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Träfflista för sökning "AMNE:(NATURAL SCIENCES Mathematics Discrete Mathematics) "

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  • Asratian, Armen S., et al. (författare)
  • Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs
  • 2009
  • Ingår i: Journal of Graph Theory. - : Wiley Periodicals Inc.. - 0364-9024 .- 1097-0118. ; 61:2, s. 88-97
  • Tidskriftsartikel (refereegranskat)abstract
    • An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph.
  • 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.
  • 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.
  • Kiselman, Christer, 1939- (författare)
  • Functions on discrete sets holomorphic in the sense of Ferrand, or monodiffric functions of the second kind
  • 2008
  • Ingår i: Science in China Series A. - 1006-9283 .- 1862-2763. ; 51:4, s. 604-619
  • Tidskriftsartikel (refereegranskat)abstract
    • We study the class of functions called monodiffric of the second kind by Isaacs. They are discrete analogues of holomorphic functions of one or two complex variables. Discrete analogues of the Cauchy-Riemann operator, of domains of holomorphy in one discrete variable, and of the Hartogs phenomenon in two discrete variables are investigated. Two fundamental solutions to the discrete Cauchy-Riemann equation are studied: one with support in a quadrant, the other with decay at infinity. The first is easy to construct by induction; the second is accessed via its Fourier transform.
  • 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.
  • Andrén, Lina J., 1980- (författare)
  • Avoidability by Latin squares of arrays of even order
  • Annan publikation (övrigt vetenskapligt)abstract
    • We prove that for any k and any 2k × 2k array A such that no cell in A contains more than   k/2550 symbols, and no symbol occurs more than k/2550 times in any row or column, there is a Latin square such that no 2550cell in the Latin square contains a symbol that occurs in the corresponding cell in A. This proves a conjecture of Häggkvist [8] in the special case of arrays with even side.
  • Andrén, Lina J., 1980- (författare)
  • Avoidability of random arrays
  • Annan publikation (övrigt vetenskapligt)abstract
    • An n×n array that in each cell contains a subset of the symbols 1, . . . , n is avoidable if there exists a Latin square of order n such that no cell in the Latin square contains a symbol which belongs to the set of symbols in the corresponding cell of the array. Some results on deterministic conditions for avoidability of arrays have been found, but here we study the problem of having an array with randomly assigned subsets of C in its cells. This is equivalent to the problem of list-edge-coloring  with randomly assigned lists from the set {1, . . . , n}. We show that an array where each symbol appears in each cell with probability p will be avoidable with very high probability even if p is such that the expected number of symbols forbidden in each cell is slightly higher than what deterministic theorems can prove is avoidable.
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