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  • 1.
    Hedberg, Claes
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Martinet, Philippe
    Non-linear dynamics in granular materials2007In: The universality of nonclassical nonlinearity, with applications to / [ed] Paolo, Pier, New York: Springer , 2007, p. 327-336Chapter in book (Other academic)
    Abstract [en]

    This book comes as a result of the research work developed in the framework of two large international projects: the European Science Foundation (ESF) supported program NATEMIS (Nonlinear Acoustic Techniques for Micro-Scale Damage Diagnostics) (of which Professor Delsanto was the European coordinator, 2000-2004) and a Los Alamos-based network headed by Dr. P.A. Johnson. The main topic of both programs and of this book is the description of the phenomenology, theory and applications of nonclassical Nonlinearity (NCNL). In fact NCNL techniques have been found in recent years to be extremely powerful (up to more than 1000 times with respect to the corresponding linear techniques) in a wide range of applications, including Elasticity, Material Characterization, Ultrasonics, Geophysics to Maintenance and Restoration of artifacts (paintings, stone buildings, etc.). The book is divided into three parts: Part I - defines and describes the concept of NCNL and its universality and reviews several fields to which it may apply; Part II - describes the phenomenology, theory, modelling and virtual experiments (simulations); Part III -discusses some of the most relevant experimental techniques and applications.

  • 2.
    Ibragimov, Nail H.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Approximate transformation groups2008Book (Other academic)
    Abstract [en]

    These notes provide an easy to follow introduction to the topic and are based on my talks at various conferences, in particular on the plenary lecture at the International Workshop on ``Differential equations and chaos" (University of Witwatersrand, Johannesburg, South Africa, January 1996). The book is prepared for the new graduate course ``Approximate transformation groups" that will be given at Blekinge Institute of Technology during January-March, 2009.

  • 3.
    Ibragimov, Nail H.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Archives of ALGA: volume 92012Collection (editor) (Other academic)
    Abstract [en]

    Volume 9 contains articles of different authors.

  • 4.
    Ibragimov, Nail H.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Integration of second-order linear equations via linearization of Riccati's equations2007In: Archives of ALGA, ISSN 1652-4934, Vol. 4, p. 71-75Article in journal (Refereed)
    Abstract [en]

    The test for linearization of the Riccati equations by a change of the dependent variable, proved by the author in 1989, is utilized for integration of second-order linear equations by quadratures.

  • 5.
    Ibragimov, Nail H.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Selected works. Volume 42009Book (Other academic)
    Abstract [en]

    Volume IV contains papers written during 1996-2007. The main topics in this volume include Equivalence groups and invariants of differential equations, Extension of Eulers’ method of integration of hyperbolic equations to parabolic equations, Invariant and formal Lagrangians, Conservation laws.

  • 6.
    Ibragimov, Nail H.
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Computer Algebra Programs in Group Analysis and Education2006Conference paper (Refereed)
    Abstract [en]

    Lie group analysis provides a universal tool for tackling considerable numbers of differential equations even when other means of integration fail. In fact, group analysis is the only effective method for solving nonlinear differential equations analytically. However the philosophy of Lie groups in the theory of differential equations did not enjoy widespread acceptance in the past and the subject has been neglected in university programs. One of the main aims of ALGA is to improve the situation by developing courses based on group analysis. But the problem is that calculation of symmetries is a lengthy process and this can scare students. The calculation can be simplified by using computer algebra packages. We started to use one of them for teaching engineering students at BTH. This project was supported by STINT, Swedish Foundation for International Cooperation in Research and Higher Education.

  • 7.
    Ibragimov, Nail H.
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Thidé, Bo
    Adjoint systems and conservation laws for symmetrized electromagnetic equations with a dual Ohm´s law2006In: Archives of ALGA, ISSN 1652-4934, Vol. 3Article in journal (Refereed)
  • 8.
    Ibragimov, Nail H.
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Thidé, Bo
    Conservation laws for symmetrised electromagnetic equations with a dual Ohm's law2007Conference paper (Refereed)
    Abstract [en]

    In all areas of physics, conservation laws are essential since they allow us to draw conclusions of our physical system under study in an indirect but efficient way. Electrodynamics, in terms of the standard Maxwell electromagnetic equations for fields in vacuum, exhibit a rich set of symmetries to which conserved quantities are associated. We have derived conservation laws for Dirac's symmetric version of the Maxwell-Lorentz microscopic equations, allowing magnetic charges and magnetic currents, where the latter, just as electric currents, are assumed to be described by a linear relationship between the field and the current, i.e. an Ohm's law. We find that when we use the method of Ibragimov to construct the conservation laws, they will contain two new adjoint vector fields which fulfil Maxwell-like equations. In particular, we obtain conservation laws for the electromagnetic field which are nonlocal in time.

  • 9.
    Ibragimov, Nail H.
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Thidé, Bo
    Conservation laws for the Maxwell-Dirac equations with dual Ohm's law2007In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, no 5Article in journal (Refereed)
    Abstract [en]

    Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov [J. Math. Anal. Appl. 333, 311-320 (2007)], we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and magnetic charges obey linear conductivity laws (dual Ohm's law). We find that this linear system allows for conservation laws which are nonlocal in time. (c) 2007 American Institute of Physics.

  • 10.
    Ibragimov, Nail H.
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Thidé, Bo
    Then, H.
    Sjöholm, J.
    Palmer, K.
    Bergman, J.
    Carozzi, T.D.
    Istomin, YaN
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Utilization of photon orbital angular momentum in the low-frequency radio domain2007In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 99, no 8Article in journal (Refereed)
    Abstract [en]

    We show numerically that vector antenna arrays can generate radio beams that exhibit spin and orbital angular momentum characteristics similar to those of helical Laguerre-Gauss laser beams in paraxial optics. For low frequencies (1 GHz), digital techniques can be used to coherently measure the instantaneous, local field vectors and to manipulate them in software. This enables new types of experiments that go beyond what is possible in optics. It allows information-rich radio astronomy and paves the way for novel wireless communication concepts.

  • 11.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Self-Adjointness and Quasi-Self-Adjointness of the Magma Equation2008Conference paper (Refereed)
    Abstract [en]

    A recent theorem on nonlocal conservation laws is applied to a magma equation modelling a melt migration through the Earth´s mantle. It is shown that the equation in question is quasi-self-adjoint. The self-adjoint equations are singled out. Nonlocal and local conservation densities are obtained using the symmetries of the magma equation.

  • 12.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Symmetries and conservation laws2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided. Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws. One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed.

  • 13.
    Lennerstad, Håkan
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Matematikens dubbelnatur –undflyende innehåll,självtillräckligt språk2005In: Utbildning och Demokrati, ISSN 1102-6472, E-ISSN 2001-7316, Vol. 14, no 2, p. 27-55Article in journal (Refereed)
    Abstract [en]

    This article discusses the role in mathematics of its formal language, here called Mathematish. This language became significant when symbolic mathematics gradually replaced rhetoric mathematics. Mathematics gained in efficiency and calculation became dominant. It is claimed that this happened on the expense of mathematical interpretation, except for those who intuitively understand Mathematish. It is also claimed by linguistic arguments that the structure of a language isnaturally non-articulated for intuitive learners, often teachers, while teaching requires articulation. Languages are often excluding. Therelationship between content and language in mathematics is described from several viewpoints. Three distinct types of mathematical knowl-edge are suggested: 1. How to successfully use Mathematish rules, 2. Mathematish rules (computer programmable grammar), 3. Ideas and meanings of mathematics, e.g. applications and metaphors. Non-formal ways of hinting mathematical ideas and meanings, shedding light on both Mathematish and content, are suggested.

  • 14.
    Nyqvist, Robert
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Asymptotic behaviour of numbers of cycles of dynamical systems in finite fields2007In: Proceedings of the Jangjeon Mathematical Society, ISSN 1598-7264, Vol. 10, no 1, p. 1-6Article in journal (Refereed)
  • 15.
    Rakus-Andersson, Elisabeth
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Complementary Solutions in Diagnostic Models2007In: Studies in Fuzziness and Soft Computing, ISSN 1434-9922, E-ISSN 1860-0808, Vol. 212, p. 63-91Article in journal (Refereed)
    Abstract [en]

    We should admit that the case of patient P1 in Ex. 3.16 has not been very easy to solve especially when you consider the proper interpretation of PD3. By equipping us with equal values of the membership degrees it has not made it easy enough to make the proper choice of an unknown diagnosis. © 2007 Springer.

  • 16.
    Rakus-Andersson, Elisabeth
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Jogréus, Claes
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    The Choquet and Sugeno Integrals as Measures of Total Effectiveness of Medicines2007Conference paper (Refereed)
    Abstract [en]

    The concepts of the Choquet and Sugeno integrals, based on a fuzzy measure, can be adopted as useful tools in estimation of the total effectiveness of a drug when appreciating its positive influence on a collection of symptoms typical of a considered diagnosis. The expected effectiveness of the medicine is evaluated by a physician as a verbal expression for each distinct symptom. By converting the words at first to fuzzy sets and then numbers we can regard the effectiveness structures as measures in the Choquet and Sugeno problem formu-lations. After comparing the quantities of total effectiveness among medicines, expressed as the values of the Choquet or Sugeno integrals, we accomplish the selection of the most efficacious drug.

  • 17.
    Rakus-Andersson, Elisabeth
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Zettervall, Hang
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Erman, Maria
    Blekinge Institute of Technology, School of Engineering, Department of Signal Processing.
    Prioritisation of weighted strategies in multiplayer games with fuzzy entries of the payoff matrix2010In: International Journal of General Systems, ISSN 0308-1079, E-ISSN 1563-5104, Vol. 39, no 3, p. 291-304Article in journal (Refereed)
    Abstract [en]

    We explore the classical model of a two-player game to select the best strategies, where action is expected to maintain the values of a certain variable on the neutral level. By inserting fuzzy sets as payoff values in the game matrix, we facilitate the procedure of formulations of payoff expectations by players. Instead of making inconvenient decisions about the choice of accurate numerical entries of the matrix, the players are able to use words, which should simplify communication between them when designing the preliminaries of the game. The players also have the possibility of making a ranking of their favourite strategies. At the next stage of the play, we involve group decision-making in order to aggregate results coming from several paired games, when more than two players contradict each other.

  • 18.
    Rudenko, Oleg
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Hedberg, Claes
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science. Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering. Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences. Blekinge Institute of Technology, Department of Telecommunications and Mathematics.
    A new equation and exact solutions describing focal fields in media with modular nonlinearity2017In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 89, no 3, p. 1905-1913Article in journal (Refereed)
    Abstract [en]

    Brand-new equations which can be regarded as modifications of Khokhlov–Zabolotskaya–Kuznetsov or Ostrovsky–Vakhnenko equations are suggested. These equations are quite general in that they describe the nonlinear wave dynamics in media with modular nonlinearity. Such media exist among composites, meta-materials, inhomogeneous and multiphase systems. These new models are interesting because of two reasons: (1) the equations admit exact analytic solutions and (2) the solutions describe real physical phenomena. The equations model nonlinear focusing of wave beams. It is shown that inside the focal zone a stationary waveform exists. Steady-state profiles are constructed by the matching of functions describing the positive and negative branches of exact solutions of an equation of Klein–Gordon type. Such profiles have been observed many times during experiments and numerical studies. The non-stationary waves can contain singularities of two types: discontinuity of the wave and of its derivative. These singularities are eliminated by introducing dissipative terms into the equations—thereby increasing their order. © 2017 The Author(s)

1 - 18 of 18
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