Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings

p(>= 2)-cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the whole metric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity points and fixed points is also investigated as well as some related properties of composed self-mappings from the union of any two adjacent subsets, belonging to the initial set of subsets, to themselves.

Stability and Limit Oscillations of a Control Event-Based Sampling Criterion

This paper investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

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

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Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane

This paper provides a review of important results concerning the Geometrical Theory of Diffraction and Geometrical Optics. It also reviews the properties of the existing solution for the problem of diffraction of a time harmonic plane wave by a half-plane. New mathematical expressions are derived for the wave fields involved in the problem of diffraction of a time harmonic plane wave by a quarter-plane, including the secondary radiated waves. This leads to a precise representation of the diffraction coefficient describing the diffraction occurring at the corner of the quarter-plane. Our results for the secondary radiated waves are an important step towards finding a formula giving the corner diffraction coefficient everywhere. © 2012 The authors.

On the application of differential geometry to MDO

Multidisciplinary Design Optimization (MDO) is a methodology for optimizing large coupled systems. Over the years, a number of different MDO decomposition strategies, known as architectures, have been developed, and various pieces of analytical work have been done on MDO and its architectures. However, MDO lacks an overarching paradigm which would unify the field and promote cumulative research. In this paper, we propose a differential geometry framework as such a paradigm: Differential geometry comes with its own set of analysis tools and a long history of use in theoretical physics. We begin by outlining some of the mathematics behind differential geometry and then translate MDO into that framework. This initial work gives new tools and techniques for studying MDO and its architectures while producing a naturally arising measure of design coupling. The framework also suggests several new areas for exploration into and analysis of MDO systems. At this point, analogies with particle dynamics and systems of differential equations look particularly promising for both the wealth of extant background theory that they have and the potential predictive and evaluative power that they hold. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Knowledge based strategy: appraising knowledge creation capability in organisations.

This thesis sets out a journey which culminates in the development of an analytical framework, the "Organisational Creativity Appraisal" which is intended to assist organisations in evaluating their ability to support and develop creativity. This framework is derived from the common thread of the thesis, which is drawn from a range of research and consultancy projects, and the resulting published work, spanning an eight year period, centring on the role of knowledge and creativity in the strategy and performance of organisations. The literature of strategy, learning and creativity increasingly recognises that organisational context is critical to the formation of strategy, to the content of the strategy and to its successful implementation. The thesis explores the ways in which learning and creativity, the basis of knowledge-based strategy, are influenced by organisational context or social architecture. The research explores the ways in which managers can gain greater understanding of the social architectures of their organisations so as to assist in supporting their strategic development. The central core of the thesis is the nine published papers upon which it is based but it also derives from the broader perspective of my published work in the form of both articles and books. The thesis further draws upon my own experience as a leader and manager in the context of university business schools and as a consultant, researcher and developer in the context of a range of international private and public sector organisations. The work is based upon a premise that theory should inform practice and that practice should inform theory. The "Organisational Creativity Appraisal" framework is informed by both theory and practice and is intended to assist in management practice. There is no assumption that management research can arrive at prescriptions for managerial and organisational behaviour. On the other hand management research can usefully inform management and organisational behaviour, as long as it is employed in a critically reflective manner. The "Organisational Creativity Appraisal" presented in this work should be regarded as the framework in its present form which is likely to develop further as my research progresses in the future.

Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface

Mishuris, G; Kuhn, G., (2001) 'Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface', Zeitschrift f?r Angewandte Mathematik und Mechanik 81(12) pp.811-826 RAE2008

The numerical modelling of multi-physics phenomena: The shape casting process

In this paper a computer simulation tool capable of modelling multi-physics processes in complex geometry has been developed and applied to the casting process. The quest for high-quality complex casting components demanded by the aerospace and automobile industries, requires more precise numerical modelling techniques and one that need to be generic and modular in its approach to modelling multi-processes problems. For such a computer model to be successful in shape casting, the complete casting process needs to be addressed, the major events being:-• Filling of hot liquid metal into a cavity mould • Solidification and latent heat evolution of liquid metal • Convection currents generated in liquid metal by thermal gradients • Deformation of cast and stress development in solidified metal • Macroscopic porosity formation The above phenomena combines the analysis of fluid flow, heat transfer, change of phase and thermal stress development. None of these events can be treated in isolation as they inexorably interact with each other in a complex way. Also conditions such as design of running system, location of feeders and chills, moulding materials and types of boundary conditions can all affect on the final cast quality and must be appropriately represented in the model.

PHYSICA - A software environment for the modelling of multi-physics phenomena

A brief description of a software environment in FORTRAN77 for the modelling of multi-physics phenomena is given. The numerical approach is based on finite volume methods but extended to unstructured meshes (ie. FV-UM). A range of interacting solution procedures for turbulent fluid flow, heat transfer with solidification/melting and elasto-visco-plastic solid mechanics are implemented in the first version of PHYSICA, which will be released in source code form to the academic community in late 1995.

Using an interactive software environment for the parallelization of real-world scientific applications

The parallelization of real-world compute intensive Fortran application codes is generally not a trivial task. If the time to complete the parallelization is to be significantly reduced then an environment is needed that will assist the programmer in the various tasks of code parallelization. In this paper the authors present a code parallelization environment where a number of tools that address the main tasks such as code parallelization, debugging and optimization are available. The ParaWise and CAPO parallelization tools are discussed which enable the near automatic parallelization of real-world scientific application codes for shared and distributed memory-based parallel systems. As user involvement in the parallelization process can introduce errors, a relative debugging tool (P2d2) is also available and can be used to perform nearly automatic relative debugging of a program that has been parallelized using the tools. A high quality interprocedural dependence analysis as well as user-tool interaction are also highlighted and are vital to the generation of efficient parallel code and in the optimization of the backtracking and speculation process used in relative debugging. Results of benchmark and real-world application codes parallelized are presented and show the benefits of using the environment