Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

12 p.

E-safety: quick self-assessment tool 2012

The old Ofsted school inspection framework introduced in September 2009 has been re-designed to be applied to the adult sector. An action plan and completion dates have been added. Whilst Ofsted are no longer restricting overall grade if an organisation receives a grade of 4, in e-safety they still want to see that learners feel safe.

Self-Help Groups

“‘Self-Help Groups’ are … “... A way to start working that helps to build up the social connections which people find useful in support of their livelihoods objectives” “... Helping people to agree things and to speak together, giving people a stronger voice in decision-making and in negotiating with more powerful forces” “... A way of increasing the effectiveness of local actions” “... Providing easier access to micro-credit and other resources and services” (Pdf contains 4 pages).

On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Determinants of self-reported smoking and misclassification during pregnancy, and analysis of optimal cut-off points for urinary cotinine: a cross-sectional study

10 p.

STM study on the self-assembly of oligothiophene-based organic semiconductors

The self-assembly properties of a series of functionalized regioregular oligo(3-alkylthiophenes) were investigated by using scanning tunneling microscopy (STM) at the liquid-solid interface under ambient conditions. The characteristics of the 2-D crystals formed on the (0001) plane of highly ordered pyrolitic graphite (HOPG) strongly depend on the length of the p-conjugated oligomer backbone, on the functional groups attached to it, and on the alkyl substitution pattern on the individual thiophene units. Theoretical calculations were performed to analyze the geometry and electronic density of the molecular orbitals as well as to analyze the intermolecular interactions, in order to obtain models of the 2-D molecular ordering on the substrate.

Control of gene expression by modulated self-assembly

Numerous transcription factors self-assemble into different order oligomeric species in a way that is actively regulated by the cell. Until now, no general functional role has been identified for this widespread process. Here, we capture the effects of modulated self-assembly in gene expression with a novel quantitative framework. We show that this mechanism provides precision and flexibility, two seemingly antagonistic properties, to the sensing of diverse cellular signals by systems that share common elements present in transcription factors like p53, NF-kappa B, STATs, Oct and RXR. Applied to the nuclear hormone receptor RXR, this framework accurately reproduces a broad range of classical, previously unexplained, sets of gene expression data and corroborates the existence of a precise functional regime with flexible properties that can be controlled both at a genome-wide scale and at the individual promoter level.