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  • 1.
    Axelsson, B.O.M.
    et al.
    Luleå tekniska universitet.
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Grönlund, Anders
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    Studies of the main cutting force at and near a cutting edge1993In: European Journal of Wood and Wood Products, ISSN 0018-3768, E-ISSN 1436-736X, Vol. 51, no 1, p. 43-48Article in journal (Refereed)
    Abstract [en]

    The present work is a study of how various parameters affect the cutting forces at, and near a cutting edge when cutting wood at full speed and with all cutting edges of the tool. Statistical methods from experimental results are used to develop a model

  • 2.
    Burtseva, Evgeniya
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Arctic University of Norwa.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Multi–dimensional Hardy type inequalities in Hölder spaces2018In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 12, no 3, p. 719-729Article in journal (Refereed)
    Abstract [en]

    Most Hardy type inequalities concern boundedness of the Hardy type operators in Lebesgue spaces. In this paper we prove some new multi-dimensional Hardy type inequalities in Hölder spaces.

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    fulltext
  • 3. Burtseva, Evgeniya
    et al.
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Potential type operators in PDEs and their applications2017In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1798, article id 020178Article in journal (Refereed)
    Abstract [en]

     We prove the boundedness of Potential operator in weighted generalized Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation in r3 with a free term in such a space. We also give a short overview of some typical situations when Potential type operators arise when solving PDEs.

  • 4.
    Euler, Marianna
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Euler, Norbert
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Reciprocal Bäcklund transformations of autonomous evolution equations2009In: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 159, no 3, p. 418-427Article in journal (Refereed)
  • 5.
    Euler, Marianna
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Euler, Norbert
    Lundberg, Staffan
    Reciprocal Bäcklund transformations of autonomous evolution equations2009In: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 159, no 3, p. 770-778Article in journal (Refereed)
    Abstract [en]

    We discuss the construction of reciprocal Bäcklund transformations for evolution equations using integrating factors of zeroth and higher orders with their corresponding conservation laws. As an example, we consider the Harry Dym equation and the Schwarzian KdV equation.

  • 6.
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Experimental investigations in wood machining related to cutting forces, sawdust gluing, and surface roughness1994Licentiate thesis, comprehensive summary (Other academic)
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    FULLTEXT01
  • 7.
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On adjoint symmetries and reciprocal Bäcklund transformations of evolution equations2009Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    The aim of this Licentiate Thesis is to discuss special transformations and so-called adjoint symmetries of nonlinear partial differential equations. Nonlinear partial differential equations play an important role in the description of many physical phenomena. In order to understand the phenomena, modelled by the equations mentioned above, it is therefore necessary to obtain and analyze the solutions and the conservation laws of these equations. In this Thesis we investigate some methods to obtain conservation laws and transformations between nonlinear partial differential equations and moreover to classify nonlinear partial differential equations with respect to those methods.The main emphasis is on adjoint symmetries and transformations of evolution equations. In particular we study the adjoint symmetries and the construction of reciprocal Bäcklund transformations for evolution equations.

    Download full text (pdf)
    FULLTEXT01
  • 8.
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On adjoint symmetries of a class of evolution equations2008Report (Other academic)
    Abstract [en]

    In this Paper we study the adjoint symmetries for a class of third-order evolution equations in (1+1) dimensions. We assume that the equations admit adjoint symmetries of maximum order 2, and we obtain the complete classification with respect to this property. Examples of adjoint symmetries and integrating factors for the Korteweg-de Vries and the Schwarzian-Korteweg-de Vries equations are given.

    Download full text (pdf)
    FULLTEXT01
  • 9.
    Lundberg, Staffan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On precise differentiation formula for weighted singular integrals of Sobolev functions2014In: 10th International conference on mathematical problems in engineering, aerosace and sciences: ICNPAA 2014 : Narvik, Norway, 15–18 July 2014 / [ed] Seenith Sivasundaram, Melville, NY: American Institute of Physics (AIP), 2014, p. 621-626Conference paper (Refereed)
    Abstract [en]

    In various applications there appear integral equations of the first kind with a kernel which has a logarithmic singularity. The corresponding classes of well-posedness for such equations are Sobolev spaces. We prove the differentiation formulas for weighted singular integrals, which appear in such study, with the goal of its further application to integral equations.

  • 10.
    Lundberg, Staffan
    Faculty of Science and Technology, Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, Narvik, Norway.
    Studies of some Operators of Harmonic Analysis in certain Function Spaces with Applications to PDEs2018Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The study in this PhD thesis aims at development of certain mathematical methods used in applications, in particular, in the study of regularity properties of solutions in various mathematical models described by Partial Differential Equations (PDEs). To this end, we study various operators of harmonic analysis in certain function spaces, since solutions to many PDEs may be expressed in terms of such operators.

    This PhD thesis consists of four papers (papers A–D) and an Introduction.

    In Paper A we introduce a version of weighted anisotropic mixed norm Morrey spaces and anisotropic Hardy operators. We derive conditions for boundedness of these operators in such spaces. We also reveal the role of these operators in the solving of some degenerate hyperbolic PDEs of some class.

    In Paper B we prove the boundedness of potential operators in weighted generalised Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Helmholtz equationin R3 with a free term in such a space. We also give a short overview of some typical situations when potential type operators arise when solving PDEs.

    In Paper C we study the boundedness of some multidimensional Hardy type operators in Hölder spaces and derive some new results of interest also in the theory of inequalities.

    In Paper D we prove some differentiation formulas for weighted singular integrals, which we suppose to apply in our future studies concerning the solution of some integral equations of the first kind.

    These new results are put into a more general frame in an Introduction, where also crucial parts of previous research by the candidate (e.g. published in two Licentiate theses) are briefly described. Note, in particular, that this PhD thesis may be regarded as a more theoretically based continuation of the Licentiate thesis in Wood Technology. This important link is carefully described in the Introduction.

  • 11.
    Lundberg, Staffan
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Grönlund, Anders
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    Axelsson, Bengt
    Luleå tekniska universitet.
    Cutting forces at and near a cutting edge1992In: Better wood products through science : All-Division 5 conference "Forest Products": All-Division 5 conference "Forest Products", Nancy, France, August 23 - 28, 1992, Nancy: ENGREF , 1992Conference paper (Refereed)
  • 12.
    Lundberg, Staffan
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Porankiewicz, B.
    Agriculture University of Pouznan.
    Erratum: Studies of non-contact methods for roughness measurements on wood surfaces1996In: European Journal of Wood and Wood Products, ISSN 0018-3768, E-ISSN 1436-736X, Vol. 54, p. 72-Article in journal (Other academic)
    Download full text (pdf)
    fulltext
  • 13.
    Lundberg, Staffan
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Porankiewicz,, Bolesław
    University of Zielona Góra, Agriculture University of Pouznan.
    Studies of non-contact methods for roughness measurements related to wood surfaces1995In: Akademia Rolnicza, Poznan. Roczniki. Mechaniczna Technologia Drewna, ISSN 0137-1800, Vol. 29/30, no 280, p. 71-78Article in journal (Refereed)
  • 14.
    Lundberg, Staffan
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, Natasha
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On some hyperbolic type equations and weighted anisotropic Hardy operators2017In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 40, no 5, p. 1414-1421Article in journal (Refereed)
    Abstract [en]

    We introduce a version of weighted anisotropic Morrey spaces and anisotropic Hardy operators. We find conditions for boundedness of these operators in such spaces. We also reveal the role of these operators in solving some classes of degenerate hyperbolic partial differential equations.

1 - 14 of 14
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