Principal Functions


Book Description

During the decade and a half that has elapsed since the intro duction of principal functions (Sario [8 J), they have become impor tant tools in an increasing number of branches of modern mathe matics. The purpose of the present research monograph is to systematically develop the theory of these functions and their ap plications on Riemann surfaces and Riemannian spaces. Apart from brief background information (see below), nothing contained in this monograph has previously appeared in any other book. The basic idea of principal functions is simple: Given a Riemann surface or a Riemannian space R, a neighborhood A of its ideal boundary, and a harmonic function s on A, the principal function problem consists in constructing a harmonic function p on all of R which imitates the behavior of s in A. Here A need not be connected, but may include neighborhoods of isolated points deleted from R. Thus we are dealing with the general problem of constructing harmonic functions with given singularities and a prescribed behavior near the ideal boundary. The function p is called the principal function corresponding to the given A, s, and the mode of imitation of s by p. The significance of principal functions is in their versatility.




Principal Functions


Book Description

During the decade and a half that has elapsed since the intro duction of principal functions (Sario [8 J), they have become impor tant tools in an increasing number of branches of modern mathe matics. The purpose of the present research monograph is to systematically develop the theory of these functions and their ap plications on Riemann surfaces and Riemannian spaces. Apart from brief background information (see below), nothing contained in this monograph has previously appeared in any other book. The basic idea of principal functions is simple: Given a Riemann surface or a Riemannian space R, a neighborhood A of its ideal boundary, and a harmonic function s on A, the principal function problem consists in constructing a harmonic function p on all of R which imitates the behavior of s in A. Here A need not be connected, but may include neighborhoods of isolated points deleted from R. Thus we are dealing with the general problem of constructing harmonic functions with given singularities and a prescribed behavior near the ideal boundary. The function p is called the principal function corresponding to the given A, s, and the mode of imitation of s by p. The significance of principal functions is in their versatility.




Contextual Design


Book Description

This is the only book that describes a complete approach to customer-centered design, from customer data to system design. Readers will be able to develop the work models that represent all aspects of customer work practices.




Regulation of health care professionals


Book Description

In this consultation paper, the Law Commissions of England and Wales, Scotland and Northern Ireland are seeking views on the regulation of health care professionals in the UK and social workers in England. In their first joint consultation, the Commissions are asking how a new legal framework would: give the regulators increased flexibility in the use of their powers while ensuring public accountability; enable them to ensure proper standards of professional education, conduct and practice; and have at its heart a duty on the regulators to protect the public. It makes provisional proposals which seek to simplify and modernise the law and establish a streamlined, transparent and responsive system of regulation of health care professionals, and in England only, the regulation of social workers




Research in Progress


Book Description







Hearings


Book Description




Stretching Exercises Encyclopedia


Book Description

Presents a series of stretching exercises, complete with anatomical illustrations that show the different muscle groups involved in each move, instructions on adopting proper postures, and tips on avoiding common mistakes.




Science, Mysticism and Psychical Research


Book Description

Science, mysticism, and psychical research are generally thought to be irreconcilable; this book centres on a towering synthesis achieved by the late Michael Whiteman, an Associate Professor of Applied Mathematics at the University of Cape Town. It is revolutionary; Whiteman was able to meld mathematical physics and general science with psychical research and Indian and Western mystical texts, clarified by a life-time of psychical and mystical experience, and coupled with an extensive knowledge of philosophy and psychology. Part One is about the experience of states, spaces, and worlds other than physical. It provides essential groundwork for understanding the psychical and mystical. Whiteman’s own experience is combined with evidence ranging from quantum mechanics to the Upanishads. Part Two centres on two murder cases that Whiteman studied, as an entry to the concept of the corporate structure of personality, and the workings of the mind in personal development. Part Three covers his analysis of ancient texts based on his understanding as a mystic. His interpretations differ radically from standard treatments. Part Four investigates his exploration of non-physical existence. Part Five considers the mystical life, including Whiteman’s own, and how it relates to physical laws. The book concludes with a brief biography.