Proceedings from the EAUMP 10 th Anniversary Conference

175 Pages·2013·2.67 MB·English

COVER PAGE
i
List of Participants
Sn. Name Country Sn. Name Country
1 HerbertFleischner Austria 41 MohamedEltom Sudan
2 EleonoraCiriza Italy 42 MpinganzimaLydie Sweden
3 AndrewMasibayi Kenya 43 PravinaGajjar Sweden
4 BenOwinoObiero Kenya 44 BjrnTextorius Sweden
5 BenardKipchumba Kenya 45 OlofSvensson Sweden
6 BernardNzimbi Kenya 46 BengtOveTuresson Sweden
7 DamianMaing Kenya 47 ChristerKiselman, Sweden
8 DavidAngwenyi Kenya 48 FredrikBerntsson Sweden
9 EmmaAnyika Kenya 49 LeifAbrahamsson Sweden
10 GeorgeMuhua Kenya 50 PaulVanderlin Sweden
11 IdahOrowe Kenya 51 PeterSundin, Sweden
12 IsaacKipchirchir Kenya 52 RikardBogvad Sweden
13 IviviMwaniki Kenya 53 VitalijTjatyrko Sweden
14 JamenH.We’re Kenya 54 AgnesJoseph Tanzania
15 JamesOkwoyo Kenya 55 AkiliBabi Tanzania
16 JohnNderitu Kenya 56 AlexXaveryMatofali Tanzania
17 JosephineWairimu Kenya 57 AllenMushi Tanzania
18 KevinOketch Kenya 58 AnnaMwanjoka Tanzania
19 KithelaMille Kenya 59 BeathaNgonyani Tanzania
20 LydiahMusiga Kenya 60 CharlesMahera Tanzania
21 MasindeWamalwa Kenya 61 ChristianAlphonce Tanzania
22 OngaroNyang’au Kenya 62 E.S.Massawe Tanzania
23 PatrickWeke Kenya 63 EdithLuhanga Tanzania
24 PhilipNgare Kenya 64 EgbertMujuni Tanzania
25 RachelMbogo Kenya 65 EmalineJoseph Tanzania
26 RichardSimwa Kenya 66 EmmanuelEvarest Tanzania
27 WaihenyaKamau Kenya 67 EuniceMureithi Tanzania
28 WycliffNyang’era Kenya 68 Greyson. Kakiko Tanzania
29 FanjaRakotondrajao Madagascar 69 IsambiSailonMbalawata Finland
30 BernardO.Ikhimwin Nigeria 70 JohnMwaonanji Tanzania
31 EwaenK.yOsawaru Nigeria 71 JonasP.Senzige Tanzania
32 CassienHabyarimana Rwanda 72 JosephaV.Itambu Tanzania
33 DesireKarangwa Rwanda 73 JudithPande Tanzania
34 FrodualdMinani Rwanda 74 LilianOlengeile Tanzania
35 GahirimaMichael. Rwanda 75 MashakaMkandawile Tanzania
36 IsidoreMahara Rwanda 76 MosesMwale Tanzania
37 ENshimyumuremyi Rwanda 77 MpeleJames Tanzania
38 ThomasBizimana Rwanda 78 Mpeshe,SaulC. Tanzania
39 AbdouSene Senegal 79 AugustinoIsdory Tanzania
40 OluwoleDanielMakinde S.Africa 80 MuhayaKagemulo Tanzania
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Sn. Name Country Sn. Name Country
81 MussaAlly Tanzania 104 MukalaziHerbert Uganda
82 PitosSeleka Tanzania 106 NanyondoJosephine Uganda
83 SaidSima Tanzania 107 NdagireMajorine Uganda
84 SantoshKumar Tanzania 108 OpioIsmai Uganda
85 ShabanNyimvua Tanzania 109 SanyuShaban Uganda
86 SilasS.Mirau Tanzania 111 TumuramyeFredKacumita Uganda
87 SoudKhalfaMohamed Tanzania 112 TushemerirwePhionah Uganda
88 SylvesterE.Rugeihyamu Tanzania 113 TushemerirwePhionah Uganda
89 TheresiaBonifasi Tanzania 114 VincentSsembatya Uganda
90 TheresiaMarijani Tanzania 115 WalakiraDavidDdumba Uganda
91 UlediA.Ngulo Tanzania 116 WanderaOgana Uganda
92 YawNkansah-Gyekye Tanzania 117 DavidHenwood UK
93 AnguzuCollins Uganda 118 admanabhanSeshaiyer USA
94 AropM. Uganda 119 AlasfordM.Ngwengwe Zambia
95 BuletwendaCharles Uganda 120 AnthonyMosesMwale Zambia
96 JohnMango Uganda 121 IlwaleKwalombota Zambia
97 JumaKasoz iUganda 122 Issac. D.Tembo Zambia
98 KitayimbwaMulindwaJohn Uganda 123 JohnMusonda Zambia
99 KitoLuliroSilas Uganda 124 MbokomaMainza Zambia
100 LikisoRemoWinniefred Uganda 125 MervisKikonkoShamalambo Zambia
101 LivingstoneLuboobi Uganda 126 MubangaLombe Zambia
102 MasetteSimon Uganda 127 TrevorChilomboChimpinde Zambia
103 MirumbeGeoffreyIsmail Uganda
iii
Forewords
TheEastAfricanUniversitiesMathematicsProgramme(EAUMP)isacollaborationprojectbe-
tweenEasternAfricaUniversitiesandInternationalScienceProgramme(ISP)ofUppsalaUni-
versity, Sweden. The project started in 2002, and the currently participating universities in the
region are University of Dar es Salaam, University of Nairobi, Makerere University, National
University of Rwanda, Kigali Institute of Technology and University of Zambia. The main
objective of the programme is to promote cooperation and exchange of ideas in mathematical
researchandteachingofmathematicsandtostimulatecommunicationbetweenmathematicians
intheEasternAfricanRegionandbeyond.
The first EAUMP Conference was held in Nairobi, Kenya, from 18th March to 21st March
2003. Due to the success of the conference it was decided to hold such a conference regularly.
The Department of Mathematics of the University of Dar es Salaam agreed to hold the 2nd
EAUMPconferencetocelebrate10thanniversaryoftheprogramme.
The proceedings, which follow, consist of speeches, papers and abstracts presented at the 2nd
EAUMPConference,heldatTheNelsonMandelaAfricanInstituteofScienceandTechnology,
Arusha, Tanzania from 22nd to 25th August 2012. More than 125 participants from about 10
countriesattendedtheconference. Theconferenceprogramwascomprisedof6invitedplenary
lectures,andmorethan45contributedtalkswerepresentedanddiscussed.
Theaimsoftheconferencewere:
• Tostimulateregionalandinternationalcollaborationinresearchandtraining.
• ToprovideaforumforinteractionofAfricanMathematiciansandothersfromthedevel-
opedcountriesforresearchexperience.
• To introduce African Mathematicians from the region to some fundamental techniques
andrecentdevelopmentsinthesefields,thusformingresearchcollaborations.
• ToupdatetheknowledgeofAfricanMathematicians,particularlylecturersandM.Sc../Ph.D.
studentswhoarestationedathome,tostartpursuingtheseareasasresearchinterest.
Thesuccessoftheconferencecouldnothavebeenregisteredwithoutconcertedeffortfromthe
Local organizing committee in the Department of Mathematics and the EAUMP coordinators
committee. Iwouldthereforeliketoextendmyheartfeltthankstothefollowing.
LocalOrganizingCommittee
• Dr. EgbertMujuni Chairperson
• Dr. Sylvester. E.Rugeihyamu EAUMPcoordinator
• Dr. EuniceMureithi Member
• Dr. TheresiaMarijani Secretary
• Mr. EmmanuelEvarest Member
iv
EAUMPCoordinatingCommittee
• Dr. SylvesterE.Rugeihyamu(CoordinatorofUniversityofDaresSalaam)
• Prof. PatrickG.O.Weke(CoordinatorofUniversityofNairobi)
• Dr. JumaKasozi(CoordinatorofMakerereUniversity)
• Dr. IsaacTembo(CoordinatorofUniversityofZambia)
• Dr. IsidoreMahara(CoordinatorofNationalUniversityofRwanda)
• Mr. MichaelGahirima(CoordinatorofKigaliInstituteofScienceandTechnology)
• Dr. JohnM.Mango(InterNetworkCoordinator,MakerereUniversity)
Acknowledgement
Withoutfinances,notmuchcouldhavebeenattained. Iwouldlikeextendmythanksfollowing
associations,agenciesandinstitutionsfortheirgeneroussupport.
• InternationalScienceProgramme(ISP)ofUppsalaUniversity,Sweden.
• TWAS-TheAcademyScienceoftheDevelopingWorld.
• TheInternationalMathematicalUnion-CommitteeforDevelopingCountries(IMUCDC).
• NORAD(ThroughNOMAProjectinMathematicsDepartment,UDSM).
• TheGermanAcademicExchangeService(DAAD).
• UniversityofDaresSalaamGenderCentre.
• UniversityofDaresSalaam,DirectorateofResearch.
• TanzaniaCommunicationsRegulatoryAuthority(TCRA).
• TanzaniaCommissionforScienceandTechnology(COSTECH).
Prof. E.S.Massawe
Head,MathematicsDepartment,UDSMandOverallEAUMPCoordinator
v
Contents
ListofParticipants ii
Forewords iv
SPEECHES 1
Prof. E.S.Massawe: WelcomeSpeech . . . . . . . . . . . . . . . . . . . . . . . . 1
Dr. John M. Mango: Eastern Africa Universities Mathematics program (EAUMP -
NetworkOrigin,Operation,AchievementstheFutureandChallenges. . . . . . 3
Prof. RwekazaMukandala: WelcomeSpeech . . . . . . . . . . . . . . . . . . . . 8
Prof. MakameMnyaaMbarawa: OPENINGSPEECH . . . . . . . . . . . . . . . 9
PAPERS 11
M.E.A.ElTom: AProposedResearchAgendainMathematicsEducationinAfrica 11
Paul Vaderlind: Mathematical Competitions for Gifted Students: Organization and
Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
PatrickG.O.Weke: EstimationofIBNRClaimsReservesUsingLinearModels . . 26
O. D. Makinde: Heat Transfer Analysis of a Convecting and Radiating Two Step
ReactiveSlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
MervisKikonko: Non-DefiniteSturm-LiouvilleProblemsTwoTurningPoints . . . 52
S.A.Sima,M.AliandI.Campbell: TheThreeLayersMaizeCropOptimalDistri-
butionNetworkinTanzania . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
SantoshKumar: ASurveyoftheDevelopmentofFixedPointTheory . . . . . . . . 72
Livingstone S. Luboobi: Epediomological Modelling at Macro and Micro Levels:
TheCaseofHIV/AIDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Christian Baruka Alphonce: Analysis of Cell Phone User’s Loyalty in Tanzania
UsingMarkovChains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
SoudK.Mohamed: DerivativesoverCertainFiniteRings . . . . . . . . . . . . . . 98
EleonoraCiriza: Bifurcationresultsonsymplecticmanifolds . . . . . . . . . . . . 108
JohnMusonda: ThreeSystemsofOrthogonalPolynomialsandAssociatedOperators120
ABSTRACTS 155
Christer Kiselman: Asymptotic Properties of The Delannoy Numbers and
SimilarArrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
VitalijA.Chatyrko: The(Dis)connectednessofProductsintheBoxTopology 155
vi
Frerik Berntsson: Identification of Coefficients in Parabolic Equations Using
MeasurementsontheBoundary . . . . . . . . . . . . . . . . . . . . . 155
Padmanabhan Seshaiyer: Multidisciplinary Research in Mathematical Sci-
ences With Applications to Real World Problems in Biological, Bio-
InspiredandEngineeringSystems . . . . . . . . . . . . . . . . . . . . 156
WanderaOgana: EpidemicPotentialforMalariainEpidemiologicalZonesin
Kenya . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
FanjaRakotondrajao,: HowtoManipulateDerangements . . . . . . . . . . . 156
AbdouSene: TheDynamicsofPopulationsinWetlands . . . . . . . . . . . . 157
IsambiSailonMbalawataandSimoSarkka: AdaptiveMarkovChainMonte
CarloUsingVariationalBayesianAdaptiveKalmanFilter . . . . . . . 157
Patrick G. O. Weke: Linear Estimation of Location and Scale Parameters for
LogisticDistributionBasedonConsecutiveOrderStatistics . . . . . . 158
Lydia Musiga: A Stochastic Model for Planning a Compartmental Education
SystemandSupplyofManpower . . . . . . . . . . . . . . . . . . . . 158
EmmaAnyikaandPatrickWeke: FinancialSectorPerformanceEnhancers . 158
Mashaka Mkandawile: Estimating the List Size Using Bipartite Graph for
ColouringProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Emaline Joseph, Kgosimore and Teresia Marijani: Mathematical Modeling
ofPneumoniaTransmissionDynamics . . . . . . . . . . . . . . . . . . 159
David Ddumba Walakira: Hydrodynamics of Shallow Water Equations: A
CaseStudyofLakeVictoria . . . . . . . . . . . . . . . . . . . . . . . 159
J.W.Mwaonanji: BoundaryLayerFlowOveraMovingatSurfaceWithTem-
peratureDependentViscosity . . . . . . . . . . . . . . . . . . . . . . 160
EuniceMureithi: Absolute-ConvectiveInstabilityofMixedForced-FreeCon-
vectionBoundaryLayers . . . . . . . . . . . . . . . . . . . . . . . . . 160
MosesMwale: OptimalPremiumPolicyofanInsuranceFirmWithDelay . . . 160
G.I.Mirumbe,VincentSSembatya,RikardBgvadandJanErikBjork: On
the Coexistence of Distributional and Rational Solutions for Ordinary
DifferentialEquationsWithPolynomialCoefficients . . . . . . . . . . 161
PhilipNgare: OnModellingandPricingIndexLinkedCatastropheDerivatives 161
Lusungu Mbiliri, Charles Mahera, and Sure Mataramvura: Optimal Port-
folioManagementWhenStocksareDrivenbyMeanRevertingProcesses162
EgbertMujuni: OnHubNumberofHypercubeandGridGraphs . . . . . . . 162
VincentASsembatya: FixedPointsofHomeomorphismsofKnasterContinua 162
IsaacDanielTembo: ContinuityofInversionintheAlgebraofLocality-Mea-
surableOperators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
vii
HerbertFleischner: UniquelyHamiltonianGraphs . . . . . . . . . . . . . . . 163
Kitayimbwa M. John, Joseph Y. T. Mugisha and Robert A. Saenz: The
RoleofBackwardMutationsontheWithinHostDynamicsOfHIV-1 . 163
Kipchirchir, I. C.: Comparative Study of the Distributions Used To Model
Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
TheresiaMarijani: AWithinHostModelofBloodStageMalaria . . . . . . . 164
Wilson Mahera Charles: Application of Stochastic Differential Equations to
ModelDispersionofPollutantsinShallowWater . . . . . . . . . . . . 165
R. W. Mbogo, L. LuboobiJ. W. Odhiambo: Stochastic Model for In-Host
HIVVirusDynamicsWithTherapeuticIntervention . . . . . . . . . . 165
F. Berntsson, V. Kozlov, L. Mpinganzima, and B.O. Turesson: An Alter-
nating Iterative Procedure for the Cauchy Problem for the Helmholtz
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
viii
THE 2ND EASTERN AFRICA UNIVERSITIES MATHEMATICS
PROGRAMME (EAUMP) CONFERENCE
TheNelsonMandelaAfricanInstituteofScienceandTechnology,Arusha,Tanzania
August22nd-25th,2012
Welcome Speech
by
Prof. E.S.Massawe
Head,MathematicsDepartment,UniversityofDarEsSalaam
Guest of Honour, Minister of Communication, Science & Technology, Tanzania, Hon. Prof.
MakameMnyaaMbarawa(MP),
TheViceChancelloroftheUniversityofDaresSalaam,ProfessorRwekazaMkandala
The Vice Chancellor Nelson Mandela African Institute of Science and Technology, Professor
BurtonMwamila
HeadofISPandDirectorofChemistryProgram,ProfessorPeterSundin
DirectorofMathematicsProgram,ProfessorLeifAbrahamsson
DelegatesfromISP
Distinguishedguestsandvisitors,
DearParticipants,
LadiesandGentlemen,
On behalf of the Department of mathematics, University of Dar es Salaam and on my own
behalf, I wish to take this opportunity to welcome you all the invited guests and participants
andespeciallyyoutheguestofhonour,theMinisterofCommunication,Science&Technology,
Tanzania, Hon. Prof. Makame Mnyaa Mbarawa, to this important Congress. Please do feel at
home.
GuestofHonour
The Eastern Africa Universities Mathematics Programme (EAUMP) Network was established
in 2002 to further the mathematical sciences in the Eastern Africa Region. The main objective
of the Network is to promote cooperation and exchange of ideas in mathematical research and
teachingofmathematicsandtostimulatecommunicationbetweenmathematiciansintheEast-
ernAfricaRegionandbeyond. TheNetwork,sinceitsfoundation,hasbeenorganizingschools
and workshops and conferences. One of the objectives of these workshops and conferences is
to bring together researchers from various branches of mathematics and related fields, and to
simulateintersectionandcooperation.
GuestofHonour
EAUMP is a non-political and non-profit making Network devoted to the promotion of re-
search, teaching and learning of mathematics at all levels. We are very proud of this because
recent years have seen unprecedented growth of interest in the application of mathematical
ideasandtechniquestoproblemsinScienceandTechnologyinindustry.
1
GuestofHonour
EAUMPisawareoftheimportantroleofthemathematicsresearchersinpromotingthesubject.
Inthisconference,weshallhaveaseriesofpresentationsandgroupdiscussionsintheareasof
puremathematics,FinancialMathematics,Epidemiology,MathematicsfortheIndustry,Theo-
retical Fluid Dynamics, Statistics, Mathematics Education, Computer Science and Theoretical
Physics. Theprogramwillincludekeynotespeakers,esteemedresearchersandregularpresen-
tations.
GuestofHonour
EAUMPwasfoundin2002. Thisyearwearecelebratingthe10thAnniversaryoftheEAUMP
Network. Performance of EAUMP in the last 10 years gives one confidence that the EAUMP
will survive the next 10 years and beyond as an important and active Network. Schools and
Conferences of this type will have to continue. Schools and Conferences of EAUMP are the
lifelineoftheNetworkasisthecaseofmostprofessionalorganizations
GuestofHonour
Finally I will like to say that, our motto is ”We build for the Future”. The future success of
EAUMP will depend on the continued cooperation and commitment of all the members of
EAUMPandotherstakeholders.
GuestofHonour
Allow me on behalf of all the EAUMP members to thank all those who in various ways have
supportedour Conferenceand specificallythe InternationalScience Programme(ISP) ofUpp-
salaUniversity,Sweden,TheMinistryofCommunication,ScienceandTechnology,Tanzania,
CommissionforScienceandTechnology(COSTECH),Tanzania,TheAcademiScienceofthe
Developing World (TWAS), The European Mathematical Society - Committee for Develop-
ing Countries (EMS-DC), The German Academic Exchange Service (DAAD), The University
of Dar es Salaam, The University of Dar es Salaam Gender Centre, the University of Dar es
Salaam Directorate of Research, NORAD through NOMA Project, Tanzania Communications
RegulatoryAuthority(TCRA)andAllnodesoftheEAUMPnetwork
Iwouldalsoliketothankthelocalorganizingcommitteeandallthosebehindthesceneforthe
excellentjobdoneintermsofmakingusstayinArushahappily.
Onceagain,youareallwarmlywelcome.
Thankyou.
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