• Title/Summary/Keyword: invariant measure

Search Result 106, Processing Time 0.026 seconds

INVARIANT MEASURE AND THE EULER CHARACTERISTIC OF PROJECTIVELY ELAT MANIFOLDS

  • Jo, Kyeong-Hee;Kim, Hyuk
    • Journal of the Korean Mathematical Society
    • /
    • v.40 no.1
    • /
    • pp.109-128
    • /
    • 2003
  • In this paper, we show that the Euler characteristic of an even dimensional closed projectively flat manifold is equal to the total measure which is induced from a probability Borel measure on RP$^{n}$ invariant under the holonomy action, and then discuss its consequences and applications. As an application, we show that the Chen's conjecture is true for a closed affinely flat manifold whose holonomy group action permits an invariant probability Borel measure on RP$^{n}$ ; that is, such a closed affinly flat manifold has a vanishing Euler characteristic.

AFFINE MANIFOLD WITH MEASURE PRESERVING PROJECTIVE HOLONOMY GROUP

  • Park, Yeong-Su
    • Bulletin of the Korean Mathematical Society
    • /
    • v.38 no.1
    • /
    • pp.157-161
    • /
    • 2001
  • In this paper, we prove that an affine manifold M is finitely covered by a manifold $\overline{M}$ where $\overline{M}$ is radiant or the tangent bundle of $\overline{M}$ has a conformally flat vector subbundle of the projective holonomy group of M admits an invariant probability Borel measure. This implies that$x^M$is zero.

  • PDF

ITERATES OF WEIGHTED BEREZIN TRANSFORM UNDER INVARIANT MEASURE IN THE UNIT BALL

  • Lee, Jaesung
    • Korean Journal of Mathematics
    • /
    • v.28 no.3
    • /
    • pp.449-457
    • /
    • 2020
  • We focus on the interations of the weighted Berezin transform Tα on Lp(τ), where τ is the invariant measure on the complex unit ball Bn. Iterations of Tα on L1R(τ) the space of radial integrable functions played important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. Here, we introduce more properties on iterations of Tα on L1R(τ) and observe differences between the iterations of Tα on L1(τ) and Lp(τ) for 1 < p < ∞.

ON RELATION AMONG COHERENT, DISTORTION AND SPECTRAL RISK MEASURES

  • Kim, Ju-Hong
    • The Pure and Applied Mathematics
    • /
    • v.16 no.1
    • /
    • pp.121-131
    • /
    • 2009
  • In this paper we examine the relation among law-invariant coherent risk measures with the Fatou property, distortion risk measures and spectral risk measures, and give a new proof of the relation among them. It is also shown that the spectral risk measure satisfies the monotonicity with respect to stochastic dominance and the comonotonic additivity.

  • PDF

INVARIANT GRAPH AND RANDOM BONY ATTRACTORS

  • Fateme Helen Ghane;Maryam Rabiee;Marzie Zaj
    • Journal of the Korean Mathematical Society
    • /
    • v.60 no.2
    • /
    • pp.255-271
    • /
    • 2023
  • In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

THE GENERALIZED ANALOGUE OF WIENER MEASURE SPACE AND ITS PROPERTIES

  • Ryu, Kun-Sik
    • Honam Mathematical Journal
    • /
    • v.32 no.4
    • /
    • pp.633-642
    • /
    • 2010
  • In this note, we introduce the definition of the generalized analogue of Wiener measure on the space C[a, b] of all real-valued continuous functions on the closed interval [a, b], give several examples of it and investigate some important properties of it - the Fernique theorem and the existence theorem of scale-invariant measurable subsets on C[a, b].

Iris Recognition Based on a Shift-Invariant Wavelet Transform

  • Cho, Seongwon;Kim, Jaemin
    • International Journal of Fuzzy Logic and Intelligent Systems
    • /
    • v.4 no.3
    • /
    • pp.322-326
    • /
    • 2004
  • This paper describes a new iris recognition method based on a shift-invariant wavelet sub-images. For the feature representation, we first preprocess an iris image for the compensation of the variation of the iris and for the easy implementation of the wavelet transform. Then, we decompose the preprocessed iris image into multiple subband images using a shift-invariant wavelet transform. For feature representation, we select a set of subband images, which have rich information for the classification of various iris patterns and robust to noises. In order to reduce the size of the feature vector, we quantize. each pixel of subband images using the Lloyd-Max quantization method Each feature element is represented by one of quantization levels, and a set of these feature element is the feature vector. When the quantization is very coarse, the quantized level does not have much information about the image pixel value. Therefore, we define a new similarity measure based on mutual information between two features. With this similarity measure, the size of the feature vector can be reduced without much degradation of performance. Experimentally, we show that the proposed method produced superb performance in iris recognition.