Abstract We consider the propagation of stratified fluid through a contraction near resonance, for which the governing asymptotic equation is the forced KdV equation. Steady solutions of this equation are sought which have constant, but differing amplitudes upstream and downstream of the contraction, and for which leading order dispersive effects are retained. A numerical algorithm is outlined ...

In many iterative optimization methods, fixed-point theory enables the analysis of convergence rate via contraction factor associated with linear approximation operator. While this characterizes asymptotic convergence, it does not explain non-linear behavior these algorithms in non-asymptotic regime. letter, we take into account effect first-order error and present a closed-form bound on terms ...

We prove a limit theorem for the total Steiner k-distance of a random b-ary recursive tree with weighted edges. The total Steiner k-distance is the sum of all Steiner k-distances in a tree and it generalises the Wiener index. The limit theorem is obtained by using a limit theorem in the general setting of the contraction method. In order to use the contraction method we prove a recursion formul...

Let T be a periodic time scale. We use a fixed point theorem due to Krasnoselskii to show that the nonlinear neutral dynamic equation with infinite delay x(t) = −a(t)x(t) + (Q(t, x(t− g(t))))) + ∫ t −∞ D (t, u) f (x(u)) ∆u, t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the...

Let T be a periodic time scale. We use a fixed point theorem due to Krasnosel’skĭı to show that the nonlinear neutral dynamic equation with delay x(t) = −a(t)x(t) + (Q(t, x(t), x(t− g(t))))) +G ` t, x(t), x(t− g(t)) ́ , t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the aid ...

A perpetuity takes the form D = R∞ 0 e −Γ(t−)dΛ (t). In this paper, we develop large deviation theory for D in a context in which the accumulated discount process, Γ, is small. More precisely, in this paper we provide: 1) logarithmic large deviations that hold in great generality in both discrete and continuous time, and 2) exact asymptotics derived in the iid (independent and identically distr...

By introducing a new concept called “set-valued asymptotic contraction of final type” in metric spaces, the existence and uniqueness of compact fixed sets for such mappings have been obtained. Furthermore, by adding additional conditions, we prove the existence and uniqueness of endpoints for these maps. 2010 Mathematics Subject Classification: 47H10; 54C60

The paper is concerned with the asymptotic behavior of solutions to a second order nonlinear differential equation u′′ + f (t, u) = 0. Using the Banach contraction principle, we establish global existence of solutions which satisfy u(t) = At + o(tν) as t→ +∞, where A ∈ R and ν ∈ (0, 1].

The non-linear evolution of a stratified perturbation in a three dimensional expanding Universe is considered. A general Lagrangian scheme (Q model) is introduced and numerical investigations are performed. The asymptotic contraction of the core of the agglomeration is studied. A power-law scaling is detected and an heuristic interpretation of the numerical findings is provided. An asymptotic e...

This paper proves exponential asymptotic stability of discrete-time filters for the estimation of solutions to stochastic difference equations, when the observation noise is bounded. No assumption is made on the ergodicity of the signal. The proof uses the Hilbert projective metric, introduced into filter stability analysis by Atar and Zeitouni [1], [2]. It is shown that when the signal noise i...