On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

Some Results on Fixed and Best Proximity Points of Multivalued

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

Designing Spaces for Effective Learning: A guide to 21st century learning space design

Increasing investment in estate and learning technologies, combined with the need for more cost-effective space utilisation, is making it increasingly important for senior managers to keep abreast of new thinking about the design of technology-rich learning spaces. Designing Spaces for Effective Learning, one of a series of guides, was launched at the JISC Conference 2006 which helped to meet this need. A visually-rich publication, it was designed to promote better understanding of what makes an effective design for the 21 century and to summarise the key points to consider when approaching a refurbishment or new-build project. The publication takes the reader on a ’walk through’ an educational institution, exploring the relationship between learning technologies and innovative examples of physical space design at each stage of the journey. Discussion of the key points is illustrated by ten case studies from further and higher education, and floor plans from AMA Alexi Marmot Associates, architects and space planners, which provide up-to-date guidelines on the integration of technologies into teaching and learning accommodation.

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

12 p.

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.

Complete agent based simulation of mini-grids

EuroPES 2009

Catechol 2,3-dioxygenase-assisted cleavage of aromatics by “anaerobic” termite gut spirochetes and genomic evidence of a complete meta-pathway

The termite hindgut microbial ecosystem functions like a miniature lignocellulose-metabolizing natural bioreactor, has significant implications to nutrient cycling in the terrestrial environment, and represents an array of microbial metabolic diversity. Deciphering the intricacies of this microbial community to obtain as complete a picture as possible of how it functions as a whole, requires a combination of various traditional and cutting-edge bioinformatic, molecular, physiological, and culturing approaches. Isolates from this ecosystem, including Treponema primitia str. ZAS-1 and ZAS-2 as well as T. azotonutricium str. ZAS-9, have been significant resources for better understanding the termite system. While not all functions predicted by the genomes of these three isolates are demonstrated in vitro, these isolates do have the capacity for several metabolisms unique to spirochetes and critical to the termite system’s reliance upon lignocellulose. In this thesis, work culturing, enriching for, and isolating diverse microorganisms from the termite hindgut is discussed. Additionally, strategies of members of the termite hindgut microbial community to defend against O₂-stress and to generate acetate, the “biofuel” of the termite system, are proposed. In particular, catechol 2,3-dioxygenase and other meta-cleavage catabolic pathway genes are described in the “anaerobic” termite hindgut spirochetes T. primitia str. ZAS-1 and ZAS-2, and the first evidence for aromatic ring cleavage in the phylum (division) Spirochetes is also presented. These results suggest that the potential for O₂-dependent, yet nonrespiratory, metabolisms of plant-derived aromatics should be re-evaluated in termite hindgut communities. Potential future work is also illustrated.