Search results for "ergodic theory"

Dynamic stability of plane elastic frames

1982

Abstract The stability of plane elastic frames subjected to a vertical foundation motion of the stationary, ergodic type is investigated. The equations of motion are obtained in modal co-ordinates, with account taken of many modes of vibration. The problem is subsequently reduced to the study of only the first mode of vibration. By considering a particular case, the stability domains are sketched as functions of the variation of the rigidities of the beam-column connecting joints and as functions of the number of stories.

Fractional master equations and fractal time random walks

1995

Fractional master equations containing fractional time derivatives of order 0\ensuremath{\le}1 are introduced on the basis of a recent classification of time generators in ergodic theory. It is shown that fractional master equations are contained as a special case within the traditional theory of continuous time random walks. The corresponding waiting time density \ensuremath{\psi}(t) is obtained exactly as \ensuremath{\psi}(t)=(${\mathit{t}}^{\mathrm{\ensuremath{\omega}}\mathrm{\ensuremath{-}}1}$/C)${\mathit{E}}_{\mathrm{\ensuremath{\omega}},\mathrm{\ensuremath{\omega}}}$(-${\mathit{t}}^{\mathrm{\ensuremath{\omega}}}$/C), where ${\mathit{E}}_{\mathrm{\ensuremath{\omega}},\mathrm{\ensuremat…

Extensions of cocycles for hyperfinite actions and applications

1997

Given a countable, hyperfinite, ergodic and measure-preserving equivalence relationR on a standard probability space (X, ℬ, μ) and an elementW of the normalizerN (R) ofR, we investigate the problem of extendingR-cocycles to\(\bar R\), where\(\bar R\) is the relation generated byR andW. As an application, we obtain that for a Bernoulli automorphism the smallest family of natural factors in sense of [6] consists of all factors. Given an automorphism which is embeddable in a measurable flow and a compact, metric group, we show that for a typical cocycle we cannot lift the whole flow to the centralizer of the corresponding group extension.

Classes of sum-of-cisoids processes and their statistics for the modeling and simulation of mobile fading channels

2013

Published version of an article in the journal: EURASIP Journal on Wireless Communications and Networking. Also available from the publisher at: http://dx.doi.org/10.1186/1687-1499-2013-125 Open access In this paper, we present a fundamental study on the stationarity and ergodicity of eight classes of sum-of-cisoids (SOC) processes for the modeling and simulation of frequency-nonselective mobile Rayleigh fading channels. The purpose of this study is to determine which classes of SOC models enable the design of channel simulators that accurately reproduce the channel’s statistical properties without demanding information on the time origin or the time-consuming computation of an ensemble ave…

Bayesian inference in Markovian queues

1994

This paper is concerned with the Bayesian analysis of general queues with Poisson input and exponential service times. Joint posterior distribution of the arrival rate and the individual service rate is obtained from a sample consisting inn observations of the interarrival process andm complete service times. Posterior distribution of traffic intensity inM/M/c is also obtained and the statistical analysis of the ergodic condition from a decision point of view is discussed.

Mode coupling approach to the ideal glass transition of molecular liquids: Linear molecules

1997

The mode coupling theory (MCT) for the ideal liquid glass transition, which was worked out for simple liquids mainly by Gotze, Sjogren, and their co-workers, is extended to a molecular liquid of linear and rigid molecules. By use of the projection formalism of Zwanzig and Mori an equation of motion is derived for the correlators S[sub lm,l[sup (prime)]m[sup (prime)]]([bold q],t) of the tensorial one-particle density rho [sub lm]([bold q],t), which contains the orientational degrees of freedom for l(greater-than)0. Application of the mode coupling approximation to the memory kernel results into a closed set of equations for S[sub lm,l[sup (prime)]m[sup (prime)]]([bold q],t), which requires t…

Weak convergence theorems for asymptotically nonexpansive mappings and semigroups

2001

Statistical Properties of Generalized Strain Criterion for Multiaxial Random Fatigue

1989

ABSTRACT Statistical properties of generalized criterion of the maximum shear and normal strains on the fracture plane have been presented, Functions of probability distribution and spectral density of the equivalent strain have been analysed on the assumption that a random tensor of strain state is a six-dimensional stationary and ergodic Gaussian process. The expected value and variance of the equivalent strain have been determined as well. From spectral analysis a new limitation has been derived for extension of some multiaxial cyclic fatigue criteria to random loadings. It is connected with the fact that in some cases the frequency band of the equivalent strain is greater than that for …

On ergodic operator means in Banach spaces

2016

We consider a large class of operator means and prove that a number of ergodic theorems, as well as growth estimates known for particular cases, continue to hold in the general context under fairly mild regularity conditions. The methods developed in the paper not only yield a new approach based on a general point of view, but also lead to results that are new, even in the context of the classical Cesaro means.

Contractivity results in ordered spaces. Applications to relative operator bounds and projections with norm one

2016

This paper provides various “contractivity” results for linear operators of the form I−C where C are positive contractions on real ordered Banach spaces X. If A generates a positive contraction semigroup in Lebesgue spaces Lp(μ), we show (M. Pierre's result) that A(λ−A)−1 is a “contraction on the positive cone”, i.e. A(λ−A)−1x≤x for all x∈L+p(μ)(λ>0), provided that p⩾2.  We show also that this result is not true for 1 ⩽ p<2. We give an extension of M. Pierre's result to general ordered Banach spaces X under a suitable uniform monotony assumption on the duality map on the positive cone X+. We deduce from this result that, in such spaces, I−C is a contraction on X+ for any positive projection…