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Beyond Perturbation: Introduction to the Homotopy Analysisby Shijun Liao
Chapman & Hall/CRC 2003; US$ 119.95Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. The author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is the first book to explore the details of this valuable new approach. more...
Shape Optimization and Optimal Designby John Cagnol; Micheal P. Polis; Jean-Paul Zolesio
Marcel Dekker Inc 2001; US$ 229.95This volume presents developments and advances in modelling passive and active control systems governed by partial differential equations. It emphasizes shape analysis, optimal shape design, controllability, nonlinear boundary control, and stabilization. more...
Moving Shape Analysis and Controlby Marwan Moubachir
CRC Press 2006; US$ 99.95Moubachir (INRA) and Zol sio (CNRS and INRIA, France) provide a mathematical analysis of problems related to the evolution of domains in two or three dimensions, as applied to engineering applications such as free surface flows, phase changes, fracture and contact problems, fluid-structure interaction in civil transport vehicles, stayed-cable bridg more...
Lectures on Homotopy Theoryby R.A. Piccinini
Elsevier 1992; US$ 210.00The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the n th homotopy group of the sphere S n , for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of S n are trivial and that the third homotopy group of S 2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps. Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac... more...
Algebraic Models in Geometryby Yves Félix; John Oprea; Daniel Tanré
Oxford University Press, UK 2008; US$ 55.00A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory. - ;Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also for geometers who are faced with problems requiring topological approaches and thus need a simple and concrete introduction to... more...
Statistical Models of Shapeby Rhodri Davies; Carole Twining; Chris Taylor
Springer 2008; US$ 129.00Deformable shape models have wide application in computer vision and biomedical image analysis. This book addresses a key issue in shape modelling: establishment of a meaningful correspondence between a set of shapes. Correspondence has traditionally been established by manual annotation of the data, however this is a time-consuming and error-prone process that does not extend easily to 3D. Thus, almost all applications of statistical shape models have been restricted to 2D objects. This book explores a particular approach to establishing correspondence that casts model-building as an optimisation problem. A general framework is established to find the correspondence that optimises an objective function of model quality. Efficient methods,... more...
Stable Homotopy Around the Arf-Kervaire Invariantby Victor P. Snaith
Springer 2009; US$ 99.00Describes important techniques of stable homotopy theory, applying them to the long-standing problem of the existence of framed manifolds with odd Arf-Kervaire invariant. This work opens with an account of the necessary algebraic topology background. more...
Shape and Shape Theoryby D. G. Kendall; D. Barden; T. K. Carne; H. Le
John Wiley & Sons, Ltd. 2009; US$ 263.00Shape and Shape Theory D. G. Kendall Churchill College, University of Cambridge, UK D. Barden Girton College, University of Cambridge, UK T. K. Carne King's College, University of Cambridge, UK H. Le University of Nottingham, UK The statistical theory of shape is a relatively new topic and is generating a great deal of interest and comment by statisticians, engineers and computer scientists. Mathematically, 'shape' is the geometrical information required to describe an object when location, scale and rotational effects are removed. The theory was pioneered by Professor David Kendall to solve practical problems concerning shape. This text presents an elegant account of the theory of shape that has evolved from Kendall's work. Features include:... more...
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John Wiley & Sons, Ltd. 2008; US$ 167.00'Homology' as a concept became increasingly elusive during the course of the 20th century. The central debates and controversies concern both fundamental definitions and the nature of the criteria by which homology is judged. Attempts to move away from comparative morphology to ideas based on developmental pathways have tended to founder on the fact that developmental pathways evolve and that similar cells or tissues or structures in animals will often have different developmental origins. The use of information about conserved molecules in seemingly conserved developmental processes has also proven controversial. In molecular biology, the use of the term 'homology' has given rise to more debate, although here the issue seems to involve... more...
