Institutt for matematikk og statistikk: Recent submissions
Now showing items 341-360 of 394
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Extensions of groups and modules
(Master thesis; Mastergradsoppgave, 2010)The main goal of this thesis is to build up detailed constructions and give complete proofs for the extension functors of modules and groups, which we define using cohomology functors. Further, we look at the relations that appear between these and short exact sequences of modules, respectively groups. We calculate also several concrete cohomology groups, and build extensions that are described by ... -
Multi-fractal stochastic modeling of the auroral electrojet index
(Master thesis; Mastergradsoppgave, 2009-12-15)In this thesis we have analyzed the Auroral Electrojet (AE) Index over the years 2000 to 2005, a time series consisting of over 3 000 000 data points. The aim is to describe this data as a multi-fractal stochastic process. We first introduce a class of random multiplicative measures, which provide the multi-fractality in the stochastic processes that will be defined later. We also review the ... -
Kompleksiteten til noen kryptologisk viktige algoritmer
(Master thesis; Mastergradsoppgave, 1990-04-04)Denne hovedfagsoppgaven har som mål å sammenligne teoretisk og praktisk kompleksitet til algoritmer som har stor kryptologisk betydning. Et av målene er å avsløre den skjulte konstanten bak O-notasjonen, slik at algoritmene kan sammenlignes på et reelt grunnlag. I tillegg er det sett på sammenheng mellom sikkerhet, størrelsen på tall, asymptotisk og praktisk kompleksitet. Spesielt algoritmer som ... -
Nijenhuis tensors in pseudoholomorphic curves neighborhoods
(Working paper; Arbeidsnotat, 2000)In this paper we consider the normal forms of almost complex structures in a neighborhood of pseudoholomorphic curve. We define normal bundles of such curves and study the properties of linear bundle almost complex structures. We describe 1-jet of the almost complex structure along a curve in terms of its Nijenhuis tensor. For pseudoholomorphic tori we investigate the problem of pseudoholomorphic ... -
Symmetry approaches for reductions of PDEs, differential constraints and Lagrange-Charpit method
(Journal article; Tidsskriftartikkel; Peer reviewed, 2007-12-20)Many methods for reducing and simplifying differential equations are known. They provide various generalizations of the original symmetry approach of Sophus Lie. Plenty of relations between them have been noticed and in this note a unifying approach will be discussed. It is rather close to the differential constraint method, but we make this rigorous basing on recent advances in compatibility ... -
Strictly non-proportional geodesically equivalent metrics have htop(g) = 0
(Journal article; Tidsskriftartikkel; Peer reviewed, 2004-10-24)If a closed manifold M possesses two Riemannian metrics which have the same unparameterized geodesics and are not strictly proportional at each point, then the topological entropy of both geodesic flows is zero. This is the main result of the paper and it has many dynamical and topological corollaries. In particular, such a manifoldM should be finitely covered by the product of a rationally ... -
Invariants and submanifolds in almost complex geometry
(Chapter; Bokkapittel, 2007-12-20)In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of higher-dimensional pseudoholomorphic submanifolds. -
The Kobayashi pseudodistance on almost complex manifolds
(Working paper; Arbeidsnotat, 1997-03-06)We extend the definition of the Kobayashi pseudodistance to almost complex manifolds and show that its familiar properties are for the most part preserved. We also study the automorphism group of an almost complex manifold and finish with some examples. -
Anomaly of linearization and auxiliary integrals
(Chapter; Bokkapittel, 2007-12-20)In this note we discuss some formal properties of universal linearization operator, relate this to brackets of non-linear differential operators and discuss application to the calculus of auxiliary integrals, used in compatibility reductions of PDEs. -
Examples of integrable sub-Riemannian geodesic flows
(Journal article; Tidsskriftartikkel; Peer reviewed, 2001-10-22)We exhibit examples of sub-Riemannian metrics with integrable geodesic flows and positive topological entropy. -
Existence of close pseudoholomorphic disks for almost complex manifolds and an applications to Kobayashi-Royden pseudonorm
(Journal article; Tidsskriftartikkel; Peer reviewed, 2000-02-23)It is proved in the paper that near every pseudoholomorphic disk on an almost complex manifold a disk of almost the same size in any close direction passes. As an application the Kobayashi-Royden pseudonorm for almost complex manifolds is defined and studied. -
Tangent and normal bundles in almost complex geometry
(Journal article; Tidsskriftartikkel; Peer reviewed, 2005-06-10)We define and study pseudoholomorphic vector bundles structures, particular cases of which are tangent and normal bundle almost complex structures. As an application we deduce normal forms of 1-jets of almost complex structures along a pseudoholomorphic submanifold. In dimension four we relate these normal forms to the problem of pseudoholomorphic foliation of a neighborhood of a curve and the ... -
Invariant characterization of Liouville metrics and polynomial integrals
(Journal article; Tidsskriftartikkel; Peer reviewed, 2007-09-04)A criterion in terms of differential invariants for a metric on a surface to be Liouville is established. Moreover, in this paper we completely solve in invariant terms the local mobility problem of a 2D metric, considered by Darboux: How many quadratic in momenta integrals does the geodesic flow of a given metric possess? The method is also applied to recognition of other polynomial integrals ... -
Deformation of big pseudoholomorphic disks and application to the Hanh pseudonorm
(Journal article; Tidsskriftartikkel; Peer reviewed, 2003-04-14)We simplify proof of the theorem that close to any pseudoholomorphic disk there passes a pseudoholomorphic disk of arbitrary close size with any pre-described sufficiently close direction. We apply these results to the Kobayashi and Hanh pseudodistances. It is shown they coincide in dimensions higher than four. The result is new even in the complex case. -
Point classification of 2nd order ODEs: Tresse classification revisited and beyond
(Chapter; Bokkapittel, 2008-09-26)In 1896 Tresse gave a complete description of relative differential invariants for the pseudogroup action of point transformations on the 2nd order ODEs. The purpose of this paper is to review, in light of modern geometric approach to PDEs, this classification and also discuss the role of absolute invariants and the equivalence problem. -
Involutivity of field equations
(Working paper; Arbeidsnotat, 2009-02-10)We prove involutivity of Einstein and Einstein-Maxwell equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kähler theory are derived. -
Applying the ICM algorithm for separating pictures consisting of two main parts, background and object application to fMRI recordings and mole pictures
(Master thesis; Mastergradsoppgave, 2009-05-15)This work concentrates on using the ICM algorithm for image restoration. The algorithm has been applied to fMRI recordings and mole pictures -
Distributing a private key generator in Ad hoc Networks
(Master thesis; Mastergradsoppgave, 2009-05-15)A Mobile Ad hoc Network (MANET) is a wireless network that does not rely on a fixed infrastructure. These characteristics make algorithms that route network traffic particularly vulnerable to attack. Mechanisms used to protect against such attacks often depend on cryptographic keys. Since the nodes in a MANET have limited resources, designing methods for cryptographic key management is ... -
Theory of linear G-difference equations
(Journal article; Tidsskriftartikkel; Peer reviewed, 1997-12-17)We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants of the action of the symmetry group. Linear equations are modules over the skew group algebra, solutions are morphisms relating a given equation to other ... -
The categorical theory of relations and quantization
(Working paper; Arbeidsnotat, 2001-10-30)In this paper we develops a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to be symmetric monoidal categories in their own right and are found to be isomorphic to certain categories of A−A bicomodules. Properties of relations are ...