By a dynamical system (X, T ) we mean the action of the semigroup (Z,+) on a metrizable topological space X induced by a continuous selfmap T : X → X. Let M(X) denote the set of all compatible metrics on the space X. Our main objective is to show that a selfmap T of a compact space X is a Banach contraction relative to some d1 ∈ M(X) if and only if there exists some d2 ∈ M(X) which, regarded as...

A semi{discrete spatial nite diierence approximation and two fully discrete nite diierence approximations to the complex Ginzburg{Landau equation are considered in this paper. The existence of an inertial manifold is proved inside a discrete H 1 absorbing ball for the semi{discrete approximation by showing certain spectral properties hold for the linear operator and certain Lipschitz properties...

Essential extensions and p-extensions have been studied for commutative rings with identity in various articles, such as [2], [3], and [13]. The present article applies these concepts to certain subrings of C(X). Moreover, the article introduces a new ring extension, called a pg-extension, and determines its relation to both essential extension and p-extension. It turns out that the pg-extensio...

In this paper, we study nonlinear analytic methods for linear contractive operators in Banach spaces. Using these results, we obtain some new strong convergence theorems for commutative families of linear contractive operators in Banach spaces. In the results, the limit points are characterized by sunny generalized nonexpansive retractions.

Previously we extended the utility of mapping-by-sequencing by combining it with sequence capture and mapping sequence data to pseudo-chromosomes that were organized using wheat-Brachypodium synteny. This, with a bespoke haplotyping algorithm, enabled us to map the flowering time locus in the diploid wheat Triticum monococcum L. identifying a set of deleted genes (Gardiner et al., 2014). Here, ...

We examine qualitative properties of solutions of self-consistent Poisson-NernstPlanck (PNP) systems, including uniqueness. In the case of vanishing permanent charge, the predominant case studied, our results unveil a rich structure inherent in these systems, one that is determined by the boundary conditions and the signs of the oppositely charged carrier fluxes. A particularly significant spec...

In this paper, we develop existence and uniqueness criteria to certain class of three point boundary value problems associated with third order nonlinear fuzzy differential equations, with the help of Green’s functions and contraction mapping principle.

1 Local Existence of Evolution Equations 2 1.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 The contraction mapping principle . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Local Existence for Evolution Partial Differential Equations . . . . . . . . . . . . 5 1.4 Local Existence for Nonlinear Heat and Hartree Equations . . . . . . . ...

\noindent We study the concept of complementarity, introduced by Bagchi and Quesne in [Phys. Lett. A {\bf 301}, 173 (2002)], between pseudo-Hermiticity weak a rigorous mathematical viewpoint coordinate transformations when system has position-dependent mass. first determine, under modified-momentum, generating functions identifying complexified potentials $V_\pm(x)$ both concepts $\widetilde\et...

We consider random walks on the mapping class group whose support generates a nonelementary subgroup and contains a pseudo-Anosov map whose invariant Teichmüller geodesic is in the principal stratum For such random walks, we show that mapping classes along almost every infinite sample path are eventually pseudo-Anosov whose invariant Teichmüller geodesics are in the principal stratum. This prov...