Cohomogeneity one Kähler and Kähler–Einstein manifolds with one singular orbit I

Let M be a cohomogeneity one manifold of a compact semisimple Lie group G with one singular orbit \(S_0 = G/H\). Then M is G-diffeomorphic to the total space \(G \times _H V\) of the homogeneous vector bundle over \(S_0\) defined by a sphere transitive representation of G in a vector space V. We describe all such manifolds M which admit an invariant Kähler structure of standard type. This means that the restriction \(\mu : S = Gx = G/L \rightarrow F = G/K \) of the moment map of M to a regular orbit \(S=G/L\) is a holomorphic map of S with the induced CR structure onto a flag manifold \(F = G/K\), where \(K = N_G(L)\), endowed with an invariant complex structure \(J^F\). We describe all such standard Kähler cohomogeneity one manifolds in terms of the painted Dynkin diagram associated with \((F = G/K,J^F)\) and a parameterized interval in some T-Weyl chamber. We determine which of these manifolds admit invariant Kähler–Einstein metrics.     

Polar and coisotropic actions on Kähler manifolds

The main result of the paper is that a polar action on a compact irreducible homogeneous Kähler manifold is coisotropic. This is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics.

     

Multifractal structure in Latin-American market indices

We study the multifractal nature of daily price and volatility returns of Latin-American stock markets employing the multifractal detrended fluctuation analysis. Comparing with the results obtained for a developed country (US) we conclude that the multifractality degree is higher for emerging markets. Moreover, we propose a stock market inefficiency ranking by considering the multifractality degree as a measure of inefficiency. Finally, we analyze the sources of multifractality quantifying the contributions of two factors, the long-range correlations of the time series and the broad fat-tail distributions. We find that the multifractal structure of Latin-American market indices can be mainly attributed to the latter.     

Chaotic dynamics in a vertically driven planar pendulum

Using elementary phase-plane analysis, combined with results from the theory of topological horseshoes and linked twist maps, we prove the presence of chaos-like dynamics for a vertically driven planar pendulum and other, more general, related equations.     

A fourth‐order method for numerical integration of age‐ and size‐structured population models

In many applications of age‐ and size‐structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Because quadratures can be designed with any order of accuracy, one can obtain numerical approximations of the solutions with very fast convergence. In this article, we present a general framework and a specific example of a fourth‐order method based on composite Newton‐Cotes quadratures for a size‐structured population model. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Bayesian estimation and prediction for the transformed Wiener degradation process

This paper proposes some Bayesian inferential procedures for the transformed Wiener (TW) process, a new degradation process that has been recently suggested in the literature to describe degradation phenomena where degradation increments are not necessarily positive and depend stochastically on the current degradation level. These procedures have been expressly conceived to allow one incorporating into the inferential process the type of prior information, on meaningful physical characteristics of the observed degradation process, that is generally available in practical settings. Several different prior distributions are proposed, each of them reflecting a specific degree of knowledge on the observed phenomenon. Simple strategies for eliciting the prior hyper‐parameters from the available prior information are provided. Estimates of the TW process parameters and some functions thereof are retrieved by adopting a Monte Carlo Markov Chain technique. Procedures that allow predicting the degradation increment, the useful life of a new unit, and the remaining useful life of a used unit are also provided. Finally, an application is developed on the basis of a set of real degradation measurements of some infrared light‐emitting diodes, widely used in communication systems. The obtained results demonstrate the feasibility of the proposed Bayesian approach and the flexibility of the TW process.     

Zorn's Matrices and Finite Index Subloops#

Zorn's Algebra ?(R) has a multiplicative function called determinant with properties similar to the usual one. The set of elements in ?(R) with determinant 1 is a Moufang loop that we will denote by IΓ. In our main result we prove that if R is a Dedekind algebraic number domain that contains a unit of infinite order, each finite index subloop ?, such that IΓ has the weak Lagrange property relative to ?, is a congruence subloop.     

Dérivée en s=1 de la fonction L p-adique du carré symétrique dʼune courbe elliptique sur un corps totalement réel

We prove a formula for the derivative of the p-adic L-function associated with the symmetric square representation of an elliptic curve over a totally real field in which p is inert, under certain assumptions on the conductor. In particular, this proves a conjecture of Greenberg on trivial zeros. The method is to generalize unpublished calculations of Greenberg and Tilouine.     

Fast mixing for independent sets,colorings, and other models on trees

We study the mixing time of the Glauber dynamics for general spin systems on the regular tree, including the Ising model, the hard‐core model (independent sets), and the antiferromagnetic Potts model at zero temperature (colorings). We generalize a framework, developed in our recent paper (Martinelli, Sinclair, and Weitz, Tech. Report UCB//CSD‐03‐1256, Dept. of EECS, UC Berkeley, July 2003) in the context of the Ising model, for establishing mixing time O(nlog n), which ties this property closely to phase transitions in the underlying model. We use this framework to obtain rapid mixing results for several models over a significantly wider range of parameter values than previously known, including situations in which the mixing time is strongly dependent on the boundary condition. We also discuss applications of our framework to reconstruction problems on trees. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007