First, for a process {U(t, τ)∣t ≥ τ}, we introduce a new concept, called the weak D-pullback exponential attractor, which is a family of sets {ℳ(t)∣t ≤ T}, for any T ∈ ℝ, satisfying the following: (i) ℳ(t) is compact, (ii) ℳ(t) is positively invariant, that is, U(t, τ)ℳ(τ) ⊂ ℳ(t), and (iii) there exist k, l > 0 such that dist(U(t, τ)B(τ), ℳ(t)) ≤ ke (-(t-τ)); that is, ℳ(t) pullback exponential ...

In the description of the long-time behavior of solutions to nonautonomous differential equations the notion of a pullback attractor plays a similar role as the global attractor in autonomous dynamical systems. We present the theorem on the existence of a pullback attractor if the evolution process is a family of closed operators. The abstract result is formulated in the context of the smoothin...

In this paper, firstly we introduce the concept of norm-to-weak continuous cocycle in Banach space and give a technical method to verify this kind of continuity, then we obtain some abstract results for the existence of pullback attractors about this kind of cocycle, using the measure of noncompactness. As an application, we prove the existence of pullback attractors in H 1 0 of the cocycle ass...

The catalase multi-gene family in Arabidopsis includes three genes encoding individual subunits which associate to form at least six isozymes that are readily resolved by non-denaturing gel electrophoresis. CAT1 and CAT3 map to chromosome 1, and CAT2 maps to chromosome 4. The nucleotide and deduced amino acids sequences of the three coding regions are highly related to each other and to other c...

The existence of a pullback attractor is established for the singularly perturbed FitzHughNagumo system defined on the entire space Rn when external terms are unbounded in a phase space. The pullback asymptotic compactness of the system is proved by using uniform a priori estimates for far-field values of solutions. Although the limiting system has no global attractor, we show that the pullback...

gene/compound/concentration combination examined. The reThe role of hydrogen peroxide (H2O2) and various antioxidants in the regulation of expression of the three Cat and Gst1 sponse of each gene to each antioxidant compound tested was unique, suggesting that the ability of these compounds to genes of maize (Zea mays L.) has been investigated. Low concentrations of H2O2 appeared to inhibit Cat1...

BACKGROUND True 3D reconstruction of coronary arteries in patients based on intravascular ultrasound (IVUS) may be achieved by fusing angiographic and IVUS information (ANGUS). The clinical applicability of ANGUS was tested, and its accuracy was evaluated quantitatively. METHODS AND REUSLTS: In 16 patients who were investigated 6 months after stent implantation, a sheath-based catheter was used...

A nonautonomous or cocycle dynamical system that is driven by an autonomous dynamical system acting on a compact metric space is assumed to have a uniform pullback attractor. It is shown that discretization by a one-step numerical scheme gives rise to a discrete time cocycle dynamical system with a uniform pullback attractor, the component subsets of which converge upper semi continuously to th...

In this article, we prove the existence of a random attractor of the stochastic three-component reversible Gray-Scott system on infinite lattice with additive noise. We use a transformation of addition involved with Ornstein-Uhlenbeck process, for proving the pullback absorbing property and the pullback asymptotic compactness of the reaction diffusion system with cubic nonlinearity.