems in Banach spaces with respect to gradient relations, which encompasses many of the notions of generalized gradients that appear in the literature. We stress the fact that our approach is not dependent on function spaces and therefore applies equally well to functions on metric spaces as to operator algebras. In particular, we consider analogues of Dirichlet and obstacle problems, as well as first eigenvalue problems, and formulate conditions for the existence of solutions and their uniqueness. Moreover, we investigate to what extent a lattice structure may be introduced on ( ordered) Banach spaces via a norm-minimizing variational problem. A multitude of examples is provided to illustrate the versatility of our approach. (C) 2015 Elsevier Ltd. All rights reserved.

  • 115.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Choe, Jaigyoung
    Korea Institute Adv Study, South Korea.
    Hoppe, Jens
    Royal Institute Technology, Sweden.
    Noncommutative Minimal Surfaces2016In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 106, no 8, p. 1109-1129Article in journal (Refereed)
    Abstract [en]

    We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass representation.

  • 116.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Grosse, Harald
    Mathematical Physics, Austria .
    Deformed noncommutative tori2012In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 53, no 7, p. 073505-Article in journal (Refereed)
    Abstract [en]

    We recall a construction of non-commutative algebras related to a one-parameter family of (deformed) spheres and tori, and show that in the case of tori, the *-algebras can be completed into C*-algebras isomorphic to the standard non-commutative torus. As the former was constructed in the context of matrix (or fuzzy) geometries, it provides an important link to the framework of non-commutative geometry, and opens up for a concrete way to study deformations of non-commutative tori. Furthermore, we show how the well-known fuzzy sphere and fuzzy torus can be obtained as formal scaling limits of finite-dimensional representations of the deformed algebras, and their projective modules are described together with connections of constant curvature.

  • 117.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Holm, Christoffer
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    A noncommutative catenoid2018In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 108, no 7, p. 1601-1622Article in journal (Refereed)
    Abstract [en]

    A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a Laplace operator from the connection and showing that the embedding coordinates are harmonic. Furthermore, an integral is defined and the total curvature is computed. Finally, classes of left and right modules are introduced together with constant curvature connections, and bimodule compatibility conditions are discussed in detail.

  • 118.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Hoppe, Jens
    Sogang University, South Korea .
    The world as quantized minimal surfaces2013In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 723, no 4-5, p. 397-400Article in journal (Refereed)
    Abstract [en]

    It is pointed out that the equations less thanbrgreater than less thanbrgreater thanSigma(d)(i=1)[X-i, [X-i, X-j]] = 0 less thanbrgreater than less thanbrgreater than(and its super-symmetrizations, playing a central role in M-theory matrix models) describe non-commutative minimal surfaces - and can be solved as such.

  • 119.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Hoppe, Jens
    Sogang University, South Korea .
    Huisken, Gerhard
    Max Planck Institute for Gravitational Physics, Germany .
    Multi-linear Formulation of Differential Geometry and Matris Regularizations2012In: Journal of differential geometry, ISSN 0022-040X, E-ISSN 1945-743X, Vol. 91, no 1, p. 1-39Article in journal (Refereed)
    Abstract [en]

    We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi-linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingartens formula, the Ricci curvature, and the Codazzi-Mainardi equations. For matrix analogues of embedded surfaces, we define discrete curvatures and Euler characteristics, and a non-commutative Gauss-Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of matrices representing the embedding coordinates, and explicit examples are provided. Furthermore, we illustrate the fact that techniques from differential geometry can carry over to matrix analogues by proving that a bound on the discrete Gauss curvature implies a bound on the eigenvalues of the discrete Laplace operator.

  • 120.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Huisken, Gerhard
    University of Tubingen, Germany.
    Pseudo-Riemannian Geometry in Terms of Multi-Linear Brackets2014In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 104, no 12, p. 1507-1521Article in journal (Refereed)
    Abstract [en]

    We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)Kahler geometry.

  • 121.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Kitouni, Abdennour
    Université de Haute-Alsace, France.
    Makhlouf, Abdenacer
    Université de Haute-Alsace, France.
    Silvestrov, Sergei
    Mälardalens Högskola, Västerås, Sweden.
    Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras2014In: ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS (AGMP), SPRINGER , 2014, Vol. 85, p. 123-144Conference paper (Refereed)
    Abstract [en]

    The aim of this paper is to compare the structure and the cohomology spaces of Lie algebras and induced 3-Lie algebras.

  • 122.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Wilson, Mitsuru
    University of Western Ontario, Canada.
    On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere2017In: JOURNAL OF GEOMETRY AND PHYSICS, ISSN 0393-0440, Vol. 111, p. 126-141Article in journal (Refereed)
    Abstract [en]

    We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere. (C) 2016 Elsevier B.V. All rights reserved.

  • 123.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Wilson, Mitsuru
    University of Western Ontario, Canada.
    Riemannian curvature of the noncommutative 3-sphere2017In: Journal of Noncommutative Geometry, ISSN 1661-6952, E-ISSN 1661-6960, Vol. 11, no 2, p. 507-536Article in journal (Refereed)
    Abstract [en]

    In order to investigate to what extent the calculus of classical (pseudo-) Riemannian manifolds can be extended to a noncommutative setting, we introduce pseudo-Riemannian calculi of modules over noncommutative algebras. In this framework, it is possible to prove an analogue of Levi-Civitas theorem, which states that there exists at most one torsion-free and metric connection for a given (metric) module, satisfying the requirements of a real metric calculus. Furthermore, the corresponding curvature operator has the same symmetry properties as the classical Riemannian curvature. As our main motivating example, we consider a pseudo-Riemannian calculus over the noncommutative 3-sphere and explicitly determine the torsion-free and metric connection, as well as the curvature operator together with its scalar curvature.

  • 124.
    Aronsson, Gunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Examples of infinity harmonic functions having singular lines2006Report (Other academic)
  • 125.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Five Geometric Principles for Injection Molding2003In: International polymer processing, ISSN 0930-777X, E-ISSN 2195-8602, Vol. 18, no 1, p. 91-94Article in journal (Refereed)
    Abstract [en]

    A condensed presentation of some results of a geometric character, concerning the injection molding of plastics, is given here. The author has derived these results from mathematical arguments and some simplifying assumptions, besides the usual Hele-Shaw flow conditions.

    The presentation here is intended for readers with an interest in polymer processing, rather than mathematics, so that the mathematical derivations are omitted in some cases, and sketchy in other cases. Instead we try to explain the results using figures, intuitive arguments and a few inevitable formulas. Since the experimental verification of the results is still very incomplete, we prefer to present them as proposed principles. Comments and suggestions for improvement are very welcome.

  • 126.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    INTERPOLATION UNDER A GRADIENT BOUND2009In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, ISSN 1446-7887, Vol. 87, no 1, p. 19-35Article in journal (Refereed)
    Abstract [en]

    This paper deals with the interpolation of given real boundary values into a bounded domain in Euclidean n-space, under a prescribed gradient bound. It is well known that there exist an upper solution (ail inf-convolution) and a lower solution (a sup-convolution) to this problem, provided that a certain compatibility condition is satisfied. If the upper and lower solutions coincide somewhere in the domain, then several interesting consequences follow. They are considered here. Basically, the upper and lower solutions must be regular wherever they coincide.

  • 127.
    Aronsson, Gunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Interpolation under a gradient bound and infimal convolutions2007Report (Other academic)
  • 128.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On certain minimax problems and Pontryagin’s maximum principle2010In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 37, no 1-2, p. 99-109Article in journal (Refereed)
    Abstract [en]

    This paper deals with minimax problems for nonlinear differential expressions involving a vector-valued function of a scalar variable under rather conventional structure conditions on the cost function. It is proved that an absolutely minimizing (i.e. globally and locally minimizing) function is continuously differentiable. A minimizing function is also continuously differentiable, provided a certain extra condition is satisfied. The variational method of V.G. Boltyanskii, developed within optimal control theory, is adapted and used in the proof. The case of higher order derivatives is also considered.

  • 129.
    Aronsson, Gunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On certain minimax problems and the Pontryagin maximum principle2008Report (Other academic)
    Abstract [en]

      

  • 130.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On Production Planning and Activity Periods2015Report (Other academic)
    Abstract [en]

    Consider a company which produces and sells a certain product on a market with highly variable demand. Since the demand is very high during some periods, the company will produce and create a stock in advance before these periods. On the other hand it costs money to hold a big stock, so that some balance is needed for optimum. The demand is assumed to be known in advance with sufficient accuracy. We use a technique from optimal control theory for the analysis, which leads to so-called activity periods. During such a period the stock is positive and the production is maximal, provided that the problem starts with zero stock, which is the usual case. Over a period of one or more years, there will be a few activity periods. Outside these periods the stock is zero and the policy is to choose production = the smaller of [demand, maximal production]. The “intrinsic time length” is a central concept. It is simply the maximal time a unit of the product can be stored before selling without creating a loss.

  • 131.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Production planning, activity periods and passivity periods2015Report (Other academic)
    Abstract [en]

    Consider a company which produces and sells a certain product on a market with highly variable demand. Since the demand is very high during some periods, the company will produce and create a stock in advance before these periods. On the other hand it costs money to hold a big stock, so that some balance is needed for optimum. The demand is assumed to be known in advance with sufficient accuracy. We use a technique from optimal control theory for the analysis, which leads to so-called activity periods. During such a period the stock is positive and the production is maximal, provided that the problem starts with zero stock, which is the usual case. Over a period of one or more years, there will be a few activity periods. Outside these periods the stock is zero and the policy is to choose production = the smaller of [demand, maximal production]. The “intrinsic time length” is a central concept. It is simply the maximal time a unit of the product can be stored before selling without creating a loss.

  • 132.
    Aronsson, Gunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Simulering av formfyllnadsförlopp vid formsprutning av plast enligt avståndsmodellen2004In: Workshop i tillämpad matematik,2004, 2004Conference paper (Other academic)
  • 133.
    Aronsson, Gunnar
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Barron, E.N.
    Loyola University of Chicago, IL 60660 USA .
    L-infinity Variational Problems with Running Costs and Constraints2012In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 65, no 1, p. 53-90Article in journal (Refereed)
    Abstract [en]

    Various approaches are used to derive the Aronsson-Euler equations for L-infinity calculus of variations problems with constraints. The problems considered involve holonomic, nonholonomic, isoperimetric, and isosupremic constraints on the minimizer. In addition, we derive the Aronsson-Euler equation for the basic L-infinity problem with a running cost and then consider properties of an absolute minimizer. Many open problems are introduced for further study.

  • 134.
    Aronsson, Gunnar
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Crandall, M.G.
    Department of Mathematics, Univ. of California, Santa Barbara, Santa Barbara, CA 93106.
    Juutinen, P.
    Department of Mathematics, P.O. Box 35, FIN-40014 Jyväskylä, Finland.
    A tour of the theory of absolutely minimizing functions2004In: Bulletin of the American Mathematical Society, ISSN 0273-0979, E-ISSN 1088-9485, Vol. 41, no 4, p. 439-505Article in journal (Refereed)
    Abstract [en]

    These notes are intended to be a rather complete and self-contained exposition of the theory of absolutely minimizing Lipschitz extensions, presented in detail and in a form accessible to readers without any prior knowledge of the subject. In particular, we improve known results regarding existence via arguments that are simpler than those that can be found in the literature. We present a proof of the main known uniqueness result which is largely self-contained and does not rely on the theory of viscosity solutions. A unifying idea in our approach is the use of cone functions. This elementary geometric device renders the theory versatile and transparent. A number of tools and issues routinely encountered in the theory of elliptic partial differential equations are illustrated here in an especially clean manner, free from burdensome technicalities - indeed, usually free from partial differential equations themselves. These include a priori continuity estimates, the Harnack inequality, Perron's method for proving existence results, uniqueness and regularity questions, and some basic tools of viscosity solution theory. We believe that our presentation provides a unified summary of the existing theory as well as new results of interest to experts and researchers and, at the same time, a source which can be used for introducing students to some significant analytical tools.

  • 135.
    Aronsson, Gunnar
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Crandall, Michael G
    Juutinen, Petri
    A Tour of the Theory of Absolutely Minimizing Functions2004Report (Other academic)
  • 136.
    Aronsson, Gunnar
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Crandall, Michael
    Mathematics University of California.
    Juutinen, Petri
    Mathematics University of Jyväskylä.
    A TOUR OF THE THEORY OF ABSOLUTELY MINIMIZING FUNCTIONS2004In: Bulletin of the American Mathematical Society, ISSN 0273-0979, E-ISSN 1088-9485, Vol. 41, no 4, p. 439-505Article in journal (Refereed)
    Abstract [en]

    A detailed analysis of the class of absolutely minimizing functions in Euclidean spaces and the relationship to the infinity Laplace equation

  • 137.
    Aronsson, Gunnar
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Evans, LC
    Linkoping Univ, Dept Math, Linkoping, Sweden Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA.
    An asymptotic model for compression molding2002In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 51, no 1Article in journal (Refereed)
    Abstract [en]

    We discuss an idealized model for compression molding, had by taking an asymptotic limit for highly non-Newtonian materials. We interpret the changing pressure distributions as being dictated by a Monge-Kantorovich mass transfer on a fast time scale, and thereby derive a nonlocal geometric law of motion for the air/plastic interface.

  • 138.
    Arques, Joakim
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Den interaktiva skrivtavlans effekt på elevattityder i matematikundervisning: En litteraturstudie om elevers inställning till den interaktiva skrivtavlan2018Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med denna litteraturstudie var att undersöka vilken effekt den interaktiva skrivtavlan har på elevattityder. De fyra elevattityderna som identifieras definierades med hjälp av Tapias (1996, 2004) arbete med Attitudes Towards Mathematics Instrument (ATMI), och fokuserar på vad elever tycker och känner om matematik.

    Litteraturstudien visar att elevernas attityder mot matematiken påverkas av användandet av en interaktiv skrivtavla i matematikundervisningen. Studien visar att två av fyra attityder påverkas positivt av den interaktiva skrivtavlan, en attityd visade otydliga effekter, och en attityd visade på en för liten effekt för att tillåta några slutsatser.

  • 139.
    Artal, Enrique
    et al.
    Univ Zaragoza, Spain.
    Costa, Antonio F.
    UNED, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Correction: Professor Maria Teresa Lozano and universal links (vol 87, pg 441, 1987)2018In: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 112, no 3, p. 621-621Article in journal (Other academic)
    Abstract [en]

    Unfortunatelly an erratum appears in the foreword of this volume.

    We claim that one of the authors of the article On universal groups and three-manifolds, Invent. Math. 87 (1987), no. 3, 441–456 is W. Witten. The correct name of this author is Wilbur Carrington Whitten. W. C. Whitten is not the father of the fields medallist E. Witten, as we claim there.

  • 140.
    Artal, Enrique
    et al.
    Univ Zaragoza, Spain.
    Costa, Antonio F.
    UNED, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Professor Maria Teresa Lozano and universal links2018In: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, Vol. 112, no 3, p. 615-620Article in journal (Other academic)
    Abstract [en]

    María Teresa, Maite, Lozano is a great person and mathematician, in these pages we can only give a very small account of her results trying to resemble her personality. We will focus our attention only on a few of the facets of her work, mainly in collaboration with Mike Hilden and José María Montesinos because as Maite Lozano pointed out in an international conference in Umeå University in June 2017, where she was a plenary speaker:

    I am specially proud of been part of the team Hilden-Lozano-Montesinos (H-L-M), and of our mathematical achievements

  • 141.
    Artal, Enrique
    et al.
    Departamento de Matemáticas, IUMA, Universidad de Zaragoza, C. Pedro Cerbuna 12, 50009 Zaragoza, Spain.
    Costa, Antonio F.Departamento de Matemáticas Fundamentales, UNED, Paseo Senda del Rey 9, 28040 Madrid, Spain.Izquierdo, MilagrosLinköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Special Issue: Dedicated to María Teresa Lozano conmemorating her 70th Birthday2018Collection (editor) (Refereed)
  • 142.
    Arwidsson, Anna-Karin
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Säberg, Clara
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Interaktiva skrivtavlor tar tid: En litteraturstudie om lärares erfarenheter av och förhållningssätt till interaktiva skrivtavlor med fokus på matematikundervisning2013Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Med bakgrund i läraryrkets professionaliseringsprocess, som bland annat efterlyser lärares reflekterande och utvärderande förhållningssätt i sin yrkesutövning, avser denna studie att sammanställa och redovisa lärares erfarenheter av och förhållningssätt till IST-användning främst inom ämnet matematik. Genom att studera andra lärares upplevelser av och förhållningssätt till sitt IST-användande kan man öka sitt egna medvetande. Denna litteraturstudie syftar därför till att öka medvetenheten om de interaktiva skrivtavlornas effekter för matematikundervisningen och lärarens arbete.

    Studiens resultat visar att de interaktiva skrivtavlorna kan bidra med flera positiva förändringar, men för att det ska bli konkreta effekter för lärarna och undervisningen måste en rad andra förändringar först ske. Den mest framträdande faktorn som framkommit i litteraturen är att lärarna upplever att de behöver få möjligheter till en utökad fortbildning och tid till att utveckla sina tekniska och pedagogiska kompetenser. Litteraturen pekar på att en fullgod fortbildning är avgörande för hur väl den interaktiva skrivtavlan kan integreras i undervisningen och för att lärare ska utveckla en säkerhet i att hantera verktyget.

  • 143.
    Asami-Johansson, Yukiko
    Linköping University, Department of Mathematics. Linköping University, Faculty of Educational Sciences.
    Designing Mathematics Lessons Using Japanese Problem Solving Oriented Lesson Structure: A Swedish case study2015Licentiate thesis, monograph (Other academic)
    Abstract [en]

    This licentiate thesis is concerned with applying the Japanese problem solving oriented (PSO) teaching approach to Swedish mathematics classrooms. The overall aim of my research project is to describe and investigate the viability of PSO as design tool for teaching mathematics. The PSO approach is a variation of a more general Japanese teaching paradigm referred to as “structured problem solving”. These teaching methods aim to stimulate the process of students’ mathematical thinking and have their focus on enhancing the students’ attitudes towards engaging in mathematical activities. The empirical data are collected using interviews, observations and video recordings over a period of nine months, following two Swedish lower secondary school classes. Chevallard’s anthropological framework is used to analyse which mathematical knowledge is exposed in the original Japanese lesson plans and in the lessons observed in the classrooms. In addition, Brousseau’s framework of learning mathematics is applied to analyse the perception of individual students and particular situations in the classroom.

    The results show that the PSO based lesson plans induce a complex body of mathematical knowledge, where different areas of mathematics are linked. It is found that the discrepancy between the Japanese and Swedish curriculum cause some limitations for the adaptation of the lesson plans, especially in the area of Geometry. Four distinct aspects of the PSO approach supporting the teaching of mathematics are presented.

  • 144.
    Asekritova, Irina
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Carro, Maria J.
    Univ Barcelona, Spain.
    Kruglyak, Natan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Soria, Javier
    Univ Barcelona, Spain.
    Rearrangement estimates for A(infinity) weights2019In: Revista Matemática Complutense, ISSN 1139-1138, E-ISSN 1988-2807, Vol. 32, no 3, p. 731-743Article in journal (Refereed)
    Abstract [en]

    We find a new characterizations of an A(infinity) weight omega, in terms of the decreasing rearrangement of the restriction of omega to cubes Q.

  • 145.
    Asekritova, Irina
    et al.
    Linnaeus University.
    Cerda, Joan
    University of Barcelona.
    Kruglyak, Natan
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    The Riesz-Herz equivalence for capacitary maximal functions2012In: REVISTA MATEMATICA COMPLUTENSE, ISSN 1139-1138, Vol. 25, no 1, p. 43-59Article in journal (Refereed)
    Abstract [en]

    We prove a Riesz-Herz estimate for the maximal function associated to a capacity C on a"e (n) , M (C) f(x)=sup (Qa andlt; x) C(Q)(-1)a andlt;andlt; (Q) |f|, which extends the equivalence (Mf)(au)(t)a parts per thousand integral f (auau)(t) for the usual Hardy-Littlewood maximal function Mf. The proof is based on an extension of the Wiener-Stein estimates for the distribution function of the maximal function, obtained using a convenient family of dyadic cubes. As a byproduct we obtain a description of the norm of the interpolation space (L(1), L(1,C))(1/p,p), where L(1), C denotes the Morrey space based on a capacity.

  • 146.
    Asekritova, Irina
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Cobos, Fernando
    Complutense University of Madrid.
    Kruglyak, Natan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Interpolation of Closed Subspaces and Invertibility of Operators2015In: Journal of Analysis and its Applications, ISSN 0232-2064, Vol. 34, no 2015, p. 1-15Article in journal (Refereed)
    Abstract [en]

    Let (Y0,Y1) be a Banach couple and let Xj be a closed complemented subspace of Yj, (j = 0,1). We present several results for the general problem of finding necessary and sufficient conditions on the parameters (θ, q) such that the real interpolation space (X0,X1)θ,q is a closed subspace of (Y0,Y1)θ,q. In particular, we establish conditions which are necessary and sufficient for the equality (X0,X1)θ,q = (Y0,Y1)θ,q, with the proof based on a previous result by Asekritova and Kruglyak on invertibility of operators. We also generalize the theorem by Ivanov and Kalton where this problem was solved under several rather restrictive conditions, such as that X1 = Y1 and X0 is a subspace of codimension one in Y0. 

  • 147.
    Asekritova, Irina
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Karlovich, Yuri
    University of Autonoma Estado Morelos, Mexico.
    Kruglyak, Natan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    One-sided invertibility of discrete operators and their applications2018In: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 92, no 1, p. 39-73Article in journal (Refereed)
    Abstract [en]

    For p is an element of [1, infinity], we establish criteria for the one-sided invertibility of binomial discrete difference operators A = aI - bV on the space l(p) = l(p)(Z), where a, b is an element of l(infinity), I is the identity operator and the isometric shift operator V is given on functions f. lp by (Vf)(n) = f (n+ 1) for all n is an element of Z. Applying these criteria, we obtain criteria for the one-sided invertibility of binomial functional operators A = aI - bU(alpha) on the Lebesgue space L-p(R+) for every p is an element of [1, infinity], where a, b is an element of L-infinity (R+), a is an orientation-preserving bi-Lipschitz homeomorphism of [0, +infinity] onto itself with only two fixed points 0 and infinity, and U-alpha is the isometric weighted shift operator on L-p(R+) given by U(alpha)f = (alpha)(1/p)(f circle alpha). Applications of binomial discrete operators to interpolation theory are given.

  • 148.
    Asekritova, Irina
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Kruglyak, Natan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Necessary and sufficient conditions for invertibility of operators in spaces of real interpolation2013In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 264, no 1, p. 207-245Article in journal (Refereed)
    Abstract [en]

    Let A be a bounded linear operator from a couple (X-0, X-1) to a couple (Y-0, Y-1) such that the restrictions of A on the end spaces X-0 and X-1 have bounded inverses defined on Y-0 and Y-1, respectively. We are interested in the problem of how to determine if the restriction of A on the space (X-0, XI)(theta,q) has a bounded inverse defined on the space (Y-0, Y-1)(theta,q). In this paper, we show that a solution to this problem can be given in terms of indices of two subspaces of the kernel of the operator A on the space X-0 + X-1.

  • 149.
    Asekritova, Irina
    et al.
    Växjö University.
    Kruglyak, Natan
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    The Besicovitch covering theorem and near-minimizers for the couple (L-2, BV)2010In: Proceedings of the Estonian Academy of Sciences, ISSN 1736-6046, E-ISSN 1736-7530, Vol. 59, no 1, p. 29-33Article in journal (Refereed)
    Abstract [en]

    Let Omega be a rectangle in R-2. A new algorithm for the construction of a near-minimizer for the couple (L-2 (Omega); BV(Omega)) is presented. The algorithm is based on the Besicovitch covering theorem and analysis of local approximations of the given function f is an element of L-2 (Omega).

  • 150.
    Asekritova, Irina
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Kruglyak, Natan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Mastylo, Mieczyslaw
    University of Poznan, Poland.
    Interpolation of Fredholm Operators2016In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 295, p. 421-496Article in journal (Refereed)
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