Institutt for matematikk og statistikk: Nye registreringer
Viser treff 381-394 av 394
-
Dynamics and entropy in the Zhang model of Self-Organized Criticality
(Working paper; Arbeidsnotat, 2005-09-12)We give a detailed study of dynamical properties of the Zhang model, including evaluation of topological entropy and estimates for the Lyapunov exponents and the dimension of the attractor. In the thermodynamic limit the entropy goes to zero and the Lyapunov spectrum collapses.1 -
Entropy via multiplicity
(Working paper; Arbeidsnotat, 2005-09-30)The topological entropy of piecewise affine maps is studied. It is shown that singularities may contribute to the entropy only if there is angular expansion and we bound the entropy via the expansion rates of the map. As a corollary we deduce that non-expanding conformal piecewise affine maps have zero topological entropy. We estimate the entropy of piecewise affine skew-products. Examples of ... -
The Capabilities of the EISCAT Svalbard Radar for Inter-hemispheric Coordinated Studies
(Journal article; Tidsskriftartikkel; Peer reviewed, 2002)In this article we want to present the EISCAT Svalbard Radar (ESR) in some detail, as well as some of the instruments of interest for ionospheric and magnetospheric research that are located in the vicinity of it. We particularly describe how this instrument cluster, close to the geomagnetic conjugate point of the Chinese Antarctic Zhongshan station, can contribute to inter-hemispheric coordinated ... -
Unsupervised segmentation of skin lesions
(Master thesis; Mastergradsoppgave, 2008-11-15)During the last decades, the incidence rate of cutaneous malignant melanoma, a type of skin cancer developing from melanocytic skin lesions, has risen to alarmingly high levels. As there is no effective treatment for advanced melanoma, recognizing the lesion at an early stage is crucial for successful treatment. A trained expert dermatologist has an accuracy of around 75 % when diagnosing melanoma, ... -
Two models of population genetics
(Master thesis; Mastergradsoppgave, 2008-06-02)The production of proteins in a cell is a regulated process. This means that the cell will only produce a type of protein when that type is needed. A fundamental step where this regulation occurs is at gene transcription. It is observed that transcription is regulated differently for different genes, and the question is therefore asked: why has evolution come up with different modes of transcriptional ... -
Large eddy simulation of homogeneous isotropic turbulence
(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
(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
(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
(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
(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
(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
(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
(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
(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. ...