Domain decomposition methods for welding problems

This paper, a 2-D non-linear electric arc-welding problem is considered. It is assumed that the moving arc generates an unknown quantity of energy which makes the problem an inverse problem with an unknown source. Robust algorithms to solve such problems e#ciently, and in certain circumstances in real-time, are of great technological and industrial interest. There are other types of inverse problems which involve inverse determination of heat conductivity or material properties [CDJ63][TE98], inverse problems in material cutting [ILPP98], and retrieval of parameters containing discontinuities [IK90]. As in the metal cutting problem, the temperature of a very hot surface is required and it relies on the use of thermocouples. Here, the solution scheme requires temperature measurements lied in the neighbourhood of the weld line in order to retrieve the unknown heat source. The size of this neighbourhood is not considered in this paper, but rather a domain decomposition concept is presented and an examination of the accuracy of the retrieved source are presented. This paper is organised as follows. The inverse problem is formulated and a method for the source retrieval is presented in the second section. The source retrieval method is based on an extension of the 1-D source retrieval method as proposed in [ILP].

[Crossword] Crossword solution - by Parsman

Tony Mann provides the crossword solution under the pseudonym of Parsman.

EMPHASIS

Report on EMPHASIS Seminar Series by Tony Mann

[Book review] Reviews. Peter Aughton, The Transit of Venus: The Brief, Brilliant Life of Jeremiah Horrocks, Father of British Astronomy, Orion, 2004

Book review of: Peter Aughton, The Transit of Venus: The Brief, Brilliant Life of Jeremiah Horrocks, Father of British Astronomy, Orion, 2004, 0-297-84721-x, £18.99.

[Book review] Owen Gingerich, The Book Nobody Read: In Pursuit of the Revolutions of Nicolaus Copernicus, Heinemann, 2004

Tony Mann reviews: Owen Gingerich, The Book Nobody Read: In Pursuit of the Revolutions of Nicolaus Copernicus, Heinemann, 2004, 0-434-01315-3, £12.99.

[Book review] Reviews. Scarlett Thomas, PopCo, London and New York: Fourth Estate, 2004

Book review of: Scarlett Thomas, PopCo, London and New York: Fourth Estate, 2004. 1-84115-763-5, £12.99.

[Book review] The Oxford Murders

Review of the book 'The Oxford Murders' by Guillermo Martínez (trans. by Sonia Soto), Abacus, 2005, £9.99, pp 208, ISBN 0-349-11721-7

[Book review] Piero della Francesca: A Mathematician's art by J.V. Field, Yale University Press.

Review of the book 'Piero della Francesca: A Mathematician’s Art' by J.V. Field, Yale University Press, 420 pp, £35 ISBN 0300103425.

Popular lectures report

This is a report of two lectures held by the London Mathematical Society: a) What Computers Cannot Do by Dr Alan Slomson; b) The Mathematics of Shrek by Dr Joan Lazenby.

[Report] LMS 'Book of Presidents' Launch

Report of the London Mathematical Society meeting to launch "The Book of Presidents, 1865-1965, London Mathematical Society" by Susan Oakes, Alan Pears and Adrian Rice, London Mathematical Society, 2005, ISBN: 978-0950273419

[Book review] Mathematics and Culture II

Review of Mathematics and Culture II. Visual Perfection: Mathematics and Creativity, Michele Emmer (Ed.), Springer, 2005 ISBN: 978-3-540-21368-0

Case-based retrieval of 3-dimensional shapes for the design of metal castings

This paper describes research into retrieval based on 3-dimensional shapes for use in the metal casting industry. The purpose of the system is to advise a casting engineer on the design aspects of a new casting by reference to similar castings which have been prototyped and tested in the past. The key aspects of the system are the orientation of the shape within the mould, the positions of feeders and chills, and particular advice concerning special problems and solutions, and possible redesign. The main focus of this research is the effectiveness of similarity measures based on 3-dimensional shapes. The approach adopted here is to construct similarity measures based on a graphical representation deriving from a shape decomposition used extensively by experienced casting design engineers. The paper explains the graphical representation and discusses similarity measures based on it. Performance measures for the CBR system are given, and the results for trials of the system are presented. The competence of the current case-base is discussed, with reference to a representation of cases as points in an n-dimensional feature space, and its principal components visualization. A refinement of the case base is performed as a result of the competence analysis and the performance of the case-base before and after refinement is compared.

Case based adaptation using interpolation over nominal values

In this paper we propose a method for interpolation over a set of retrieved cases in the adaptation phase of the case-based reasoning cycle. The method has two advantages over traditional systems: the first is that it can predict “new” instances, not yet present in the case base; the second is that it can predict solutions not present in the retrieval set. The method is a generalisation of Shepard’s Interpolation method, formulated as the minimisation of an error function defined in terms of distance metrics in the solution and problem spaces. We term the retrieval algorithm the Generalised Shepard Nearest Neighbour (GSNN) method. A novel aspect of GSNN is that it provides a general method for interpolation over nominal solution domains. The method is illustrated in the paper with reference to the Irises classification problem. It is evaluated with reference to a simulated nominal value test problem, and to a benchmark case base from the travel domain. The algorithm is shown to out-perform conventional nearest neighbour methods on these problems. Finally, GSNN is shown to improve in efficiency when used in conjunction with a diverse retrieval algorithm.

A framework for e-learning: a blended solution?: current developments in technology-assisted education

This paper describes a Framework for e-Learning and presents the findings of a study investigating whether the use of Blended Learning can fulfill or at least accommodate some of the human requirements presently neglected by current e-Learning systems. This study evaluates the in-house system: Teachmat, and discusses how the use of Blended Learning has become increasingly prevalent as a result of its enhancement and expansion, its relationship to the human and pedagogical issues, and both the positive and negative implications of this reality. [From the Authors]