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  • 1. Avdonina, Elena D.
    et al.
    Ibragimov, Nail H.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Heat conduction in anisotropic media: Nonlinear self-adjointness and conservation laws2012In: Discontinuity, Nonlinearity and Complexity, ISSN 2164-6376, Vol. 1, no 3, p. 237-251Article in journal (Refereed)
    Abstract [en]

    Nonlinear self-adjointness of the anisotropic nonlinear heat equation is investigated. Mathematical models of heat conduction in anisotropic media with a source are considered and a class of self-adjoint models is identified. Conservation laws corresponding to the symmetries of the equations in question are computed.

  • 2. Gosson, Maurice de
    On the classical and quantum evolution of Lagrangian half-forms in phase space1999In: ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE, ISSN 0246-0211, p. 547-573Article in journal (Refereed)
    Abstract [en]

    The local expressions of a Lagrangian half-form on a quantized Lagrangian submanifold of phase space are the wavefunctions of quantum mechanics. We show that one recovers Maslov's asymptotic formula for the solutions to Schrodinger's equation if one transports these half-forms by the flow associated with a Hamiltonian H. We then consider the case when the Hamiltonian flow is replaced by the flow associated with the Bohmian, and are led to the conclusion that the use of Lagrangian half-forms leads to a quantum mechanics on phase space. (C) Elsevier, Paris.

  • 3. Gosson, Maurice de
    On the notion of phase in mechanics2004In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, p. 7297-7314Article in journal (Refereed)
    Abstract [en]

    The notion of phase plays an essential role in both semiclassical and quantum mechanics. But what is exactly a phase, and how does it change with time? It turns out that the most universal definition of a phase can be given in terms of Lagrangian manifolds by exploiting the properties of the Poincare-Cartan form. Such a phase is defined, not in configuration space, but rather in phase-space and is thus insensitive to the appearance of caustics. Surprisingly enough, this approach allows us to recover the Heisenberg-Weyl formalism without invoking commutation relations for observables.

  • 4. Gosson, Maurice de
    Phase Space Quantization and the Uncertainty Principle,2003In: Physics Letters : Section A, ISSN 0375-9601 , Vol. 317, no 5-6, p. 365-369Article in journal (Refereed)
    Abstract [en]

    We replace the usual heuristic notion of quantum cell by that of 'quantum blob', which does not depend on the dimension of phase space. Quantum blobs, which are defined in terms of symplectic capacities, are canonical invariants. They allow us to prove an exact uncertainty principle for semiclassically quantized Hamiltonian systems. (C) 2003 Elsevier B.V. All rights reserved.

  • 5. Gosson, Maurice de
    Symplectic quantam cells and Wigner and Husimi functions2005In: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, Vol. 129, no 3, p. 211-226Article in journal (Refereed)
    Abstract [en]

    We propose a definition of quantum cells which is invariant under symplectic transformations. We use this notion to the study of positivity properties of the Wigner and Husimi functions, which allows us to precise and to improve known results. © 2004 Elsevier SAS. Tous droits réservés.

  • 6. Gosson, Maurice de
    The cohomological interpretation of the indices of Robbin and Salamon.2003In: Mathematical Physics Studies, ISSN 0921-3767 , Vol. NA, no 4Article in journal (Refereed)
    Abstract [en]

    22 : The cohomological interpretation of the indices of Robbin and Salamon, (with S. de Gosson), Jean Leray ´99 Conference Proceedings, Math. Phys. Studies 4, Kluwer Academic Press, 2003

  • 7. Gosson, Maurice de
    The Optimal Pure Gaussian State Canonically Associated to a Gaussian Quantum State2004In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 330, no 3-4, p. 161-167Article in journal (Refereed)
    Abstract [en]

    We show, using the symplectically invariant notion of 'quantum blob', that it is possible to attach a canonical optimal Gaussian pure state to an arbitrary quantum state. When at least one pair of conjugate variables satisfies the minimum uncertainty condition, then the associated Gaussian is uniquely determined up to an overall phase factor. (C) 2004 Elsevier B.V. All rights reserved

  • 8. Gosson, Maurice de
    The Principles of Classical and Quantum Mechanics2002In: Hardcover / [ed] cientific, World, London-Singapore: Imperial College Press , 2002Chapter in book (Other academic)
    Abstract [en]

    This book is devoted to a symplectic approach of classical and quantum mechanics

  • 9. Gosson, Maurice de
    et al.
    Gosson, Serge de
    Symplectic Path Intersections and the Leray Index2001Conference paper (Refereed)
    Abstract [en]

    We define a Maslov index for symplectic paths by using the properties of Leray's index for pairs of Lagrangian paths. Our constructions are purely topological, and the index we define satisfies a simple system of five axioms. The fifth axiom establishes a relation between the spectral flow of a family of symmetric matrices and the Maslov index

  • 10. Gosson, Maurice de
    et al.
    Gosson, Serge de
    The cohomological interpretationof the indices of Robbin and Salamon2003In: Karlskrona Conference in the Honor of Jean Leray / [ed] Gosson, M. de, Dordrecht: Kluwer , 2003Chapter in book (Other academic)
    Abstract [en]

    We compare the indices of Robbin, salöamon, and McDuff with the cohomological index defined by Leray and extended by the author

  • 11. Gosson, Maurice de
    et al.
    Gosson, Serge de
    The Cohomological Meaning of Maslov's Lagrangian Path Intersection Index1999Conference paper (Refereed)
    Abstract [en]

    We study the relation between the complete Maslov index defined by Leray and the author, and the Lagrangian path intersection index defined by Robbin and Salamon, and used by McDuff and Salamon in their study of symplectic topology.

  • 12. Gosson, Maurice de
    et al.
    Gosson, Serge de
    The Maslov Index of Periodic Hamiltonian Orbits2003In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 36, no 48, p. 615-622Article in journal (Refereed)
    Abstract [en]

    we study the Maslov index of the monodromy matrix of periodic Hamiltonian orbit, extending substantially results of other authors

  • 13. Lennerstad, Håkan
    Commensurable and rational triangles2007Report (Other academic)
    Abstract [en]

    One may ask which property the equilateral, the right isosceles, the half equilateral, and the two golden triangles, with angles (π/5),((2π)/5),((2π)/5) and (π/5),(π/5),((3π)/5), have in common. One answer is that their angles are commensurable with each other -- such triangles are commensurable. We investigate properties of this class of triangles, which is a countable subset of the entire class of triangles -- we do not distinguish between similar triangles. It can naturally be endowed with a family structure by integer triples. The equilateral is the only member of the first generation, and the other triangles mentioned above populate the first generations. A formula for the number of non-similar triangles that can be formed by triples of corners in a regular n-polygon is calculated, which gives the number of commensurable triangles at each generation. Three "metatriangles" are described -- so called because each possible triangle is represented as a point in each of them. The set of right triangles form a height in one of the metatriangles. The eye is the point of a metatriangle in the same metatriangle. In the second part of this report, triangles are studied by side length. A rational triangle is a triangle where all sides and all heights are rational numbers. We show that the right rational triangles are the Pythagorean triangles, and each non-right rational triangle consists of two Pythagorean triangles. Almost all triangles are irrational. It turns out that no Pythagorean triangle is commensurable. We prove that the only triangle with commensurable angles and also commensurable sides is the equilateral triangle.

  • 14. Lennerstad, Håkan
    The directional display1997Conference paper (Refereed)
    Abstract [en]

    The directional display contains and shows several images-which particular image is visible depends on the viewing direction. This is achieved by packing information at high density on a surface, by a certain back illumination technique, and by explicit mathematical formulas which eliminate projection deformations and make it possible to automate the production of directional displays. The display is illuminated but involves no electronic components. Patent is pending for the directional display. Directional dependency of an image can be used in several ways. One is to achieve three-dimensional effects. In contrast to that of holograms, large size and full color involve no problems. Another application of the technique is to show moving sequences. Yet another is to make a display more directionally independent than conventional displays. It is also possible and useful in several contexts to show different text in different directions with the same display. The features can be combined.

  • 15.
    Lennerstad, Håkan
    Blekinge Institute of Technology, Department of Telecommunications and Mathematics.
    The Geometry of the Directional Display1996Report (Refereed)
    Abstract [en]

    The directional display is a new kind of display which can contain and show several images -which particular image is visible depends on the viewing direction. This is achieved by packing information at high density on a surface, by a certain back illumination technique, and by explicit mathematical formulas which make it possible to automatize the printing of a display to obtain desired effects. The directional dependency of the display can be used in several different ways. One is to achieve three-dimensional effects. In contrast to that of holograms, large size and full color here involve no problems. Another application of the basic technique is to show moving sequences. Yet another is to make a display more directionally independent than today’s displays. Patent is pending for the invention in Sweden.

  • 16.
    Lennerstad, Håkan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    The n -dimensional Stern-Brocot tree2019In: International Journal of Number Theory, ISSN 1793-0421Article in journal (Refereed)
    Abstract [en]

    This paper generalizes the Stern-Brocot tree to a tree that consists of all sequences of n coprime positive integers. As for n = 2, each sequence P is the sum of a specific set of other coprime sequences, its Stern-Brocot set B(P), where |B(P)| is the degree of P. With an orthonormal base as the root, the tree defines a fast iterative structure on the set of distinct directions in ℤ+n and a multiresolution partition of S+n-1. Basic proofs rely on a matrix representation of each coprime sequence, where the Stern-Brocot set forms the matrix columns. This induces a finitely generated submonoid SB(n, ℕ) of SL(n, ℕ), and a unimodular multidimensional continued fraction algorithm, also generalizing n = 2. It turns out that the n-dimensional subtree starting with a sequence P is isomorphic to the entire |B(P)|-dimensional tree. This allows basic combinatorial properties to be established. It turns out that also in this multidimensional version, Fibonacci-type sequences have maximal sequence sum in each generation. © 2019 World Scientific Publishing Company.

  • 17.
    Lennerstad, Håkan
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    The n-dimensional Stern-Brocot tree2012Report (Other academic)
    Abstract [en]

    The n-dimensional Stern-Brocot tree consists of all sequences (p₁, ...,p_{n}) of positive integers with no common multiple. The relatively prime sequences can be generated branchwise from each other by simple vector summation, starting with an ON-base, and controlled by a generalized Euclidean algorithm.The tree induces a multiresolution partition of the first quadrant of the (n-1)-dimensional unit sphere, providing a direction approximation property of a sequence by its ancestors. Two matrix representations are introduced, where in both a matrix contains the parents of a sequence. From one of them the isomorphism of a subtree to the entire tree of dimension equal to the number of parents of the top sequence follows. A form of Fibonacci sequences turn out to be the sequences of fastest growing sums. The construction can be regarded an n-dimensional continued fraction, and it may invite further n-dimesional number theory.

  • 18.
    Vu, Viet Thuy
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Electrical Engineering.
    Sjögren, Thomas
    Blekinge Institute of Technology, School of Engineering, Department of Electrical Engineering.
    Pettersson, Mats
    Blekinge Institute of Technology, School of Engineering, Department of Electrical Engineering.
    Ground Moving Target Detection and Estimation with Different Sar Linear Flight Tracks2013Conference paper (Refereed)
    Abstract [en]

    The paper proposes a groundmoving target detection and estimation method aiming at UltraWide Band and -Beam (UWB) Synthetic Aperture Radar (SAR) systems. The method is developed on the moving target detection by focusing technique and requires a SAR system flying with two different linear flight tracks. The method allows us to detect ground moving target, even hidden by clutter, and to estimate the target parameters such as speed and direction of motion. The accuracy of the estimations depends strongly on the computational cost and can therefore be controlled.

  • 19.
    Vu, Viet Thuy
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Electrical Engineering.
    Sjögren, Thomas
    Blekinge Institute of Technology, School of Engineering, Department of Electrical Engineering.
    Pettersson, Mats
    Blekinge Institute of Technology, School of Engineering, Department of Electrical Engineering.
    Phase Error Calculation for Fast Time-Domain Bistatic SAR Algorithms2013In: IEEE Transactions on Aerospace and Electronic Systems, ISSN 0018-9251, E-ISSN 1557-9603, Vol. 49, no 1, p. 631-639Article in journal (Refereed)
    Abstract [en]

    In synthetic aperture radar (SAR) processing, there is a trade-off between accuracy and speed. The approximations in an algorithm help to increase the algorithm’s speed but cause deterministic phase errors which directly affect the SAR image quality. This paper discusses the phase error calculations for bistatic fast backprojection (BiFBP) and bistatic fast factorized backprojection (BiFFBP) which are essential for setting their parameters. The phase error calculation principle for bistatic SAR in comparison to monostatic SAR is presented. This principle is used to derive the maximum phase error equation.

  • 20.
    Vu, Viet Thuy
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Sjögren, Thomas
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Pettersson, Mats
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    SAR Imaging in Ground Plane Using Fast Backprojection for Mono- and Bistatic Cases2012Conference paper (Refereed)
    Abstract [en]

    The paper discusses the possibilities to reconstruct an illuminated Synthetic Aperture Radar (SAR) scene in a ground plane instead of a slant-range plane using Fast Backprojection (FBP) algorithm. Hence, two methods to reconstruct a SAR scene in a ground plane are introduced in this paper. The methods are then considered to be extended for bistatic cases where the formation of a SAR scene in a ground plane is highly recommended. The proposals are examined with simulated SAR data and the simulation results indicate that rebuilding a SAR scene in a ground plane using FBP is possible.

  • 21.
    Vu, Viet Thuy
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Electrical Engineering.
    Sjögren, Thomas
    Blekinge Institute of Technology, School of Engineering, Department of Electrical Engineering.
    Pettersson, Mats
    Blekinge Institute of Technology, School of Engineering, Department of Electrical Engineering.
    Minardi, Michael
    The Availability ff Fast Time-Domain Algorithms for Circular Sar Data Processing2012Conference paper (Refereed)
    Abstract [en]

    The paper shows an investigation of the availability of the fast time-domain algorithms to process data collected by synthetic aperture radar systems with circular apertures (CSAR). In the investigation, the reconstruction of CSAR images from data is suggested to be in a ground plane instead of a slant-range plane. The Fast Backprojection (FBP) algorithms are considered to examine the availability of time-domain algorithms for CSAR data processing. However, the availability is also applied to the Fast Factorized Backprojection (FFBP) algorithms. The simulated CSAR data with respect to the CARABAS-II parameters is used.

1 - 21 of 21
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