We study parametric resonant decay of inflaton field with emphasis on its physical meaning. We show that the parametric resonance is indeed an induced process, which means that the more numbers of produced particles, the more inflaton field decays. We also consider the dissipative effects of produced particles and find that the dissipation reduces the resonant decay rate of inflaton field.

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Contemporary avant-garde architecture is addressing the demand for an increased level of articulated complexity by means of retooling its methods on the basis of parametric design systems. The contemporary architectural style that has achieved pervasive hegemony within the contemporary architectural avant-garde can be best understood as a research programme based upon the parametric paradigma. ...

We analyze experimental survey data, with a random split into respondents who get an open-ended question on the amount of total family consumption (with follow-up unfolding brackets of the form "Is consumption $X or more?" for those who answer "don't know" or "refuse") and respondents who are immediately directed to unfolding brackets. In both cases, the entry point of the unfolding bracket seq...

If we have a parametric model for the invariant distribution of a Markov chain but cannot or do not want to use any information about the transition distribution (except, perhaps, that the chain is reversible) | what, then, is the best use we can make of the observations? It is not optimal to proceed as if the observations were i.i.d. We determine a lower bound for the asymptotic variance of es...

In this paper the second order liner differential equation

In this short note we consider wave equations with a periodic in time dissipation and discuss the effect of parametric resonance in the framework of energy estimates. The approach is based on a treatment for a generalized Mathieu equation related to the periodic dissipation term.

In this paper, we investigate the asymmetry in the tail dependence between US equity portfolios and the aggregate US market. Given the limited number of observations in the tails of a joint distribution, standard non-parametric measures of tail dependence often have poor finite-sample properties. We therefore develop a parametric model for measuring and testing asymmetry in tail dependence, usi...

The sandwich estimator, often known as the robust covariance matrix estimator or the empirical covariance matrix estimator, has achieved increasing use with the growing popularity of generalized estimating equations. Its virtue is that it provides consistent estimates of the covariance matrix for parameter estimates even when a parametric model fails to hold, or is not even specified. Surprisin...

Two types of global testing procedures for item fit to the Rasch model were evaluated using simulation studies. The first type incorporates three tests based on first-order statistics: van den Wollenberg's Q(1) test, Glas's R(1) test, and Andersen's LR test. The second type incorporates three tests based on second-order statistics: van den Wollenberg's Q(2) test, Glas's R(2) test, and a non-par...