ANNUAL REPORT 1998 The last year has been one of considerable change for the Department of Mathematics at HeriotWatt. Two longstanding members of staff, Professor Robin Knops and Mr Jim Bree, retired during the year. Robin Knops has been at HeriotWatt for 27 years, including periods as Head of Department, Dean of Science and VicePrincipal; we are pleased that he continues to be involved in the local mathematical community through ICMS and ICIAM99. In 1998 we were pleased to honour one of our former colleagues, Professor John M Ball, FRS, who was given an honorary degree in the July graduation. The department has also welcomed many new faces during the year, which started with the arrival of Professors Sergei Kuksin and Jonathan Sherratt, and Dr Robert Weston. During the summer, Drs Chris Boulter and Paul Turner were appointed, and joined us later in the year, and we look forward to the arrival of Drs Jan Kristensen and Andrew White, who have recently been appointed. With these new appointments, our research activity continues to grow and broaden. An exciting development during the year was the award of a prestigious grade 1 to a Teaching Company project, lead by Dr Dugald Duncan and Professors Chris Eilbeck and Andrew Lacey, in collaboration with Edinburgh Petroleum Services, and followup projects are building on this success. Mathematical biology is growing within the department, and a Scottish Theoretical Biology Forum, partled by Professor Jonathan Sherratt, was established during the year. Professor Cliff Beevers and the CALM group went from strength to strength, gaining a major contract in 1998 for the development of computer examinations for use in the Far East. As in previous years, members of the Department made several invited lectures at international conferences. Most notable of these was the invited address given by Professor Sergei Kuksin at the International Congress of Mathematicians in Berlin. In 1999, we look forward to a number of scientific meetings run by members
of the department at the International Centre for Mathematical Sciences,
and to the Fourth International Congress of Industrial and Applied Mathematics,
coordinated by Professor Jack Carr and Dr Michael Levitin, which will bring
several thousand mathematicians to Edinburgh.
J Howie, Head of Department
Staff Visitors Conferences Invited Papers and Seminars Service to Mathematical Community Research & other Grants Theses presented for Higher Degrees Publications Papers submitted for publication 
STAFF  
Head of Department  J Howie 
Professors  C E Beevers
K J Brown J Carr J C Eilbeck R J Knops S Kuksin A A Lacey J A Sherratt 
Professor Emeritus  O Penrose 
Honorary Professor  F M Russell 
Readers  R N Hills
D A Johnston K Khanin B P Rynne 
Senior Lecturers  D E R Clark
D B Duncan G R McGuire A R Prince 
Lecturers  C J Boulter
J Bree B P Dodds N D Gilbert M Levitin L E Nicholas C Noble H U Rahman P R Turner R A Weston D G Wilkinson M A Youngson 
Temporary Lecturers  R M Dunwell
A Lipowski 
Research Fellow  J L Marin 
Research Associates  L CruzeiroHansson
J C Dallon D J Fiddes L Notorantonio D G Wild 
Teaching Company Associate  J Tracey 
Computing Officers  M Foster
S Mowbray 
Secretaries  I Fraser
P Hampton S Meikle F Paterson 
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VISITORS
TO THE DEPARTMENT
The following made longterm visits: Bario R, Zaragoza


In addition shortterm visits were made and seminars given by the following:  
Baesens, C, Cambridge University  HandleySchachler, S, Edinburgh Petroleum Services 
Blank, Michael, Moscow  Henkel, M, LPS, Nancy 
Braden, H W, Edinburgh University  Iserles, A, Cambridge University 
Brindley, J, Leeds  Kovalev, A, Edinburgh University 
Buchstaber, V, Moscow  Kropholler, P H, Queen Mary & Westfield College 
Carstensen, C, Kiel  Lewis, M A, University of Utah 
Chaplain, M A J, Dundee  Mikhailov, S, Leeds University 
Chaves, M, Universidad Autonoma de Madrid  Nechaev, S, CNRSUniversite Paris XI & Landau Institute 
Davie, S, Edinburgh University  Pego, R, University of Maryland 
Davies, B, King"s College  Piatnitski, A, Moscow and Narvik 
Ekeland, I, Université ParisDauphine  Pohozhaev, S, Steklov Institute, Moscow 
Enolskii, V, Kiev  Pollicott, M, University of Manchester 
Evans, D, Bristol University  Richmond, N J, Leeds 
Eynard, B, Durham University  Silhavy, M, Prague 
Friedman, A, University of Minnesota  Skubachevskii, A L, Moscow 
Funken, S, Kiel  Slemrod, M, University of Wisconsin 
Gaffney, E A, Oxford  Suhov, Y, Cambridge University 
Gilson, C, Glasgow University  Ward, M, University of British Columbia 
Gonzales, R, Madrid  Weigel, M, Leipzig 
Gordon, I G, Edinburgh University  Wilson, J S, Birmingham University 
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INVITED PAPERS AND SEMINARS GIVEN BY MEMBERS OF STAFF  
Professor C E Beevers  Seminar, MATHWISE User Group, Nottingham University, January 1998 (with
J Dorner, Napier University), "CAL – Assessment by Computer"
Seminar, ICBL, HeriotWatt University, January 1998 (with Dr D G Wild), "CALM view of assessment" Seminar, Training day for mathematics examiners, Cambridge University, April 1998 (with Dr D G Wild), "Setting questions in a template" Invited talk, "Teaching over the Web" workshop, HeriotWatt University, June 1998 "Assessment in the SUMSMAN project" Conference talk "SUMSMAN Training Day" (Video conference from Napier University), September 1998, "Assessment in the SUMSMAN project" Contributed talk, "MATHWISE User Group First Annual Conference", Birmingham University, September 1998, "Using MATHWISE in a university course" Contributed talk "AltC Annual Conference", Oxford University, September 1998. "Issues of partial credit in mathematical courseware" Contributed talk, "Assessment Strand of TALISMAN Video Conference to Scottish Universities", October 1998, from Napier University studio, "The role of the computer in assessment" 
Professor J Carr  Seminar, University of Oxford, June 1998, "Coarsening"
Seminar, University of Glasgow, October 1998, "Asymptotics of nonlocal partial differential equations" Lecture, International Congress of Mathematicians, Berlin, August 1998, "LifshitzSlyozov theory of coarsening" 
Dr J C Dallon  Seminar, Brigham Young University, April 1998, "Mathematical modelling
in biology: wound healing and slime mould"
Invited talk, Workshop on "Pattern Formation and Morphogenesis: the Basic Process" (part of the IMA program on Mathematical Biology), Minnesota, 712 September 1998, "Streaming and spiral waves in slime mould" 
Professor J C Eilbeck  Seminar, University of Swansea, March 1998, "Breathers in 1D
and 2D lattices"
Conference talk, International workshop on "Transmission and Signal Processing in Nonlinear Electronics and Optics", Dijon, France, 810 June 1998, "Some studies of travelling waves on discrete systems" Conference talk, Nonlinear Science Festival, 712 December 1998 Niels Bohr Institute, Copenhagen, "Localized breathers on twodimensional lattices" 
Dr N D Gilbert  Seminar, University of Leeds, November 1998, "Groups with braid presentations" 
Professor J Howie  Seminar, UMIST, February 1998, "BestvinaBrady groups and the plus
construction"
Seminar, University of St Andrews, February 1998, "BestvinaBrady groups and the plus construction" Seminar, Université de Provence, Marseille, September 1998 "Varietes de Seifert pour les noueds rubans de dimension superieures" Seminar, Université de Provence, Marseille, September 1998, "BestvinaBrady groups and the plus construction" Seminar, University of Cambridge, November 1998. "Generalised triangle groups and the existence of free subgroups" Invited talk "Groups in Galway", Galway, 21 – 23 May 1998, "Rigidity of onerelator groups with centre" 
Dr D A Johnston  Seminar: Albert Einstein Institute, Potsdam, May 1998:, "Balls in boxes
and quantum gravity"
University of Edinburgh, September 1998, "Quantum gravity as a load of balls" Invited talk at "Quantum Geometry, Random Matrices, Statistical Models of Strings and Quantum Gravity", November 2628, Copenhagen University 
Dr K Khanin  Series of 3 talks in the Series "Seminars on Problem of Turbulence",
HeriotWatt and Edinburgh Universities, March 1998, "Random Burgers equations
and turbulence"
Seminar, University of Sussex, May 1998, "Rigidity in onedimensional dynamics" Seminar, EPFL, Lausanne, June 1998, "Rigidity in onedimensional dynamics" Seminar, Queen Mary and Westfield College, December 1998, "Dynamical systems and random Burgers equation" Invited talk, European Conference on "Probabilistic Methods in NonHyperbolic Dynamics, University of Warwick, 30 April – 4 May 1998, "Simultaneous Diophantine approximations" Invited talk, International Workshop on "Dynamical Systems", Trieste, 30 August – 21 September 1998, "Dynamical Systems and Kolmogorov"s Turbulence" and "Simultaneous Diophantine approximations" Invited talk, Minisymposium on "Dynamical Systems", Helsinki, December 1998, "Random forced Burgers equation" 
Professor R J Knops  Seminar, University of Oxford, January 1998, "Uniqueness in nonlinear
elasticity"
Seminar, University of Pisa, October 1998, "SaintVenant"s principle: the search of an engineering conjecture for mathematical verification" Conference talk, British Applied Mathematics Colloquium, Brunel University, 69 April 1998, "Spatial stability in a partially constrained elastic plate" Conference talk, Symposium "Trends in Applications of Mathematics to Mechanics", Nice, 2529 May 1998, "Uniqueness in the traction boundary value problem of nonlinear elasticity" Invited talk, Symposium on "Mechanics of Materials", Oberwolfach, August 1998, "Spatial behaviour in continua" Invited talk "2nd International Symposium, Problemi Attuali dell"Analise e della Fisica Matematica, Taormina, 1517 October 1998, "Aspects of spatial stability in elasticity" 
Professor S Kuksin  Seminar, "North British Probability Seminar", January 1998, "Stochastic
NLS equation"
Seminar, University of Cambridge, February 1998, "Turbulence in nonlinear PDEs" Seminars, University Paris VI, 6 and 8 April 1998, "KAM theory for partial differential equations" Series of 3 talks in the Series "Seminars on Problem of Turbulence", HeriotWatt and Edinburgh Universities, April and May 1998, "Theory of turbulence" Seminar, Imperial College, June 1998, "Turbulence in nonlinear PDEs" Seminar, University of Liverpool, October 1998, "How to count solutions of a nonlinear PDE in a manifold" Seminar, University of Oxford, November 1998, "Turbulence in nonlinear PDEs" Seminar, University of Surrey, November 1998 "Turbulence in nonlinear Schrödinger equation" Seminar, University of Bath, December 1998, "Elliptic equations for maps solved in manifolds" Seminar, University of Edinburgh, December 1998, "Lefschets formula from PDEs in manifolds" Invited talk, Conference in honour of Professor Novikov"s 60th birthday, Moscow, 2529 May 1998, "On persistence of finitegap solutions" Invited talks, CIME Conference " Dynamical Systems and Small Divisors", Cetraro, Italy, 1320 June, 1998, 3 lectures "KAM theory for partial differential equations" Invited talk, International Congress of Mathematicians, Berlin, 1728 August 1998, "Elements of a qualitative theory of Hamiltonian PDEs" 
Professor A A Lacey  Seminar, Instituto Superior Tecnico, Lisbon, September 1998, "A nonlocal
hyperbolic problem modelling food sterilization"
Seminar, Universidade de Beira Interior, Covilha, September 1998, "Persistence of corners in free boundaries in HeleShaw flow" Seminar, Centro de Matematica e aplicacoes Fundamentais, Universidade de Lisboa, September 1998, "A nonlocal hyperbolic problem modelling food sterilization" Invited talk, British Applied Mathematics Colloquium, Brunel University, 69 April, 1998, "Use of complexvariable theory in oilreservoir testing" 
Dr J L Marin  Seminar, University of Arizona, October 1998, "Moving breathers in
2D Hamiltonian lattices"
Seminar, Centre for NonLinear Studies, Los Alamos National Laboratory, New Mexico, October 1998, "Moving breathers in 2D Hamiltonian lattices" Talk, CECAM Conference "Nonlinear Localized Excitations in Condensed Matter and Molecular Physics", Lyon, 7 July 1998, "Moving breathers in 2D: the mica problem" 
Professor O Penrose  Seminar, Rutgers University, Mathematics Department, March 1998, "Asymptotic
behaviour of a simplified BeckerDöring equation"
Seminar, Rutgers University, Physics Department, April 1998, "Does offdiagonal longrange order help to explain superconductivity?" Seminar, University of Leoben, Austria, June 1998, "Diffusioninduced grain boundary motion" 
Dr A R Prince  Invited talk, Combinatorics "98 Conference, Palermo, 1420 June, 1998, "Covering sets of spreads in PG(3,q)" 
Dr B P Rynne  Seminar, Dundee University, April 1998, "Oscillating global continua
of positive solutions of semilinear elliptic problems"
Seminar, joint Strathclyde/Glasgow Universities Analysis Seminar, November 1998, "The Fucik spectrum: what is it and what does it look like?" 
Professor J A Sherratt  Seminar, Strathclyde University, January 1998, "Mathematical modelling
in cancer"
Seminar, University of Glasgow, May 1998, "Mathematical modelling of tumour invasion" Seminar, University of St Andrews, November 1998, "Invasive wave fronts and spatiotemporal oscillations in predatorprey systems" Colloquium, University of Edinburgh, November 1998, "Can mathematics help to cure cancer" Seminar, Glasgow Caledonian University, November 1998, "Can mathematics help to cure cancer" Invited talk, Conference on "The Mathematical Biology of Patterns and Processes", Bath, 59 April 1998, "Discrete mathematical models for cell populations" Invited talk, Gordon Conference on "Theoretical Biology and Biomathematics", Tilton, New Hampshire, USA, 712 June 1998, "Mathematical modelling of scar tissue structure" Invited talk, Workshop on "Pattern Formation and Morphogenesis: the Basic Process" (part of the IMA program on Mathematical Biology), Minnesota, 712 September 1998, "Signal range and spatial patterns in juxtacrine signalling" Invited talk, Conference on "On Growth and Form" (a meeting to commemorate the work of D"Arcy Thompson), Dundee, 2024 September 1998, "Pattern formation in cancer" 
Dr R A Weston  Conference talk, "2nd Informal UK meeting on 2D Integrable Models,
conformal Field Theory and Related Topics, Durham, April 1998", "Vertex
models with alternating spins"
Conference talk, Second Annual European TMR Conference on "Integrability, Nonperturbative Effects and symmetry in Quantum Field Theory, Durham, September 1998, "Mixing of ground states in vertex models" Lecture series, HeriotWatt University, January and February 1998, 5 lectures "The algebraic analysis of solvable lattice models" Seminar, University of Edinburgh, Department of Physics, June 1998, "Correlation functions in solvable lattice models" Seminar, Edinburgh/HeriotWatt Algebra seminar, December 1998, "Crystals, paths and walls: vertex models and crystal bases" 
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SERVICE TO THE MATHEMATICAL COMMUNITY  
Professor C E Beevers  External examiner (BSc), University of Sunderland
ViceChairman MATHWISE Executive Committee Member of SUMSMAN Committee 
Professor K J Brown  Executive Editor of Proceedings of the Royal Society of Edinburgh 
Professor J Carr  External Examiner (BSc), University of Aberdeen
External Examiner (BSc), University of Glasgow Chairman, Programme Management Committee ICIAM 99 
Dr D B Duncan  External examiner (PhD), University of Dundee
External examiner (PhD), Strathclyde University Member, Centenary Fund Committee, Edinburgh Mathematical Society Chair, North British Differential Equations Seminar 
Professor J C Eilbeck  External examiner (BSc), University of Dundee
External Examiner (DSc), University of Dijon Member of Council, Royal Society of Edinburgh 
Dr N D Gilbert  Member of EPSRC Research Fellowship Panel
External examiner (PhD), University of St Andrews 
Professor J Howie  External examiner (PhD), Queen Mary and Westfield College
External examiner (BSc), York University Member of EPSRC Mathematics College Member of Mathematics Sectional Panel of Royal Society of Edinburgh VicePresident, Edinburgh Mathematical Society Member of Executive Committee of International Centre for Mathematical Sciences Member of Editorial Board of International Journal of Algebra and Computation 
Dr D A Johnston  Mathematical Challenge organiser for Edinburgh and Borders regions
Mathematics masterclass for secondary school pupils on "The Game of Life", October 1998 External examiner (PhD), University of Oxford 
Dr K Khanin  Member of Editorial Board of the journal Dynamics and Stability
of Systems
Member of Advisory Board of the journal Chaos 
Professor R J Knops  Convener of Executive Committee of International Centre for Mathematical
Sciences
Member of Board of Directors of ICIAM 99 Ltd Member of Local Organising Group for ICIAM 99 Member of Editorial Board of Meccania VicePresident, International Society for the Interaction of Mathematics and Mechanics (ISIMM) Convener of Editorial Board for ISIMM 
Professor A A Lacey  External examiner (BSc), Strathclyde University 
Dr M Levitin  Member of Programme Management Committee, ICIAM 99 
Dr G R McGuire  External examiner (BSc), University of Glasgow 
Dr L E Nicholas  Member of IMA Scottish Committee 
Professor O Penrose  Member of the Editorial Board of the Royal Society of Edinburgh Proceedings A 
Dr A R Prince  External examiner (BSc), University of Stirling 
Professor J A Sherratt  Member of EPSRC Mathematics College and Research Grant Panel
Member of Wellcome Trust Research Grant Panel Associate Editor of the IMA Journal of Mathematics Applied in Medicine and Biology Associate Editor of the Journal of Theoretical Medicine External examiner (PhD), University of Bath External examiner (DSc), University of Technology, Sydney 
Dr R A Weston  Member of EPSRC Mathematics College
External examiner (PhD), University of Durham 
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RESEARCH AND OTHER GRANTS AND MISCELLANEOUS INCOME REPORTED IN 1998  
£80000  University of Cambridge Local Examinations Syndicate, awarded to Professor C E Beevers and the CALM group for the development of computer examinations 
£61423  EPSRC, awarded to Professor J C Eilbeck, Postdoctoral Visiting Fellowship for Dr J M Speight, 1.3.98 – 28.2.01 
£38829  EPSRC, awarded to Dr K Khanin, research into "Random Lagrangian Systems and Burgers Equation" 
£34246  EPSRC, awarded to Professor R J Knops, administrative support for ICMS 
£32380  BBSRC, awarded to Professor J A Sherratt, Earmarked postgraduate studentship: "Mathematical modelling of the spatiotemporal dynamics of cell signalling in the epidermis" 
£25000  London Mathematical Society, awarded to Professor R J Knops, support for ICIAM 99 
£24000  EPSRC, awarded to Professor R J Knops, support for ICIAM 99 
£21360  Royal Society of Edinburgh Fellowship awarded to Dr D A Johnston 
£20000  EPSRC, awarded to Professor J Carr for workshop "Hamiltonian Mechanics and Small Divisors in PDEs", June 1999 
£19182  EPSRC, awarded to Professor R J Knops, administrative support for ICMS 
£15000  Napier University, awarded to Professor C E Beevers and the CALM group to develop software for formal and informal student assessment 
£8000  EPSRC, awarded to Professor J A Sherratt, support for scientific meeting, February – July 1999, "From single cells to continua: microscale to macroscale modelling" 
£5344  Leverhulme Trust, Research Fellowship awarded to Dr D A Johnston 
£5000  Scottish Widows, awarded to Professor R J Knops, support for ICIAM 99 
£3125  EOARD awarded to Professor R J Knops, support for ICIAM 99 
£2250  British Council, ARC joint research grant awarded to Dr D A Johnston and Dr W Janke, Leipzig University 
£2000  British Council, JRP joint research grant awarded to Dr D A Johnston and Drs P Bialas and Z Burda, Jagellonian University, Krakow 
£2000  Bank of Scotland, awarded to Professor R J Knops, support for ICIAM 99 
£2000  Jaguar, awarded to Professor R J Knops, support for ICIAM 99 
£1500  Edinburgh Mathematical Society, support for ICIAM 99 
£1000  EMS Centenary Fund, support for ICMS meeting on Algebraic Geometry – the "Baker" meeting, 1922 September, 1998 
£915  London Mathematical Society, support for Scottish Algebra day, 1 May 1998, awarded to Professor J Howie 
£800  The Royal Society of Edinburgh, awarded to Professor J Carr, support for Primary Mathematics Masterclasses 
£645  British Council travel grant awarded to Dr D A Johnston to visit Professor J Smit, University of Amsterdam 
£580  British Council travel grant awarded to Dr D A Johnston to visit Dr R Loll, Albert Einstein, Institute, Potsdam, Germany 
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THESES SUCCESSFULLY PRESENTED FOR HIGHER DEGREES  
Yaroslav Zolotaryuk (PhD)  "Nonlinear dynamics of molecular and atomic chains" 
MSc in Mathematics of Nonlinear Models  joint with the University of Edinburgh 

Soren Bartels  "Electromagnetic scattering" 
Jennifer Hutchinson  "A Comparison of various algorithms for solving semiinfinite linearprogramming problems" 
Daniel Jefferson  "A numerical investigation of turbulence" 
Russell Lee  "An Autocatalator Model" 
Toby Marthews  "An investigation into the effects of nonlinear filtering on some simple weatherprediction models" 
Helen Wearing  "Mathematical modelling of juxtacrine patterning" 
Stephen Paul Womble  "An Accelerating SolitonLike Solution of a NonLinear Schrodinger Equation" 
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Publications  
Afrouzi G A, Brown K J  On a diffusive logistic equation
Jour Math Analysis and Applications Vol 225 pp 326339 1998 
Beevers C E, Fiddes D J, McGuire G R, Wild D G, Youngson M A  Interactive PastPapers for GCSE Mathematics Lander Educational Software, Glasgow, 1998 
Beevers C E, Quinney D  Mathwise diagnostic testing and assessment
Information Services & Use Vol 18 pp 191205 1998 
Benson D L, Maini P K, Sherratt J A  Unravelling the Turing bifurcation using spatially varying diffusion
coefficients
Journal of Mathematical Biology Vol 37 pp 381417 1998 
Bialas P, Burda Z, Johnston D A  Balls in boxes and quantum gravity
Nuclear Physics B (Proceedings Supplement) Vol 63 pp 763765 1998 
Boulter C J  Interface Hamiltonian with a positiondependent stiffness: a nonlinear
functional renormalization group study
Physical Review E Vol 57 pp 20622072 1998 
Boulter C J, Indekeu J O  Interfacial tension and interface delocalization phase boundary for
strongly typeI superconductors
International Journal of Thermophysics Vol 19 pp 857865 1998 
Brizhik L, CruzeiroHansson L, Eremko A  Influence of electromagnetic radiation on molecular solitons
Journal of Biological Physics, 1998 
Brown K J, Stavrakakis N  On the construction of super and subsolutions for elliptic equations
on all of Rn
Journal Nonlinear Analysis Vol 32 pp 8795 1998 
Dallon J C, Othmer H G  A continuum analysis of the chemotactic signal seen by dictyostelium
discoideum
Journal of Theoretical Biology Vol 194 pp 461483 1998 
Dallon J C, Sherratt J A  A mathematical model for fibroblast and collagen orientation
Bulletin of Mathematical Biology Vol 60 pp 101129 1998 
Duncan D B  Difference approximations of acoustic and elastic wave equations
Numerical Methods for Wave Propagation, Eds E F Toro and J F Clarke, Fluid Mechanics and its Applications Vol 47 pp 197210 1998 
Duncan D B  Proceedings of International Centre for Mathematical Sciences Conference
on Grid Adaptation in Computational PDEs; Theory and Applications, 1996,
Edinburgh
Applied Numerical Mathematics Vol 26 pp 1275 1998 
Dzhalilov A, Khanin K  Singularity of the invariant measures for homeomorhisms of the circle
with break singularities
Functional Analysis and its Applications Vol 32 pp 153162 1998 
Gilbert N D  Monoid presentations and associated groupoids
Int. J. Algebra and Computation Vol 8 pp 141152 1998 
Herrero M A, Velazquez J L, Lacey A A  Global existence for reactiondiffusion systems modelling ignition
Arch. Rat. Mechs. Anal. Vol 142 pp 219251 1998 
Howie J  Minimal seifert manifolds for higher ribbon knots
Geometry and Topology Monographs:The Epstein Birthday Schrift, Editors I Rivin C Rourke and C Series, International Press Vol 1 pp 261293 1998 
Howie J  Free subgroups in groups of small deficiency
J. Group Theory Vol 1 pp 95112 1998 
Hunton J, Turner P R  Coalgebraic algebra
Journal of Pure and Applied Algebra Vol 129 pp 297313 1998 
Johnston D A  The Yang Lee edge singularity on Feynman diagrams
J. Phys. Vol A31 pp 54615469 1998 
Johnston D A, Plechac P  Equivalence of ferromagnetic spin models on trees and random lattices
Journal of Physics A Vol 31 pp 475482 1998 
Johnston D A, Plechac P  Vertex models on Feynman diagrams
Physics Letters Vol A248 pp 3745 1998 
Khanin K  Burgers equation with random force
Proceedings of the XII International Congress in Mathematical Physics, Brisbane, July 1997 Vol 32 pp 153162 1998 
Knops R J, Lupoli C  Some recent results on SaintVenant's principle
Nonlinear Analysis and Continuum Mechanics (Eds G Buttazzo, G P Galdi, E Lanconelli and Pucci) Chapter 6 pp 6171 1998 
Knops R J, Payne L E  Spatial behaviour of energy in partially constrained thick elastic
plates
Alti dei Convegni Lincei Vol 140 pp 77104 1998 
Knops R J, Villaggio P  Transverse decay of solutions in an elastic cylinder
Meccanica Vol 33 pp 577585 1998 
Kuksin S B  A KAMtheorem for equations of the Kortewegde Vries type
Rev Math & Math Phys Vol 10 pp 164 1998 
Kuksin S B  Elements of a qualitative theory of Hamiltonian PDEs
Proceedings of the International Congress of Mathematicians (Berlin, 1998) Vol 2 pp 819829 1998 
Lacey A A  Diffusion models with blowup
Journal of Computational and Applied Mathematics Vol 97 pp 3949 1998 
Lacey A A, Ockendon J R, Sabina J  Multidimensional reaction diffusion equations with nonlinear
boundary conditions
SIAM Journal of Applied Mathematics Vol 58 pp 16221647 1998 
Levitin M  Dirichlet and Neumann heat invariants for Euclidean balls
Journal of Differential Geometry & Applications Vol 8 pp 3546 1998 
Little G, Clark D E R, Corney J R, Tuttle R  Deltavolume decomposition for multisided components
Journal of ComputerAided Design Vol 30 pp 695705 1998 
Little G, Tuttle R, Corney J R, Clark D E R  A feature complexity index
ImechE Journal of Mechanical Engineering Science – Part C Vol 212 pp 405413 1998 
Marin J L, Eilbeck J C, Russell F M  Localized moving breathers in a 2D hexagonal lattice
Phys Lett A Vol 248 pp 225229 1998 
Olsen L, Maini P K, Sherratt J A  Spatially varying equilibria of mechanical models: application to
dermal wound contraction
Mathematical Biosciences Vol 147 pp 113129 1998 
Olsen L, Maini P K, Sherratt J A, Marchant B P  Simple modelling of extracellular matrix alignment in dermal wound
healing
Journal of Theoretical Medicine Vol 1 pp 172192 1998 
Owen M R, Sherratt J A  Mathematical modelling of juxtacrine cell signalling
Mathematical Biosciences Vol 152 pp 125150 1998 
Owen M R, Sherratt J A  Modelling the macrophage invasion of tumours: effects on growth and
composition
IMA Journal of Mathematics Applied in Medicine and Biology Vol 15 pp 165185 1998 
Prince A R  The cyclic parallelisms of PG(3,5)
European Journal of Combinatorics Vol 19 pp 603612 1998 
Rahman H U  An analysis of neutron scattering spectroscopy in U20
Physica B Vol 252 pp 160166 1998 
Rahman H U  The splitting of the 3H4 multiplet in uranium dioxide
Molecular Physics Vol 94 pp 623626 1998 
Rahman H U  Crystalfield excitations in uranium dioxide
Physics Letters A Vol 240 pp 306310 1998 
Rynne B P  The structure of Rabinowitz' global bifurcating continua for generic
quasilinear elliptic equations
Nonlinear Analysis Vol 32 pp 167181 1998 
Rynne B P  Hausdorff dimension and generalized Diophantine approximation
Bulletin of the London Mathematical Society Vol 30 pp 365376 1998 
Rynne B P  The fractal dimension of quasiperiodic orbits
Ergod Theory and Dynamical Systems Vol 18 pp 14671471 1998 
Rynne B P, Dickinson H  Hausdorff dimension and a generalized form of simultaneous Diophantine
approximation
Acta Arithmetica 1998 
Sherratt J A  Invasive transition waves and their oscillatory wakes are linked by
a modulated phase resetting wave
Physica D Vol 117 pp 145166 1998 
Sherratt J A  On the transition from initial data to travelling waves in the
FisherKPP equation
Dynamics and Stability of Systems Vol 13 pp 167174 1998 
Tuttle R, Little G, Corney J R, Clark D E R  Feature recognition for NC part programming
Computers in Industry Vol 35 pp 275289 1998 
Details of publications available on http://www.ma.hw.ac.uk/maths/deptreps/  
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Copies of the above reports or reprints can be obtained by writing to the authors or to:
The Departmental Secretary
Department of Mathematics
HeriotWatt University
EdinburghEH14 4AS
Scotland, UK
Telephone + 44 131 451 3221 Fax: + 44 131 451 3249