The human visual system uses eye movements to gather visual information. They act as visual scanning processes and can roughly be divided into two different types: small movements around fixation points and larger movements between fixation points. The processes are often modeled as random walks, and recent models based on heavy tail distributions, also known as Levý flights, have been used in ...

An interesting observation is that most pairs of weakly homogeneous mappings do not possess strongly monotonic property, which one the key conditions to ensure unique solvability generalized variational inequality. This paper focuses on studying uniqueness and inequality with a pair mappings. By using weaker condition than strong monotonicity some additional conditions, we achieve several resul...

According to the recurrent frequency, many levels of points are found such as periodic points, almost weakly quasi-weakly and Banach points. In this paper, we consider symbolic dynamics show existence six refined between recurrence general recurrence. Despite fact that these all null-measure under any invariant measure, further they carry strong topological complexity. Each level is dense in wh...

We define the notions of weakly μ-countably compactness and nearly denoted by Wμ-CC Nμ-CC as generalizations μ-compact spaces in sense Csaśzaŕ generalized topological spaces. To obtain a more general setting, we via hereditary classes. Using μθ-open sets, μ-regular open spaces, many results characterizations have been presented. Moreover, use properties functions to investigate effects some typ...

Extensive (asymptotic) spatiotemporal chaos is comprised of statistically similar subsystems that interact only weakly. A systematic study of transient spatiotemporal chaos reveals extensive system behavior in all three reaction-diffusion networks for various boundary conditions. The Lyapunov dimension, the sum of positive Lyapunov exponents, and the logarithm of the transient lifetime grow lin...

converges weakly to a probability measure μ0 supported by A. The measure μ0 is called the induced Minkowskior surface measure. In this paper, we investigate Minkowski-regularity and surface measures in the case where the measured metric space is the space of continuous paths in a Riemannian manifold equipped with Wiener measure, the law of Brownian motion on this manifold. The subsets we are in...