Suppose that D ⊂ Rn, n ≥ 2, is a Lipschitz domain and let Nt(r) be the number of excursions of Brownian motion inside D with diameter greater than r which started before time t. Then rNt(r) converges as r → 0 to a constant multiple of local time on ∂D, a.s. and in Lp for all p < ∞. The limit need not exist or may be trivial (0 or ∞) in Hölder domains, non-tangentially accessible domains and dom...

A glycolytic model, which is an autocatalytic biochemical system, is solved numerically using two numerical methods based on finite-difference schemes. Method 1, the well known Euler method, is an explicit method, whereas method 2 is implicit. Although the implicit method, method 2, is first-order accurate in time it converges to the fixed point(s) for large time step, ‘. 2005 Elsevier Inc. All...

We consider the initial and boundary value problem of heat flow of equation of surfaces of constant mean curvatures. We give sufficient conditions on the initial data such that the heat flow develops finite time singularity. We also provide a new set of initial data to guarantee the existence of global regular solutions to the heat flow that converges to zero in H exponentially as time goes to ...

This paper proposes a finite-time controller for an unmanned aerial vehicle in the presence of Figures/uncertainties using fractional-order terminal sliding mode. First, contrary to existing backstepping mode controllers, this introduces new control approach quadrotor position control, which is based on fast control. Using appropriate surface, tracking error converges zero finite time while pro...

In this work, we develop a minimum action method (MAM) with optimal linear time scaling, called tMAM for short. The main idea is to relax the integration time as a functional of the transition path through optimal linear time scaling such that a direct optimization of the integration time is not required. The Feidlin-Wentzell action functional is discretized by finite elements, based on which h...

We study an initial-boundary value problem (IBVP) for a coupled Cahn-Hilliard-Hele-Shaw system that models tumor growth. For large initial data with finite energy, we prove global (local resp.) existence, uniqueness, higher order spatial regularity and Gevrey spatial regularity of strong solutions to the IBVP in 2D (3D resp.). Asymptotically in time, we show that the solution converges to a con...

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems. We show that the time average of the observation function which is not the L(m) function, whose average with r...

in this paper, a finite-time control scheme is presented for stabilization ofthe satellite chaotic attitude around its equilibrium point whenits attitude is confused by a disturbed torque. controllers and settling timeof stabilizaton are obtained, based on the lyapunov stability theoremand finite-time control scheme. this method is satisfied for any initial condition.numerical simulations are ...

The present article deals with convergence in probability in L-spaces from a functional analytic point of view. The L-spaces in question are the preduals of von Neumann algebras with finite faithful normal traces. To consider an easy example we look at the commutative case: Let (Ω,Σ, μ) be a finite measure space, let (fn) be a bounded sequence in L (Ω,Σ, μ). If (appropriately chosen representat...