Institutt for matematikk og statistikk: Recent submissions

Now showing items 381-389 of 389

    • Large eddy simulation of homogeneous isotropic turbulence 

      Zeigler, Harald Bergersen (Master thesis; Mastergradsoppgave, 2008-06-02)
      The theme for the master thesis is simulation of homogeneous, isotropic turbulence. I have shown that the energy of the velocity field is decaying in time, but the comparison to the reference solution is however invalid, due to the fact that the reference solution may have scalings that are not obvious to the observer, and that my own simulation results seemed to behave quite strange, with a sudden ...

    • A quadratic reciprocity law for elliptic curves 

      Verdure, Hugues (Journal article; Tidsskriftartikkel; Peer reviewed, 2008)
      If E is an elliptic curve, then the Galois group of the extension generated by the n-torsion points acts on these points. We prove a quadratic reciprocity law involving this group action. This law is an extension of the usual quadratic reciprocity law.

    • Factorisation patterns of division polynomials 

      Verdure, Hugues (Journal article; Tidsskriftartikkel; Peer reviewed, 2004-05)
      The choice of an elliptic curve for the implementa- tion of an elliptic curve cryptosystem requires count- ing the number of points on such a curve over a fi- nite field. An improvement of Schoof’s algorithm for counting the number of rational points on an ellip- tic curve defined over a finite field takes advantage of some factor of the division polynomials. In this paper, we study the ...

    • Light induced forces on dielectric nanospheres 

      Lundamo, Trine (Master thesis; Mastergradsoppgave, 2008-02-15)
      Waves that are reflected and refracted by material bodies also transfer momentum to these bodies. This means that the wave field induces a force on the bodies, and multiple reflections between bodies induce forces between them. Light is an electromagnetic wave phenomenon, and the waves carry energy and momentum. Hence, any object that is scattering and refracting light is also acted upon by a ...

    • Differential invariants of the 2D conformal Lie algebra action 

      Høyem, Marte Rørvik (Master thesis; Mastergradsoppgave, 2008-02-15)
      In this thises we consider the Lie algebra that corresponds to the Lie pseudogroup of all conformal transformations on the plane. This conformal Lie algebra is canonically represented as a Lie algebra of vector fields on R^2. We will find all possible representations of vector fields in R^3=J^0R^2 which projects to the canonical representation and find the algebra of scalar differential invariants ...

    • A simple criterion for the m-cyclicity of the group of rational points on an elliptic curve defined over a finite field 

      Verdure, Hugues (Journal article; Tidsskriftartikkel; Peer reviewed, 2006-02)
      We give a simple criterion for the cyclicity of the m-torsion subgroup of the group of rational points on an elliptic curve defined over a finite field of characteristic larger than 3 for m = 2, 3, 4, 6, 12.

    • The use of elliptic curves in cryptography 

      Juhas, Tibor (Master thesis; Mastergradsoppgave, 2007-06)
      The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor Miller in 1985. Being a relatively new field, there is still a lot of ongoing research on the subject, but elliptic curve cryptography, or ECC for short, has already been implemented in real-life applications. Its strength was proved in 2003 when the U.S. National Security Agency adopted ECC for protecting ...

    • Hopf algebras and monoidal categories 

      Bakke, Tørris Koløen (Master thesis; Mastergradsoppgave, 2007-06-14)
      In this thesis we study the correspondence between categorical notions and bialgebra notions, and make a kind of dictionary and grammar book for translation between these notions. We will show how to obtain an antipode, and how to define braidings and quantizations. The construction is done in two ways. First we use the properties of a bialgebra to define a monoidal structure on (co)modules over ...

    • Nature reserves as a bioeconomic management tool. A simplified modeling approach 

      Flåten, Ola; Mjølhus, Einar (Working paper; Arbeidsnotat, 2006-02)
      This paper demonstrates analytically how a nature reserve may protect the total population, realize maximum sustainable yield (MSY), maximum economic yield (MEY) and consumer surplus (CS) and how this depends on biological growth, migration, reserve size and economic parameters. The pre-reserve population is assumed to follow the logistic growth law and two post-reserve growth models are discussed. ...