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  • Kurujyibwami, Celestin (författare)
  • Admissible transformations and the group classification of Schrödinger equations
  • 2017
  • Doktorsavhandling (övrigt vetenskapligt)abstract
    • We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. The first is the construction of the new theory of uniform seminormalized classes of differential equations and its application to solving group classification problems for these classes. Point transformations connecting two equations (source and target) from the class under study may have special properties of semi-normalization. This makes the group classification of that class using the algebraic method more involved. To extend this method we introduce the new notion of uniformly semi-normalized classes. Various types of uniform semi-normalization are studied: with respect to the corresponding equivalence group, with respect to a proper subgroup of the equivalence group as well as the corresponding types of weak uniform semi-normalization. An important kind of uniform semi-normalization is given by classes of homogeneous linear differential equations, which we call uniform semi-normalization with respect to linear superposition of solutions.The class of linear Schrödinger equations with complex potentials is of this type and its group classification can be effectively carried out within the framework of the uniform semi-normalization. Computing the equivalence groupoid and the equivalence group of this class, we show that it is uniformly seminormalized with respect to linear superposition of solutions. This allow us to apply the version of the algebraic method for uniformly semi-normalized classes and to reduce the group classification of this class to the classification of appropriate subalgebras of its equivalence algebra. To single out the classification cases, integers that are invariant under equivalence transformations are introduced. The complete group classification of linear Schrödinger equations is carried out for the cases n = 1 and n = 2.The second aim is to study group classification problem for classes of generalized nonlinear Schrödinger equations which are not uniformly semi-normalized. We find their equivalence groupoids and their equivalence groups and then conclude whether these classes are normalized or not. The most appealing classes are the class of nonlinear Schrödinger equations with potentials and modular nonlinearities and the class of generalized Schrödinger equations with complex-valued and, in general, coefficients of Laplacian term. Both these classes are not normalized. The first is partitioned into an infinite number of disjoint normalized subclasses of three kinds: logarithmic nonlinearity, power nonlinearity and general modular nonlinearity. The properties of the Lie invariance algebras of equations from each subclass are studied for arbitrary space dimension n, and the complete group classification is carried out for each subclass in dimension (1+2). The second class is successively reduced into subclasses until we reach the subclass of (1+1)-dimensional linear Schrödinger equations with variable mass, which also turns out to be non-normalized. We prove that this class is mapped by a family of point transformations to the class of (1+1)-dimensional linear Schrödinger equations with unique constant mass.
  • Emamizadeh, B., et al. (författare)
  • Optimal harvesting strategy based on rearrangements of functions
  • 2018
  • Ingår i: Applied Mathematics and Computation. - Amsterdam : Elsevier. - 0096-3003 .- 1873-5649. ; 320, s. 677-690
  • Tidskriftsartikel (refereegranskat)abstract
    • We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum harvesting capacity. For this generalization, we need a completely different approach. As such, we use the theory of rearrangements of functions. We prove existence of solutions, and obtain an optimality condition which indicates that the more aggressive harvesting must be pushed toward the boundary of the domain. Furthermore, we prove that radial and Steiner symmetries of the domain are preserved by the solutions. We will also devise an algorithm for numerical solution of the problem, and present the results of some numerical experiments. © 2017 Elsevier Inc.
  • Brattström, Gudrun (författare)
  • Leonardo da Pisa : Inger Christensen och Fibonacci
  • 2008
  • Ingår i: Lyrikvännen. - 0460-0762. ; 55:6, s. 33-38
  • Tidskriftsartikel (populärvet., debatt m.m.)abstract
    • Den danska poeten Inger Christensen byggde sin diktsamling Alfabet på Fibonaccis talserie. Artikeln är en kort historisk essä över Fibonacci, och beskriver även hur talserien är konstruerad.
  • Eriksson, Kimmo, et al. (författare)
  • Optimal Expected Rank in a Two-Sided Secretary Problem
  • 2007
  • Ingår i: Operations Research. - 0030-364X .- 1526-5463. ; 55:5, s. 921-931
  • Tidskriftsartikel (refereegranskat)abstract
    • In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.
  • Eriksson, T., et al. (författare)
  • Successive Encoding of Correlated Sources
  • 1982
  • Rapport (övrigt vetenskapligt)abstract
    • The encoding of a discrete memoryless multiple source  for reconstruction of a sequence  with  is considered. We require that the encoding should be such that  is encoded first without any consideration of  , while in a seeond part of the encoding this latter sequence is encoded based on knowledge of the outcome of the first encoding. The resulting scheme is called successive encoding. We find general outer and inner bounds for the corresponding set of achievable rates along with a complete single letter characterization for the special case  . Comparisons with the Slepian-Wolf problem [3] and the Ahlswede-Körner-Wyner side information problem [2 ], [9) are carried out.
  • Feng, Bin, et al. (författare)
  • An Improved RRT Based Path Planning with Safe Navigation
  • 2014
  • Ingår i: Proceedings from the 2013 International Symposium on Vehicle, Mechanical, and Electrical Engineering, ISVMEE 2013, Taiwan, China, 21-22 December. - 9783038350033 ; , s. 1080-1083
  • Konferensbidrag (refereegranskat)abstract
    • Path planning has been a crucial problem in robotics research. Some algorithms, such as Probabilistic Roadmaps (PRM) and Rapidly-exploring Random Trees (RRT), have been proposed to tackle this problem. However, these algorithms have their own limitations when applying in a real-world domain, such as RoboCup Small-Size League (SSL) competition. This paper raises a novel improvement to the existing RRT algorithm to make it more applicable in real-world.
  • Izquierdo, Milagros, 1963-, et al. (författare)
  • Isometric Point-Circle Configurations on Surfaces from Uniform Maps
  • 2016
  • Ingår i: Springer Proceedings in Mathematics and Statistics. - : Springer-Verlag New York. - 2194-1009. ; 159, s. 201-212, s. 201-212
  • Tidskriftsartikel (refereegranskat)abstract
    • We embed neighborhood geometries of graphs on surfaces as point-circle configurations. We give examples coming from regular maps on surfaces with a maximum number of automorphisms for their genus, and survey geometric realization of pentagonal geometries coming from Moore graphs. An infinite family of point-circle v4'>v4v4 configurations on p-gonal surfaces with two p-gonal morphisms is given. The image of these configurations on the sphere under the two p-gonal morphisms is also described.
  • Lundow, Per Håkan, et al. (författare)
  • 2008
  • Ingår i: LMS Journal of Computation and Mathematics. - : Cambridge University Press. - 1461-1570 .- 1461-1570. ; 11, s. 1-14
  • Tidskriftsartikel (refereegranskat)abstract
    • The aim of this paper is to extend the previous work on transfer matrix compression in the case of graph homomorphisms. For H-homomorphisms of lattice-like graphs we demonstrate how the automorphisms of H, as well as those of the underlying lattice, can be used to reduce the size of the relevant transfer matrices. As applications of this method we give currently best known bounds for the number of 4- and 5-colourings of the square grid, and the number of 3- and 4-colourings of the three-dimensional cubic lattice. Finally, we also discuss approximate compression of transfer matrices.
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