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  • 1.
    Abrahamsson, Olle
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    A Gröbner basis algorithm for fast encoding of Reed-Müller codes2016Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
    Abstract [en]

    In this thesis the relationship between Gröbner bases and algebraic coding theory is investigated, and especially applications towards linear codes, with Reed-Müller codes as an illustrative example. We prove that each linear code can be described as a binomial ideal of a polynomial ring, and that a systematic encoding algorithm for such codes is given by the remainder of the information word computed with respect to the reduced Gröbner basis. Finally we show how to apply the representation of a code by its corresponding polynomial ring ideal to construct a class of codes containing the so called primitive Reed-Müller codes, with a few examples of this result.

  • 2.
    Adamowicz, Tomasz
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Anders
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points2014In: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430, Vol. 31, no 6, p. 1131-1153Article in journal (Refereed)
    Abstract [en]

    We study various boundary and inner regularity questions for p(.)-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for p(.)-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded p(.)-harmonic functions and give some new characterizations of W-0(1,p(.)) spaces. We also show that p(.)-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.

  • 3.
    Adamowicz, Tomasz
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Anders
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Björn, Jana
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Shanmugalingam, Nageswari
    University of Cincinnati, OH USA .
    Prime ends for domains in metric spaces2013In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 238, p. 459-505Article in journal (Refereed)
    Abstract [en]

    In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Caratheodory and Nakki. Modulus ends and prime ends, defined by means of the p-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.

  • 4.
    Aghapournahr, Moharram
    et al.
    Arak University, Iran .
    Melkersson, Leif
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Artinianness of local cohomology modules2014In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 52, no 1, p. 1-10Article in journal (Refereed)
    Abstract [en]

    Some uniform theorems on the artinianness of certain local cohomology modules are proven in a general situation. They generalize and imply previous results about the artinianness of some special local cohomology modules in the graded case.

  • 5.
    Agwa, Mohamed
    et al.
    Department of Mechanical Design and Production Engineering, Faculty of Engineering, Zagazig Egypt.
    Andersson, Lars-Erik
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Pinto da Costa, Ant´onio
    Departamento de Engenharia Civil, Instituto Superior T´ecnico and ICIST, Universidade T´ecnica de Lisboa, Avenida Rovisco Pais, 1049 􀀀 001 Lisboa, Portugal.
    Critical bounds for discrete frictional incremental problems, rateproblems and wedging problems2012Conference paper (Other academic)
    Abstract [en]

    Summary. Questions of existence and uniqueness for discrete frictional quasi-static incremental problems, rate problems and wedging problems are discussed. Various methods to compute critical bounds for the coefficient of friction which guarantee existence and uniqueness are described, as well as the sharpness of the bounds and their interdependence.

  • 6.
    Aigner, Mats
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Tjatyrko, Vitalij A.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Nyagahakwa, Venuste
    National University of Rwanda, Rwanda .
    ON COUNTABLE FAMILIES OF SETS WITHOUT THE BAIRE PROPERTY2013In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 133, no 2, p. 179-187Article in journal (Refereed)
    Abstract [en]

    We suggest a method of constructing decompositions of a topological space X having an open subset homeomorphic to the space (R-n , tau), where n is an integer greater than= 1 and tau is any admissible extension of the Euclidean topology of R-n (in particular, X can be a finite-dimensional separable metrizable manifold), into a countable family F of sets (dense in X and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of F does not have the Baire property in X.

  • 7.
    Aigner, Mats
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Tjatyrko, Vitalij
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Nyagahakwa, Venuste
    National University of Rwanda, Rwanda.
    THE ALGEBRA OF SEMIGROUPS OF SETS2015In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 116, no 2, p. 161-170Article in journal (Refereed)
    Abstract [en]

    We study the algebra of semigroups of sets (i.e. families of sets closed under finite unions) and its applications. For each n greater than 1 we produce two finite nested families of pairwise different semigroups of sets consisting of subsets of R" without the Baire property.

  • 8.
    Amankwah, Henry
    et al.
    University of Cape Coast, Ghana .
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Open-pit mining with uncertainty: A conditional value-at-risk approach2013In: Optimization Theory, Decision Making, and Operations Research Applications: Proceedings of the 1st International Symposium and 10th Balkan Conference on Operational Research / [ed] Athanasios Migdalas, Angelo Sifaleras, Christos K. Georgiadis, Jason Papathanasiou, Emmanuil Stiakakis, New York: Springer, 2013, p. 117-139Conference paper (Refereed)
    Abstract [en]

    The selection of a mine design is based on estimating net present values of all possible, technically feasible mine plans so as to select the one with the maximum value. It is a hard task to know with certainty the quantity and quality of ore in the ground. This geological uncertainty and also the future market behavior of metal prices and foreign exchange rates, which are always uncertain, make mining a high risk business. Value-at-Risk (VaR) is a measure that is used in financial decisions to minimize the loss caused by inadequate monitoring of risk. This measure does, however, have certain drawbacks such as lack of consistency, nonconvexity, and nondifferentiability. Rockafellar and Uryasev [J. Risk 2, 21-41 (2000)] introduce the Conditional Value-at-Risk (CVaR) measure as an alternative to the VaR measure. The CVaR measure gives rise to a convex optimization problem. An optimization model that maximizes expected return while minimizing risk is important for the mining sector as this will help make better decisions on the blocks of ore to mine at a particular point in time. We present a CVaR approach to the uncertainty involved in open-pit mining. We formulate investment and design models for the open-pit mine and also give a nested pit scheduling model based on CVaR. Several numerical results based on our models are presented by using scenarios from simulated geological and market uncertainties.

  • 9. Andersson, Carina
    et al.
    Losand, Elin
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Att uppleva räta linjer och grafer – erfarenheter från ett forskningsprojekt2015In: Nämnaren 2014:4, no 1, p. 21-27Article in journal (Other (popular science, discussion, etc.))
  • 10.
    Andersson, Jonathan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Asymptotic behavior and effective boundaries forage-structured population models in aperiodically changing environment2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Human activity and other events can cause environmental changes to the habitat of organisms. The environmental changes effect the vital rates for a population. In order to predict the impact of these environmental changes on populations, we use two different models for population dynamics. One simpler linear model that ignores environmental competition between individuals and another model that does not. Our population models take into consideration the age distribution of the population and thus takes into consideration the impact of demographics. This thesis generalize two theorems, one for each model, developed by Sonja Radosavljevic regarding long term upper and lower bounds of a population with periodic birth rate ; see [6] and [5]. The generalisation consist in including the case where the periodic part of the birth rate can be expressed with a finite Fourier series and also infinite Fourier series under some constraints. The old theorems only considers the case when the periodic part of the birth rate can be expressed with one cosine term. From the theorems we discover a connection between the frequency of oscillation and the effect on population growth. From this derived connection we conclude that periodical changing environments can have both positive and negative effects on the population.

  • 11.
    Andersson, Lars-Erik
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Critical bounds for frictional rate- and wedging problems2010Conference paper (Other academic)
  • 12.
    Andersson, Lars-Erik
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Existence and uniqueness for thermoelastic contact2013In: Encyclopedia of Thermal Stresses / [ed] Hetnarski, Richard B., Springer, 2013, p. -6643Chapter in book (Other academic)
    Abstract [en]

    The Encyclopedia of Thermal Stresses is an important interdisciplinary reference work.  In addition to topics on thermal stresses, it contains entries on related topics, such as the theory of elasticity, heat conduction, thermodynamics, appropriate topics on applied mathematics, and topics on numerical methods. The Encyclopedia is aimed at undergraduate and graduate students, researchers and engineers. It brings together well established knowledge and recently received results. All entries were prepared  by leading experts from all over the world, and are presented in an easily accessible format. The work is lavishly illustrated, examples and applications are given where appropriate, ideas for further development abound, and the work will challenge many students and researchers to pursue new results of their own. This work can also serve as a one-stop resource for all who need succinct, concise, reliable and up to date information in short encyclopedic entries, while the extensive references will be of interest to those who need further information. For the coming decade, this is likely to remain the most extensive and authoritative work on Thermal Stresses

  • 13.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Barber, J R.
    University of Michigan, MI USA.
    Ahn, Y-J
    Samsung SDI Central Research Centre, South Korea.
    Attractors in Frictional Systems Subjected to Periodic Loads2013In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 73, no 3, p. 1097-1116Article in journal (Refereed)
    Abstract [en]

    This paper explores the effect of initial conditions on the behavior of coupled frictional elastic systems subject to periodic loading. Previously, it has been conjectured that the long term response will be independent of initial conditions if all nodes slip at least once during each loading cycle. Here, this conjecture is disproved in the context of a simple two-node system. Counter examples are presented of “unstable” steady-state orbits that repel orbits starting from initial conditions that are sufficiently close to the steady state. The conditions guaranteeing stability of such steady states are shown to be more restrictive than those required for the rate problem to be uniquely solvable for arbitrary derivative of the external loading. In cases of instability, the transient orbit is eventually limited either by slip occurring at both nodes simultaneously, or by one node separating. In both cases a stable limit cycle is obtained. Depending on the slopes of the constraint lines, the limit cycle can involve two periods of the loading cycle, in which case it appears to be unique, or it may repeat every loading cycle, in which case distinct limit cycles are reached depending on the sign of the initial deviation from the steady state. In the case of instability an example is given of a loading for which a quasi-static evolution problem with multiple solutions exists, whereas all rate problems are uniquely solvable.

  • 14.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Barber, J. R.
    University of Michigan, MI 48109 USA.
    Ponter, A. R. S.
    University of Leicester, England.
    Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions2014In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 51, no 21-22, p. 3710-3714Article in journal (Refereed)
    Abstract [en]

    We consider the class of two or three-dimensional discrete contact problems in which a set of contact nodes can make frictional contact with a corresponding set of rigid obstacles. Such a system might result from a finite element discretization of an elastic contact problem after the application of standard static reduction operations. The Coulomb friction law requires that the tractions at any point on the contact boundary must lie within or on the surface of a friction cone, but the exact position of any stuck node (i.e., a node where the tractions are strictly within the cone) depends on the initial conditions and/or the previous history of loading. If the long-term loading is periodic in time, we anticipate that the system will eventually approach a steady periodic cycle. Here we prove that if the elastic system is uncoupled, meaning that changes in slip displacements alone have no effect on the instantaneous normal contact reactions, the time-varying terms in this steady cycle are independent of initial conditions. In particular, we establish the existence of a unique permanent stick zone T comprising the set of all nodes that do not slip after some finite number of cycles. We also prove that the tractions and slip velocities at all nodes not contained in T approach unique periodic functions of time, whereas the (time-invariant) slip displacements in T may depend on initial conditions. Typical examples of uncoupled systems include those where the contact surface is a plane of symmetry, or where the contacting bodies can be approximated locally as half spaces and Dundurs mismatch parameter beta = 0. An important consequence of these results is that systems of this kind will exhibit damping characteristics that are independent of initial conditions. Also, the energy dissipated at each slipping node in the steady state is independent of initial conditions, so wear patterns and the incidence of fretting fatigue failure should also be so independent.

  • 15.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Pinto da Costa, A.
    University of Lisbon, Portugal.
    Agwa, M. A.
    Zagazig University, Egypt.
    Existence and uniqueness for frictional incremental and rate problems - sharp critical bounds2016In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 96, no 1, p. 78-105Article in journal (Refereed)
    Abstract [en]

    We investigate frictional contact problems for discrete linear elastic structures, in particular the quasistatic incremental problem and the rate problem. It is shown that sharp conditions on the coefficients of friction for unique solvability of these problems are the same. We also give explicit expressions of these critical bounds by using a method of optimization. For the case of two spatial dimensions the conditions are formulated as a huge set of non symmetric eigenvalue problem. A computer program for solving these problems was designed and used to compute the critical bounds for some structures of relative small size, some of which appeared in the literature. The results of a variety of numerical experiments with uniform and non uniform distributions of the frictional properties are presented. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

  • 16.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Stewart, Neil F.
    Université de Montréal, Montréal, Canada.
    Introduction to the Mathematics of Subdivision Surfaces2010Book (Other academic)
    Abstract [en]

    Subdivision surfaces permit a designer to specify the approximate form of a surface defining an object and to refine and smooth the form to obtain a more useful or attractive version of the surface.

    A considerable amount of mathematical theory is required to understand the characteristics of the resulting surfaces, and this book

    • provides a careful and rigorous presentation of the mathematics underlying subdivision surfaces as used in computer graphics and animation, explaining the concepts necessary to easily read the subdivision literature;

    • organizes subdivision methods into a unique and unambiguous hierarchy to facilitate insight and understanding;

    • gives a broad discussion of the various methods and is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points.

    Introduction to the Mathematics of Subdivision Surfaces is excellent preparation for reading more advanced texts that delve more deeply into special questions of regularity. The authors provide exercises and projects at the end of each chapter. Course material, including solutions to the exercises, is available on an associated Web page.

  • 17.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Global search strategies for solving multilinear least-squares problems2012In: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, no 1, p. 12-21Article in journal (Refereed)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

  • 18.
    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.

  • 19.
    Appleby, D.M.
    et al.
    Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada.
    Bengtsson, Ingemar
    Stockholm University, Sweden .
    Brierley, Stephen
    University of Bristol, UK.
    Ericsson, Åsa
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Grassl, Markus
    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).

  • 20.
    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.

  • 21.
    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.

  • 22.
    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.

  • 23.
    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.

  • 24.
    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.

  • 25.
    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.

  • 26.
    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.

  • 27.
    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.

  • 28.
    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.

  • 29.
    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.

  • 30.
    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.

  • 31.
    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.

  • 32.
    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.

  • 33.
    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. 

  • 34.
    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.

  • 35.
    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.

  • 36.
    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)
  • 37.
    Ashjari, Hoda
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Jablonka, Eva
    Luleå tekniska universitet, Luleå.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Recognizing texts in undergraduate mathematics2012In: Proceedings 36th Conference of the International Group for the Psychology of Mathematics Education: Opportunities to Learn in Mathematics Education, Taipei-Taiwan, July 18-22, 2012. / [ed] Tso, T.Y., Department of Mathematics, National Taiwan Normal University; Taiwan Association of Mathematics Education , 2012, p. 4-245-Conference paper (Refereed)
    Abstract [en]

    Findings from interviews investigating how Swedish first year engineering students recognize undergraduate mathematics texts as being more or less “mathematical”. The results indicate a relation between the students’ understanding of the principles for knowledge classification and their success in their mathematics studies.

  • 38.
    Asratian, Armen
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Casselgren, Carl Johan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. University of Southern Denmark, Denmark.
    Solution of Vizings Problem on Interchanges for the case of Graphs with Maximum Degree 4 and Related Results2016In: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 82, no 4, p. 350-373Article in journal (Refereed)
    Abstract [en]

    Let G be a Class 1 graph with maximum degree 4 and let t amp;gt;= 5 be an integer. We show that any proper t-edge coloring of G can be transformed to any proper 4-edge coloring of G using only transformations on 2-colored subgraphs (so-called interchanges). This settles the smallest previously unsolved case of a well-known problem of Vizing on interchanges, posed in 1965. Using our result we give an affirmative answer to a question of Mohar for two classes of graphs: we show that all proper 5-edge colorings of a Class 1 graph with maximum degree 4 are Kempe equivalent, that is, can be transformed to each other by interchanges, and that all proper 7-edge colorings of a Class 2 graph with maximum degree 5 are Kempe equivalent. (C) 2015 Wiley Periodicals, Inc.

  • 39.
    Asratian, Armen
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Casselgren, Carl Johan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Petrosyan, Petros A.
    Yerevan State University, Armenia; National Academic Science, Armenia.
    Some results on cyclic interval edge colorings of graphs2018In: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 87, no 2, p. 239-252Article in journal (Refereed)
    Abstract [en]

    A proper edge coloring of a graph G with colors 1,2,,t is called a cyclic interval t-coloring if for each vertex v of G the edges incident to v are colored by consecutive colors, under the condition that color 1 is considered as consecutive to color t. We prove that a bipartite graph G of even maximum degree (G)4 admits a cyclic interval (G)-coloring if for every vertex v the degree dG(v) satisfies either dG(v)(G)-2 or dG(v)2. We also prove that every Eulerian bipartite graph G with maximum degree at most eight has a cyclic interval coloring. Some results are obtained for (a,b)-biregular graphs, that is, bipartite graphs with the vertices in one part all having degree a and the vertices in the other part all having degree b; it has been conjectured that all these have cyclic interval colorings. We show that all (4, 7)-biregular graphs as well as all (2r-2,2r)-biregular (r2) graphs have cyclic interval colorings. Finally, we prove that all complete multipartite graphs admit cyclic interval colorings; this proves a conjecture of Petrosyan and Mkhitaryan.

    The full text will be freely available from 2018-05-30 12:31
  • 40.
    Auscher, Pascal
    et al.
    Département de Mathématiques d’Orsay, Université Paris-Sud et UMR 8628 du CNRS, Orsay Cedex, France.
    Rosén, Andreas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Weighted maximal regularity estimates and solvability of non-smooth elliptic systems, II2012In: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206X, Vol. 5, no 5, p. 983-1061Article in journal (Refereed)
    Abstract [en]

    We continue the development, by reduction to a first-order system for the conormal gradient, of L2a priori estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence-form second-order complex elliptic systems. We work here on the unit ball and more generally its bi-Lipschitz images, assuming a Carleson condition as introduced by Dahlberg which measures the discrepancy of the coefficients to their boundary trace near the boundary. We sharpen our estimates by proving a general result concerning a priori almost everywhere nontangential convergence at the boundary. Also, compactness of the boundary yields more solvability results using Fredholm theory. Comparison between classes of solutions and uniqueness issues are discussed. As a consequence, we are able to solve a long standing regularity problem for real equations, which may not be true on the upper half-space, justifying a posteriori a separate work on bounded domains.

  • 41.
    Auscher, Pascal
    et al.
    Université Paris-Sud, France.
    Rosén, Andreas
    Chalmers University, Sweden.
    Rule, David
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Boundary value problems for degenerate elliptic equations and systems2015In: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, E-ISSN 1873-2151, Vol. 48, no 4, p. 951-1000Article in journal (Refereed)
  • 42.
    Avdonin, Sergey
    et al.
    University of Alaska Fairbanks, USA.
    Kozlov, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Stability estimate for an inverse problem in glaciology2012In: Analysis and Mathematical Physics, ISSN 1664-2368, E-ISSN 1664-235X, Vol. 2, no 4, p. 367-387Article in journal (Refereed)
    Abstract [en]

    We consider the problem of reconstruction of the basal velocity of a glacier by measurements of the velocity on glacier’s surface. The main result is a stability estimate in a near-surface region, which represents a multiplicative inequality and shows that small errors in measurements produce small errors in the velocity in this region.

  • 43.
    Balla, Ulrika
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Implementering av programmering i matematik åk 7-9: En litteraturstudie om tre olika programmeringsspråks lämplighet i olika matematikområden2018Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Hösten 2018 inrättas det en ny version av läroplanen från 2011 med mer fokus på programmering. Syftet med denna litteraturstudie är att sammanställa forskningslitteraturens resultat om olika programmeringsspråks lämplighet för högstadiets matematikundervisning, samt lämpliga matematikområden. Frågeställningarna jämför tre programmeringsspråk med avseende på deras lämplighet och för- och nackdelar i matematikundervisningen. Programmeringsspråken, som jämförs, är Scratch, Python och VBA (Visual Basics of Application, programmering i Microsofts kalkylprogram Excel). Litteraturstudiens resultat visar att Scratch och Python anses vara lämpliga för nybörjare och är utvecklade för att de ska vara lätta att lära sig och förstå medan VBA är det programmeringsspråk som är utvecklat för att utföra matematiska beräkningar med.

    Programmeringsspråken kan användas i matematikundervisningen på likvärdiga sätt och i de flesta matematikområdena beroende på elevernas kompetens och lärarens val av uppgifter och tillvägagångssätt. Vidare är det möjligt att eleverna kan bli mer motiverade till att lära sig matematik om de har tillgång till digitala hjälpmedel eller programmering inom matematikundervisningen

  • 44.
    Banda, Adson
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Half–Exact Coherent Functors over PIDs and Dedekind Domains2016Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    The focus of this thesis is to characterize half–exact coherent functors over principal ideal domains (PIDs) and Dedekind domains. Ever since they where discovered, coherent functors have been useful in the study of some mathematical objects. We aim to explore a little more about them in this thesis.

    We first give here a review of the general categorical notions relevant to the characterization. We also review the functors Ext(M,−) and Tor(M,−)  on the category on A–modules, where A is a commutative ring and M is an A–module.

    With the assumption that A is a commutative noetherian ring, we introduce coherent functors defined on the category of finitely generated A–modules. It is then shown in the paper that any half–exact coherent functor over a PID, and more generally over a Dedekind domain, arises from a complex of projective modules.

  • 45.
    Bang-Jensen, Jorgen
    et al.
    University of Southern Denmark, Denmark.
    Casselgren, Carl Johan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Restricted cycle factors and arc-decompositions of digraphs2015In: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 193, p. 80-93Article in journal (Refereed)
    Abstract [en]

    We study the complexity of finding 2-factors with various restrictions as well as edge-decompositions in (the underlying graphs of) digraphs. In particular we show that it is N P-complete to decide whether the underlying undirected graph of a digraph D has a 2-factor with cycles C-1, C-2, ..., C-k such that at least one of the cycles C-i is a directed cycle in D (while the others may violate the orientation back in D). This solves an open problem from J. Bang-Jensen et al., Vertex-disjoint directed and undirected cycles in general digraphs, JCT B 106 (2014), 1-14. Our other main result is that it is also N P-complete to decide whether a 2-edge-colored bipartite graph has two edge-disjoint perfect matchings such that one of these is monochromatic (while the other does not have to be). We also study the complexity of a number of related problems. In particular we prove that for every even k greater than= 2, the problem of deciding whether a bipartite digraph of girth k has a k-cycle-free cycle factor is N P-complete. Some of our reductions are based on connections to Latin squares and so-called avoidable arrays.

  • 46.
    Barletta, Giuseppina
    et al.
    University of Mediterranea Reggio Calabria, Italy.
    Cianchi, Andrea
    University of Florence, Italy.
    Mazya, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. RUDN University, Russia.
    Quasilinear elliptic equations on noncompact Riemannian manifolds2017In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 273, no 11, p. 3426-3462Article in journal (Refereed)
    Abstract [en]

    The existence of solutions to a class of quasilinear elliptic problems on noncompact Riemannian manifolds, with finite volume, is investigated. Boundary value problems, with homogeneous Neumann conditions, in possibly irregular Euclidean domains are included as a special instance. A nontrivial solution is shown to exist under an unconventional growth condition on the right-hand side, which depends on the geometry of the underlying manifold. The identification of the critical growth is a crucial step in our analysis, and entails the use of the isocapacitary function of the manifold. A condition involving its isoperimetric function is also provided. (C) 2017 Elsevier Inc. All rights reserved.

  • 47.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F.
    Departamento Matematicas Fundamentales, UNED, Madrid, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On automorphisms groups of cyclic p-gonal Riemann surfaces2013In: Journal of symbolic computation, ISSN 0747-7171, E-ISSN 1095-855X, Vol. 57, p. 61-69Article in journal (Refereed)
    Abstract [en]

    In this work we obtain the group of conformal and anticonformal automorphisms of real cyclic p-gonal Riemann surfaces, where p⩾3p⩾3 is a prime integer and the genus of the surfaces is at least (p−1)2+1(p−1)2+1. We use Fuchsian and NEC groups, and cohomology of finite groups.

  • 48.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F.
    Departamento de Matematicas Fundamentales, UNED, Madrid, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On isolated strata of pentagonal Riemann surfaces in the branch locus of moduli spaces2012In: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, Vol. 572, p. 19-24Article in journal (Refereed)
  • 49.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F.
    Departamento de Matematicas Fundamentales, UNED, Madrid, Spain.
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    On isolated strata of p-gonal Riemann surfaces in the branch locus of moduli spaces2012In: Albanian Journal of Mathematics, ISSN 1930-1235, E-ISSN 1930-1235, Vol. 6, p. 11-19Article in journal (Refereed)
  • 50.
    Bartolini, Gabriel
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Costa, Antonio F.
    UNED, Spain .
    Izquierdo, Milagros
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    ON THE CONNECTIVITY OF BRANCH LOCI OF MODULI SPACES2013In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, no 1, p. 245-258Article in journal (Refereed)
    Abstract [en]

    The moduli space M-g of compact Riemann surfaces of genus g has orbifold structure and the set of singular points of the orbifold is the branch locus B-g. In this article we show that B-g is connected for genera three, four, thirteen, seventeen, nineteen and fiftynine, and disconnected for any other genus. In order to prove this we use Fuchsian groups, automorphisms of order 5 and 7 of Riemann surfaces, and calculations with GAP for some small genera.

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