Convergence and summable almost T-stability of the random Picard-Mann hybrid iterative process

The purpose of this paper is to introduce the random Picard-Mann hybrid iterative process. We establish the strong convergence theorems and summable almost T-stability of the random Picard-Mann hybrid iterative process and the random Mann-type iterative process generated by a generalized class of random operators in separable Banach spaces. Our results are generalizations and improvements of several well-known deterministic stability results in a stochastic versio

Nonlinear ergodic theorems for asymptotically almost nonexpansive curves in a Hilbert space

We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non-Lipschitzian mappings with nonconvex domains in a Hilbert space

Genome-wide analysis to predict protein sequence variations that change phosphorylation sites or their corresponding kinases

We define phosphovariants as genetic variations that change phosphorylation sites or their interacting kinases. Considering the essential role of phosphorylation in protein functions, it is highly likely that phosphovariants change protein functions and may constitute a proportion of the mechanisms by which genetic variations cause individual differences or diseases. We categorized phosphovariants into three subtypes and developed a system that predicts them. Our method can be used to screen important polymorphisms and help to identify the mechanisms of genetic diseases

Convergence theorems of the Ishikawa type iterative sequences with errors for generalized quasi-contractive mappings in convex metric spaces

AbstractIn this paper, some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear generalized quasi-contractive mapping in convex metric spaces are proved. The results presented in this paper not only extend and improve the main results in [1–8] but also give an affirmative answer to the open question of Rhoades-Naimpally-Singh in convex metric spaces

Jamming transition in a highly dense granular system under vertical vibration

The dynamics of the jamming transition in a three-dimensional granular system under vertical vibration is studied using diffusing-wave spectroscopy. When the maximum acceleration of the external vibration is large, the granular system behaves like a fluid, with the dynamic correlation function G(t) relaxing rapidly. As the acceleration of vibration approaches the gravitational acceleration g, the relaxation of G(t) slows down dramatically, and eventually stops. Thus the system undergoes a phase transition and behaves like a solid. Near the transition point, we find that the structural relaxation shows a stretched exponential behavior. This behavior is analogous to the behavior of supercooled liquids close to the glass transition.Comment: 5 pages, 5 figures, accepted by Phys. Rev.

A New One-Step Iterative Process for Common Fixed Points in Banach Spaces

We introduce a new one-step iterative process and use it to approximate the common fixed points of two asymptotically nonexpansive mappings through some weak and strong convergence theorems. Our process is computationally simpler than the processes currently being used in literature for the purpose