This paper studies the boundedness, global asymptotic stability and periodicity for solutions of the equation xn = A + ( xn−2 xn−1 )p , n = 0, 1, . . . , with p, A ∈ (0,∞), p 6= 1, and x−2, x−1 ∈ (0,∞). It is shown that: (a) all solutions converge to the unique equilibrium, x̄ = A+1, whenever p ≤ min{1, (A+1)/2}, (b) all solutions converge to period two solutions whenever (A + 1)/2 < p < 1 and (...

This paper suggests a robust estimation procedure for the parameters of the periodic AR (PAR) models when the data contains additive outliers. The proposed robust methodology is an extension of the robust scale and covariance functions given in, respectively, Rousseeuw and Croux [29] and Ma and Genton [24], to accommodate periodicity. These periodic robust functions are used in the Yule-Walker ...

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...

Let g(x) = x/2 + 17/30 (mod 1), let ξi, i = 1, 2, ... be a sequence of independent, identically distributed random variables with uniform distribution on the interval [0, 1/15], define gi(x) = g(x)+ξi (mod 1) and. for n = 1, 2, ..., define g(x) = gn(gn−1(...(g1(x))...)). For x ∈ [0, 1) let μn,x denote the distribution of g(x). The purpose of this note is to show that there exists a unique proba...

The AdS/CFT conjecture relates quantum gravity on Anti-de Sitter (AdS) space to a conformal field theory (CFT) defined on the spacetime boundary. We interpret the CFT in terms of natural analogues of the bulk S-matrix. Our first approach finds the bulk S-matrix as a limit of scattering from an AdS bubble immersed in a space admitting asymptotic states. Next, we show how the periodicity of geode...

The object of considerations is a thin linear-elastic cylindrical shell having a periodic structure along one direction tangent to the shell midsurface. The aim of this paper is to propose a new averaged nonasymptotic model of such shells, which makes it possible to investigate free and forced vibrations, parametric vibrations, and dynamical stability of the shells under consideration. As a too...

We develop a convex approximation for two-stage mixed-integer recourse models and we derive an error bound for this approximation that depends on all total variations of the probability density functions of the random variables in the model. We show that the error bound converges to zero if all these total variations converge to zero. Our convex approximation is a generalization of the one in C...

The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz model equations for thermal convection in Rayleigh-Bénard flow is studied. Its bifurcation structure has commonly been investigated as a function of r, the normalized Rayleigh number, at fixed Prandtl number σ. The present work extends the analysis to the entire (r, σ) parameter plane. An onion l...

We study the asymptotic behavior of the solution of semi-linear PDEs. Neither periodicity nor ergodicity assumptions are assumed. The coefficients admit only a limit in a C̀esaro sense. In such a case, the limit coefficients may have discontinuity. We use probabilistic approach based on weak convergence techniques for the associated backward stochastic differential equation in the S-topology. We...