valdis laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. in this paper we introduce a new property of acts over monoids, called u-wpf which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. we also show that regu...

It is proved that in any pointed category with pullbacks, coequalizers and regular epi-mono factorizations, the class of regular epimorphisms is stable under pullback along the so-called balanced effective descent morphisms. Here “balanced” can be omitted if the category is additive. A balanced effective descent morphism is defined as an effective descent morphism p : E → B such that any subobj...

This paper presents a system for computer-aided thinking. We propose the idea of reflecting the mental world indirectly into a metric space to support such human thinking activities as externalizing and forming new ideas. We use a method that maps text-objects into metric spaces for visualizing a user’s thought space structure. Text-objects imply fragments of a user’s idea, which have several k...

The authors consider non-autonomous dynamical behavior of wave-type evolutionary equations with nonlinear damping and critical nonlinearity. These type of wave equations are formulated as continuous non-autonomous dynamical systems (cocycles). A sufficient and necessary condition for the existence of pullback attractors is established. The required compactness for the existence of pullback attr...

This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation −∆ut + α ∆ut + μ∆ u+∇ · −→ F (u) +B(u, u) = ǫg(x, t). Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor {Aǫ(t)}t∈R of the equation with ǫ > 0 converges to the global attract...

The existence of a random attractor in H1(R3)×L2(R3) is proved for the damped semilinear stochastic wave equation defined on the entire space R 3. The nonlinearity is allowed to have a cubic growth rate which is referred to as the critical exponent. The uniform pullback estimates on the tails of solutions for large space variables are established. The pullback asymptotic compactness of the rand...

In this work we obtain theoretical results on continuity of selected pullback attractors for a generalized process and consider the when system is asymptotically autonomous. As an example, apply theory nonautonomous problem with reaction diffusion equations dynamical boundary conditions, after that, some additional hypotheses family problems converging to autonomous limit show convergence their...