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Contents

Awards&Achievements

Events&Activities

Workshops&Conferences

ResearchArticle

StudentsCorner

StaffCorner

AlumniNews

UpcomingEvents

Awards & Achievements Academic Ranking of the Department

AccordingtothelatestreleaseoftheAcademicRankingofWorldUniversities(ARWU),therankingconsultancyadministeredbyShanghaiJiaoTongUniversity,ourDepartment ranked in the top 100 in mathematics over the World. ARWU uses five indicators to rankmathematicsdepartments,namely, thenumberofalumniwhohadbeenawardedtheFieldsMedalafter1951,thenumberofstaffwhohadbeenawardedtheFieldsMedalafter1961,thenumberofhighlycitedresearchersinmathematics,thenumber of papers in Science Citation Index in the mathematics field and the percentage ofpaperspublished in the top20%mathematical journals to that inallmathematicsjournals.PolyUMathematicsisNo.3inChinabehindPekingUniversityandCUHKandNo.8inAsia.WhilethelistdoesnotlistAMA’sexactranking,itisourestimatethatwearerankedbetweenNo.85–88.ThetopsixmathematicsdepartmentsintheARWUlistarePrinceton,Berkeley,Harvard,Stanford,CambridgeandUniversityofParisSud.

DEC 2009 ISSUE 6

NEWSLETTER

To facilitate learning through

excellent teaching and

research, leading expertise in

optimization, optimal control, applied statistics

and actuarial science, financial

mathematics and engineering

mathematics

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PolyU Education Info Day 2009

PolyUEducationInfoDayisthemostimportantannualpromotionalactivity of the University. It aims at helping prospective students makeappropriatechoiceofstudyprogrammes.Thisyear,theeventwasconductedsuccessfully on Saturday 26 September and attracted around 28,000visitors.

AMA’s exhibition booth was located at FG Wing. Staff membersand student helpers in uniforms prepared by Faculty of Applied Scienceand Textiles presented the Department in a very positive light. Detailedinformation about AMA programmes, research achievements, teaching &learningactivitiesweredisseminatedtovisitorsviadisplayboards,postersandpromotionalmaterial.Visitorswereattractedbyoureye-catchinggameboothandtailor-madesouvenirs.Theyparticipatedinthe“DiamondGame”by first answering a probability question followed by a more challenging problem inprobability. Thosewhogot thecorrectanswerswereawardedprizes.Otheractivitiesincludedaforumentitled“Parents’Corner”organizedbySAO,ademonstrationsessionon theBloombergFinancial InformationSystemandthreeInfoSeminarsbearingthetitle“WhathasitgottodowithMathematics?”. TheInfoSeminarsattractedabout400students,someofthemhadtositonthestepsofthelecturetheatre.

Allinall,theInfoDaywasconductedsuccessfullyandonceagainstaffandstudentshaveshowntheirgreatteamspiritintheorganizationoftheevent.

School Talks

The 3-year UGC-funded BSc (Hons) in Investment ScienceProgramme was launched successfully in September. To strengthen theawareness of our Programme in our prospective students, five school talks wereorganized for studentsof secondaryschoolsandassociatedegreesproviders, including Pui Ching Middle School (培正中學), Tang King PoSchool(鄧鏡波學校),TWGHSCGawMemorialCollege(東華三院吳祥川紀

念中學),PolyUHongKongCommunityCollegeandHKUSpaceCommunityCollege. The45-minute talkgavestudentsdetailed informationabout the

Events & Activities

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InvestmentScienceProgramme,admissionqualifications, career prospects and student development aspects through videodisplays from our teaching staff and fromprofessionalsintheIndustry.DuringtheQ&Asessions,studentswerekeentoknowaboutourDepartmentanditsprogrammes.Theseactivities helped the Department to furtheritsworkingrelationshipwithcareerteachersandschooladministrations.

Distinguished Alumni Lectures

The Department organized Distinguished Alumni Lectures and aReunionDinneronSaturday20June2009atPolyU. Wewerehappy toinvitetwodistinguishedalumnitodeliverlecturestoourstudents.TheywereDr.VictorLo(VicePresident,FidelityInvestments)whodelivereda lectureentitled “DrivingBusinesswithCutting-EdgeAnalyticsin theRealWorld”andMr.LawrenceLi (Director,CompassecoEnterprises Co. Ltd.) who gave a lecture on “The Power ofAwareness”. Students had an opportunity to talk to a numberofalumniand to learn from theirvaluableexperience incareerdevelopment.TheyalsoenjoyedspeakingtoalumniabouttheirPolyUlifeinthedistantpast.Althoughtheactivitywasorganized

duringtheH1N1outbreak,thisdidnot lessen the enthusiasm of our studentsandalumni.Over60ofthemparticipatedintheevent.

Dr.VictorLoreceivingasouvenirfromProf.Qi

Dr.CedricYiuwithagroupofstudentsattheDinner

Events & Activities

Mr.LawrenceLitalkingtotheaudience

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Research ArticleWorkshops & ConferencesWorkshop on Approximation and Optimization on the Sphere and Other Surfaces

A workshop entitled“Approximation and Optimization onthe Sphere and Other Surfaces” washeldonSaturday24October2009atPolyU. Many challenging problemsin mathematics and scientific computation were posed. TheWorkshop allowed researchleaders in the area to exchangeideas and enhance collaboration.The ten invited speakers were:Raymond Chan and Ka ShingLau fromCUHK,TonyChan fromUST, Xiaojun Chen, Ian Sloan,Rob Womersley and Liqun Qi from PolyU, Franklin Luk and MichaelNgfromHKBUandStephenSmalefrom CityU. The Workshop wasattendedbysome50participants.

Workshop on Financial Mathematics and Applied Statistics

The Department organized a workshop entitled “FinancialMathematicsandAppliedStatistics”onSaturday5December2009.TheWorkshopprovidedanopportunityforsome40researcherstobecome

acquainted with current research problems in theseareas.Theeleveninvitedspeakerswere:ShigePengfromPolyU,LixingZhufromBUHK,NicolasPrivaultandQiangZhangfromCityU,NgaiHangChanandDuanLifromCUHK,WaiKeungLiandHaiLiangYangfromHKU,RobWomersleyandPhillipYamfromPolyU,andQi

ManShaofromUST.

Prof.RaymondChan(CUHK)deliveredatalkon“SimultaneouslyInpaintinginImageandTransformedDomains”

Prof.TonyChan(HKUST)gaveatalkon“BrainMappingwithConformalandQuasi-conformalGeometry”

The Origins of Soliton Theory : A Short History TheonsetoftheIndustrialRevolutioninthemid18thCenturyinBritainsawtheconstructionofanextensivenetworkofcanalstoconnectcentresof production and their markets. These canals,designed for the purpose of commerce proved,by serendipity, to be natural laboratories for theobservationofcertainnovelhydrodynamicwaves.By the early part of the 19th Century, the basicmathematical underpinnings of hydrodynamicshadalreadybeenestablishedbysuchluminariesas Leonard Euler and Joseph Louis Lagrange.Indeed, the latter had analysed the propagationofsmallwavesonshallowwaterbymeansofhisnewtheoryofhydrodynamics.However,itwasnotuntilachancehappeningonacanalin1834thatthestudyofthemotionoflargewaterwaveswasinitiated.

Thus,inAugust1834,aScottishengineerand naval architect called John Scott Russellwas riding his horse alongside the Union CanalnearEdinburghwhenheobservedaremarkablephenomenon which was to have far-reachingscientific consequences that extend to the present day. Russell later recalled the circumstances ofhisdiscovery.

“I was observing the motion of a boatwhichwasrapidlydrawnalonganarrowchannelby a pair of horses when the boat suddenlystopped — not so the mass of water in thechannelwhichithadsetinmotion:itaccumulatedroundtheprowofthevesselinastateofviolentagitation, then suddenly leaving it behind, rolledforwardwithgreatvelocity,assumingtheformofasolitaryelevation,a roundedsmoothandwell-defined heap of water, which continued its course alongthecanalapparentlywithoutchangeofformordiminutionofspeed.”

Russelllaterreproducedthissolitarywaveinarectangulartank.Importantly,beyondacertainthreshold,thedisturbancewasaccommodatedinnot one, but two solitary waves which progressasseparatedhumpsalongthechannel.Thistwo-wavephenomenon isevident inRussell’s reportto the British Association, published in 1845.Russellhadearlierrecordedthatthespeedoftheindividual solitary waves is proportional to theirheight. A consequence of this is that a higher wave starting behind a smaller, must eventually catchit up resulting in mutual interaction. However,

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APseudo-SphericalSurface(Interior)

GeneratedbyaBT(Exterior)

[C.Rogers&W.K.Schief,BäcklundandDarbouxTransformations.

GeometryandModernApplicationsinSolitonTheory.

CambridgeTextsinAppliedMathematics,CambridgeUniversityPress,(2002)]

regrettably,thelengthofthechannelin Russell’s experiments was tooshorttoallowtheremarkablenatureof the nonlinear interaction ofthese largeamplitudewaves tobeobserved.

TheimportanceofRussell’sobservations concerning his ‘GreatWave of Translation’ were earlycalled in question-notably by Sir George Airy — the AstronomerRoyal.Thereensuedacontroversywhich was to involve some of themost eminent men of Victorianscience — in the main arrayedagainstRussell.Thematterwasnotfinally to be resolved in Russell’s favour until 1876 when LordRayleigh validated mathematicallythe shape of Russell’s solitarywave in a paper published in thePhilosophical Magazine. However,thisworkwasnotwell-knownandthecontroversyonlyendedwiththepublicationin1895ofapaperbytwoDutchscientists,Korteweg and de Vries on the propagation of long wavesadvancing ina rectangularchannel.Therein,amathematicalmodel encapsulated in the now celebrated Korteweg-deVries (KdV) equation was introduced which describes the wavepropagation inacanal inamannerconsistentwith thesolitarywaveobservationsofRussellin1834.However,itwasnot until some 130 years later that a computational study in1965byZabuskyandKruskalatPrincetononaspectsof thecelebrated Fermi-pasta-Ulam problem led to their recordingof the remarkable interaction properties of what they wereto term solitons. Thus, Zabusky and Kruskal, in an inspiredinterpretationofcomputeroutput,detectedintheKdVmodel,recurrence phenomena which we now associate with solitonsurvival following interaction. Their analysis was, however,necessarily numerical since the mathematical methodswhichwouldallow theanalytic treatmentof nonlinear solitoninteraction in the KdV equation were at that time unknown. Thesemethods,remarkablyturnouttohavetheiroriginintheworkofgeometersofthe19thCenturyoninvariancepropertiesofprivilegedsurfaces.TheseminalresultwasduetoBianchiandBäcklundwhichprovidesan iteractiveprocedure for theconstruction of a chain of pseudospherical surfaces from aknownseedsurface.

ItwastheworkofaphysicistSeegerandhiscolleaguesin Germany in 1953 that originally demonstrated that theclassical Bäcklund transformation (BT) and its associatednonlinearsuperpositionprinciplehad importantapplication intheanalysisofcrystaldislocations.Thetypicalsolitonicfeaturesto be subsequently discovered numerically by Zabusky and

Kruskal in 1965 for the KdV equation, namely preservation of velocity ofshape following interaction were allrecorded for the sine Gordon modelofcrystaldislocationtheory.However,theirworkremainslittleknowneventothisday.

TheBäcklundtransformationforthe KdV equation and its associated nonlinearsuperpositionprinciplewereconstructedin1973bytworelativistsattheJetPropulsionLaboratoriesintheUSA. The third key soliton equation, namely the nonlinear Schrödinger(NLS) equation was first derived in nonlinear optics in 1965 althoughits origins go back to hydrodynamicstudiesofvortexevolutionundertakenattheturnofthe20thCentury.In1974,the Bäcklund transformation for theNLS equation was discovered.

ThepowerofBäcklundtransformationscomesthroughtheirassociatednonlinearprinciples(permutabilitytheorems).These allow the analytic description of the evolution andcomplex nonlinear interaction of multi-soliton pulses. Thiswas early demonstrated by Lamb at United Aircraft who in1975 used the nonlinear superposition principle for the sineGordon equation to successfully predict the nature of solitonic decomposition of pulses in ruby lasers in accordance withobservedexperimentalresults.

By the early 1970s, the three canonical solitonequations namely the KdV, sine Gordon and NLS equations, together with their associated Bäcklund transformations andnonlinearsuperpositionprincipleswere inplace. In thesameperiod,thecelebratedInverseScatteringTransform(IST)wasdeveloped for solitonic equations. The IST represents a natural extensionoftheclassicalFourierTransformandagaincanbesaidtohaveitsorigininclassicalgeometryinworkofGauss.

Thus, by 1974 the skeletal theoretical structure ofSoliton Theory was established. The scene was set for anexplosionofresearchactivitythatcontinuestothepresentday.Theapplicationsabound.TheserangefromEinstein’stheoryofrelativityandthegenerationofmathematicalrepresentationsof black holes to the modelling of energy propagation alongproteinmoleculesinbiologicalDNAstructuresandthedesignof superconducting devices based on work of Josephson(NobelPrize1973).

[TheaboveisanabbreviatedandupdatedversionofanaddressgivenbyProfessorColinRogersonhiselectiontotheAustralianAcademyofScience(1999)]

Research Article

� D e p a r t m e n t o f A p p l i e d M a t h e m a t i c s

Visit to Securities & Futures Commission

Inthemorningof16November2009,41InvestmentSciencestudentsvisitedtheSecurities&FuturesCommission(SFC)atCentral foraseminaron“OverviewofSFC”.TheseminarwasconductedbyMr.JosephLee,SeniorManagerofSFCExternalRelations. During the seminar, Mr. Lee introduced the role of SFC, its organizationalstructure, regulatory role and operations. Apart from the informative presentation,educationalvideoswereshownonhealthyinvestmentmodes.

Perhapsoneofthemostsalutaryvideoclipsforstudentswasthewinningvideoof“InvestmentStoryCompetition2009”,whichportrayedanundergraduatestudentwhosoughtto make quick gains from the stock market. He placed his government tuition loan on a single stock with serious financial consequences.

At the end of the seminar, students raised several questions about the career opportunitiesanddevelopmentatSFC.Mr.Leestatedthat,althoughthemajorityoftheSFCstaffareexperiencedlegalexecutivesandlawyers,ithiresnewgraduatesfromvariousdisciplines.SFCHumanResourcesDepartmentalsovisitslocaluniversitiesfortalksandrecruitmentevents.

The visit lasted for almost 2 hours from 11:00 to 12:50. Students had anenjoyablemorningandgainedimprovedunderstandingofSFCandreceivedsoundadviceonwiseinvestment.

Students CornerICAC Talk for Final Year Investment Science Students

In the afternoon of 22 October 2009, more than 30 final year Investment Science students attended a talk by Miss Ester Poon Mei-po, Officer from ICAC Community Relations Department of Kowloon West District. During the 1-hour talk, Miss PoonintroducedHongKong’santi-corruptionlegislationandcommoncorruptionpracticesin the workplace. The importance of work ethics was impressed upon ourstudents. MissPoonalsoshowedan interestingvideoclipandsome real-life corruption cases in the banking sector. She alsobriefed our students about ICAC’s recruitment programme andcareerdevelopment.Thetalkenhancedourstudents’awarenessofpersonalethics,andinformedthemaboutaspectsofcorruptionanditsprevention.

Dr.JosephLeepresentedasouvenirtoMr.JosephLee,SeniorManagerofSFCExternalRelations

StudentsraisedquestionsonthecareeropportunitiesanddevelopmentatSFC

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University of Adelaide and his MScandPhD fromUniversityofDundeein 1977 and 1981 respectively.Sincethen,hehastakenupvariousteaching and research positions atUniversity of Kentucky, AustralianNationalUniversityandUniversityofNSW. His special fields of interest include Computational Methodsin Optimization and MathematicsFinance.

5. Francis Austin was promotedto Instructor in September2009. Our congratulations toFrancisonhispromotion.

6. ORMingKeungBenjaminresignedfromtheDepartmentinAugust to join the Hong Kong Observatory as a Scientific Officer, and SO Moon Tong Ernest left the Department in December to take up the position of Research Officer in the HongKongPoliceForce.Weconveyourbestwishestobothofthemintheirnewcareers.

7. Katie Cheung and Elaine Ching of the General Office left the Department in October and November respectively. Katiejoined PolyU’s Department of Computing as an ExecutiveOfficer, while Elaine was appointed Senior Administrative Assistant at the University’s Management and ExecutiveDevelopmentCentre.

Staff CornerDepartmental Group Photo ADepartmentalGroupPhotoforallacademic,research and supporting staff was taken before thebeginningofthe2009-2010academicyear.

Departmental Christmas Party 2009 The Department will holdits annual Christmas luncheon on24December2009attheHarbourPlaza Metropolis Hotel. ApartfromAMAstaff,guestsincludinganumber of Faculty Deans, friendsand retired colleagues are invitedtojointheparty.

Fromtheleft:Dr.SzeNungSingRaymond,Dr.ZhangHaiyuDoris,Ms.LiMangWanShermieandProf.RobWomersley

Staff Movement

1. SZE Nung Sing Raymond joinedthe Department as a Lecturer inSeptember2009.RaymondobtainedhisBSc,MPhilandPhDin2000,2002and 2005 respectively, all from theUniversityofHongKong. HewasaVisiting Scholar inAuburn Universityin the Fall Semester of 2006 and aPostdoctoralFellow in theUniversityofConnecticutfrom2006–2009.HisresearchinterestsincludeMatrixandOperatorTheory,QuantumComputingandQuantumInformation.

2. ZHANG Haiyu Doris was appointedaTutorintheDepartmentinOctober.Doris got her PhD from the City University of Hong Kongearlier this year. Her areas of interest include SpecialFunctions,AsymptoticExpansionsandODEs.

3. LI Mang Wan Shermie was appointed Assistant Officer in the DepartmentinNovember.ShewasagraduatefromPolyU’sDepartmentofChineseandBilingualStudies.BeforejoiningPolyU,sheworkedattheHongKongCommunityCollegeasan Assistant Administrative Officer.

4. Rob WOMERSLEY of the School of Mathematics andStatistics, University of New South Wales, was appointedVisitingProfessoroftheDepartmentfromSeptember2008to January 2009. Rob got his Bachelor Degree from the

� D e p a r t m e n t o f A p p l i e d M a t h e m a t i c s

Upcoming EventsDistinguished Lecture Series

The AMSS-PolyU Joint Research Institute has been organizing theDistinguishedLectureSeriesconductedbyrenownedscholarssinceitsinceptionin2006.TheobjectiveoftheSeriesistoofferaplatformfortheexchangeofideasand provide first-hand accounts of the speakers’ scholarly accomplishments in EngineeringandManagementMathematics. Wearepleased toannounce thefollowingDistinguishedLecturestobeheldinthissemester:

15 December 2009 3:00 pm – 4:30 pm

SpeakerProfessor Chi-Wang Shu,

BrownUniversity,U.S.A.

Title HighOrderMethodsforConvection

DominatedPDEs–AnOverview

Venue AG710

16 December 2009 3:00 pm – 4:30 pm

SpeakerProfessor C.F. Jeff Wu,

GeorgiaInstituteofTechnology,U.S.A.

Title StatisticalWorkinNanomaterialResearch

Venue AG710

Editorial Board

Prof.ChanCheong-ki,Dr.ChanChi-kin,Dr.ChanChun-wah(Convenor),Prof.HouShui-hung,Dr.PongTak-yunGlory,Prof.ColinRogers,Ms.VickyWu(Secretary)

DepartmentofAppliedMathematics•TheHongKongPolytechnicUniversity

Tel:(852)27666946•Fax:(852)23629045

Website:http://www.polyu.edu.hk/ama

Email: maopview@polyu.edu.hk(forenquiry)/ macwchan@polyu.edu.hk(forarticlesubmission)

Copyright©2009DepartmentofAppliedMathematics•TheHongKongPolytechnicUniversity

Alumni NewsUpdate AMA Alumni Database

Supportfromouralumniisessential

for the development of the Department.

Weurgealumnitoaccessandupdateour

DepartmentalAlumniDatabasevia

http://www.polyu.edu.hk/ama/alumninfo

sothatwewillbeabletokeepyouabreast

of the latest departmental news and

activelyinvolveyouinourfutureactivities

suchasre-uniongatheringsandsurveys.