Now showing items 21-40 of 209

    • Vanishing of the entropy pseudonorm for certain integrable systems 

      Kruglikov, Boris Serafimovich; Matveev, VS (Journal article; Tidsskriftartikkel; Peer reviewed, 2006)
    • 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.
    • 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. ...
    • Abelian equations and rank problems for planar webs 

      Goldberg, Vladislav V.; Lychagin, Valentin V. (Journal article; Tidsskriftartikkel; Peer reviewed, 2006-05-04)
      We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincar´e’s theorem: a planar 4- web of maximum rank is linearizable. We also find an invariant intrinsic characterization of planar 4-webs ...
    • Dimension of the solutions space of PDEs 

      Kruglikov, Boris; Lychagin, Valentin V. (Conference object; Konferansebidrag, 2006-10-26)
      We discuss the dimensional characterization of the solutions space of a formally integrable system of partial differential equations and provide certain formulas for calculations of these dimensional quantities.
    • Bayesian modeling and significant features exploration in wavelet power spectra 

      Divine, Dmitry V; Godtliebsen, Fred (Journal article; Tidsskriftartikkel; Peer reviewed, 2007)
    • Invariant characterization of Liouville metrics and polynomial integrals 

      Kruglikov, Boris (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 ...
    • Differential invariants of the motion group actions 

      Kruglikov, Boris; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 2007-12-20)
      Differential invariants of a (pseudo)group action can vary when restricted to invariant submanifolds (differential equations). The algebra is still governed by the Lie-Tresse theorem, but may change a lot. We describe in details the case of the motion group O(n) ⋉ R<sup>n</sup> acting on the full (unconstraint) jet-space as well as on some invariant equations.
    • Invariants and submanifolds in almost complex geometry 

      Kruglikov, Boris (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.
    • Symmetry approaches for reductions of PDEs, differential constraints and Lagrange-Charpit method 

      Kruglikov, Boris (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 ...
    • Anomaly of linearization and auxiliary integrals 

      Kruglikov, Boris (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.
    • 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.
    • A stochastic theory for temporal fluctuations in self-organized critical systems 

      Rypdal, Martin; Rypdal, Kristoffer (Journal article; Tidsskriftartikkel; Peer reviewed, 2008)
    • A propagation-separation approach to estimate the autocorrelation in a time-series 

      Divine, Dmitry V; Polzehl, J; Godtliebsen, Fred (Journal article; Tidsskriftartikkel; Peer reviewed, 2008)
    • Compatibility, multi-brackets and integrability of systems of PDEs 

      Kruglikov, Boris; Lychagin, Valentin V. (Journal article; Tidsskriftartikkel; Peer reviewed, 2008-02-20)
      We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential operators. These multi-brackets generalize the higher Jacobi- Mayer brackets, important in the study of evolutionary equations and the integrability problem. We also calculate Spencer δ-cohomology of generalized complete intersections and ...
    • Estimation of Ambiguity Functions With Limited Spread 

      Hindberg, Heidi; Olhede, Sofia C. (Research report; Forskningsrapport, 2008-04-07)
      This paper proposes a new estimation procedure for the ambiguity function of a non-stationary time series. The stochastic properties of the empirical ambiguity function calculated from a single sample in time are derived. Different thresholding procedures are introduced for the estimation of the ambiguity function. Such estimation methods are suitable if the ambiguity function is only non-negligible ...
    • Modeling temporal fluctuations in avalanching system 

      Rypdal, Martin; Rypdal, Kristoffer (Working paper; Arbeidsnotat, 2008-07-22)
      We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean field approach to sandpile dynamics by formulating it as a generalization of Itoh’s SDE. This equation contains a fractional Gaussian noise term representing the branching of an avalanche into small active clusters, ...
    • A stochastic theory for temporal fluctuations in self-organized critical systems 

      Rypdal, Martin; Rypdal, Kristoffer (Working paper; Arbeidsnotat, 2008-07-22)
      A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion coefficient is proportional to the activity. It is formulated as a generalization of the Itˆo stochastic differential equation with an anti-persistent fractional ...
    • Point classification of 2nd order ODEs: Tresse classification revisited and beyond 

      Kruglikov, Boris (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.
    • Geodesic Webs on a Two-Dimensional Manifold and Euler Equations 

      Goldberg, Vladislav V.; Lychagin, Valentin V. (Journal article; Tidsskriftartikkel; Peer reviewed, 2008-10-30)
      We prove that any planar 4-web defines a unique projective structure in the plane in such a way that the leaves of the web foliations are geodesics of this projective structure. We also find conditions for the projective structure mentioned above to contain an affine symmetric connection, and conditions for a planar 4-web to be equivalent to a geodesic 4-web on an affine symmetric surface. Similar ...