Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length, relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which the classical numerical approximations become prohibitively expensive. Asymptotic-preserving (AP) schemes are schemes that are efficient in these asymptotic regimes. The designing principle of AP schemes are to p...

The H 2 optimization problem with preview and asymptotic behavior constraints is considered in a general two-sided model matching setting. The solution is obtained in terms of two constrained Sylvester equations, associated with asymptotic behavior, and stabilizing solutions of two algebraic Riccati equations. The Riccati equations do not depend on the preview length, yet are affected by asympt...

where κ(t) is the curvature of C given as a function of the arclength t and l the length of C. See also McClure and Vitale [7] and for asymptotic formulae for approximation with respect to the Hausdorff metric in higher dimensions R. Schneider [8],[9] and P.M. Gruber [5]. In this article we extend the asymptotic formulae (1) by deriving the second terms in the asymptotic expansions of δ(C,P i n...

Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is ...

In this paper, we discuss the existence and uniqueness of fixed points for $G$-asymptotic contractions in metric spaces endowed with a graph. The result given here is a new version of Kirk's fixed point theorem for asymptotic contractions in metric spaces endowed with a graph. The given result here is a generalization of fixed point theorem for asymptotic contraction from metric s paces to metr...

In this paper we develop an asymptotic theory for estimation based on signed ranks in the ARMA model when the innovation density is symmetrical. We provide two classes of estimators and we establish their asymptotic normality with the help of the asymptotic properties for serial signed rank statistics. Finally, we compare our procedure to the one of least-squares, and we illustrate the performa...

Photon trajectories in incoherent radiation trapping for Doppler, Lorentz, and Voigt line shapes under complete frequency redistribution are shown to be Lévy flights. The jump length (r) distributions display characteristic long tails. For the Lorentz line shape, the asymptotic form is a strict power law r(-3/2), while for Doppler the asymptotic is r(-2)(ln(r)(-1/2). For the Voigt profile, the ...