Mathematical Structures and Applications: In Honor of Mahouton Norbert Hounkonnou

468 Pages·2018·4.966 MB·English

by  Toka Diagana, Bourama Toni

STEAM-H: Science, Technology, Engineering, Agriculture,
Mathematics & Health
Toka Diagana
Bourama Toni
Editors
Mathematical
Structures
and Applications
In Honor of
Mahouton Norbert Hounkonnou
STEAM-H: Science, Technology, Engineering,
Agriculture, Mathematics & Health
STEAM-H: Science, Technology, Engineering,
Agriculture, Mathematics & Health
SeriesEditor
BouramaToni
DepartmentofMathematics
HowardUniversity
Washington,DC,USA
This interdisciplinary series highlights the wealth of recent advances in the pure
and applied sciences made by researchers collaborating between fields where
mathematics is a core focus. As we continue to make fundamental advances in
various scientific disciplines, the most powerful applications will increasingly be
revealedbyaninterdisciplinaryapproach.Thisseriesservesasacatalystforthese
researchers to develop novel applications of, and approaches to, the mathematical
sciences. As such, we expect this series to become a national and international
referenceinSTEAM-Heducationandresearch.
Interdisciplinary by design, the series focuses largely on scientists and math-
ematicians developing novel methodologies and research techniques that have
benefits beyond a single community. This approach seeks to connect researchers
fromacrosstheglobe,unitedinthecommonlanguageofthemathematicalsciences.
Thus,volumesinthisseriesaresuitableforbothstudentsandresearchersinavariety
ofinterdisciplinaryfields,suchas:mathematicsasitappliestoengineering;physical
chemistryandmaterialsciences;environmental,health,behavioralandlifesciences;
nanotechnology and robotics; computational and data sciences; signal/image pro-
cessing and machine learning; finance, economics, operations research, and game
theory.
The series originated from the weekly yearlong STEAM-H Lecture series
at Virginia State University featuring world-class experts in a dynamic forum.
Contributionsreflectedthemostrecentadvances inscientificknowledgeandwere
deliveredinastandardized,self-containedandpedagogically-orientedmannertoa
multidisciplinary audience of faculty and students with the objective of fostering
studentinterestandparticipationintheSTEAM-Hdisciplinesaswellasfostering
interdisciplinary collaborative research. The series strongly advocates multidis-
ciplinary collaboration with the goal to generate new interdisciplinary holistic
approaches, instruments and models, including new knowledge, and to transcend
scientificboundaries.
Moreinformationaboutthisseriesathttp://www.springer.com/series/15560
Toka Diagana • Bourama Toni
Editors
Mathematical Structures
and Applications
In Honor of Mahouton Norbert Hounkonnou
123
Editors
TokaDiagana BouramaToni
MathematicalSciencesDepartment DepartmentofMathematics
TheUniversityofAlabamainHuntsville HowardUniversity
Hunstville,AL,USA Washington,DC,USA
ISSN2520-193X ISSN2520-1948 (electronic)
STEAM-H:Science,Technology,Engineering,Agriculture,Mathematics&Health
ISBN978-3-319-97174-2 ISBN978-3-319-97175-9 (eBook)
https://doi.org/10.1007/978-3-319-97175-9
LibraryofCongressControlNumber:2018960764
Mathematics Subject Classification: 42A16, 46B28, 46H35, 49S05, 53D30, 53D50, 53Z05, 57R57,
81T16,82C22
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Dedication
Mahouton Norbert Hounkonnou is a full professor of Mathematics and Physics
attheUniversityofAbomey-Calavi,Cotonou,Benin.Hisresearchdealswithnon-
commutative and nonlinear mathematics including differential equations, operator
theory, coherent states, quantization techniques, orthogonal polynomials, special
functions, graph theory, nonassociative algebras, nonlinear systems, noncommuta-
tivefieldtheories,andgeometricmethodsinphysics.
ProfessorHounkonnouhasauthored/coauthoredandreviewedseveralbooksand
refereed and served as an associate editor for renowned journals in mathematics,
mathematicalphysics,andtheoreticalphysics.Hehaspublishedover200refereed
research papers in outstanding ISI-ranked journals and international conference
proceedings in the fields of mathematics, mathematical physics, and theoretical
physics.
Norbert has been a visiting professor at several African, Asian, European, and
North American universities. Together with his peers at the international level,
v
vi Dedication
he founded the International Chair in Mathematical Physics and Applications
(ICMPA-UNESCO Chair) of the University of Abomey-Calavi offering multi-
university master degrees and PhD programs in mathematics with connections,
motivations, or applications to physics or in physics with important relationships
to mathematics. The best African students from about 13 French- and English-
speakingcountriesareselectedtofollowthesegraduateprograms,whichattracted
prominent and leading mathematicians and mathematical physicists around the
world who come to give lectures and supervise students’ research, what has
substantially increased international collaboration with African, Asian, American,
European,andIndianscientistsandmathematicians.
TheICMPA-UNESCOChairpresentlyhostsanInternationalConferenceSeries
(respectively,School)onContemporaryProblemsinMathematicalPhysics,which
isheldinCotonou(Benin)every2yearssince1999(respectively,eachyearsince
2005). These activities have led to a significant network of researchers connected
with the ICMPA-UNESCO Chair. The ICMPA-UNESCO Chair gets its funding
from various sources that are available in mathematics and mathematical physics
andforthedevelopmentofworld-classmathematicsandscienceinAfrica.Professor
Hounkonnouhasdirected/co-directed32PhDthesesand21masters.HisPhDand
masterstudentsarefromseveralcountriesincludingBelgium,Benin,BurkinaFaso,
Burundi,Cameroon,DemocraticRepublicofCongo,Niger,Nigeria,Senegal,Togo,
andZambia.
ProfessorHounkonnouisthechairoftheAfricanAcademyofSciencesCommis-
sion on Pan-African Science Olympiad (2014 to present), the chair of the African
Academy of Sciences Membership Advisory Committee (MAC) on Mathematical
Sciences (2013 to present), reviewer for the NANUM 2014 Award Committee
MemberoftheInternationalCongressofMathematicians(ICM2014),andTWAS
research professor in Zambia and enjoys the membership of several important
internationalscientificorganizations.
ProfessorHounkonnouisthecurrentpresidentoftheBeninNationalAcademyof
Sciences,ArtsandLetters.HismembershipextendstotheInternationalAssociation
of Mathematical Physics, American Mathematical Society, African Academy of
Sciences (AAS), The World Academy of Sciences (TWAS), UNESCO Scientific
BoardforInternationalBasicSciencesProgramme(IBSP),andtomanyothers.
Among other things, Professor Hounkonnou is a Knight of the National Order
of Benin (Chevalier de l’Ordre National du Benin). He has received a series of
recognition for the excellence of his work such as the Prize of the Third World
Academy of Sciences (TWAS) in 1996, the 2015 Tokyo University of Science
President Award, and the 2016 World Academy of Sciences C.N.R. Rao Prize
for Scientific Research “for his incisive work on noncommutative and nonlinear
mathematicsandhiscontributionstoworld-classmathematicseducation.”
Preface
The multidisciplinary STEAM-H series (Science, Technology, Engineering, Agri-
culture, Mathematics, and Health) brings together leading researchers to present
theirworkintheperspectivetoadvancetheirspecificfieldsandinawaytogenerate
a genuine interdisciplinary interaction transcending disciplinary boundaries. All
chapters therein were carefully edited and peer-reviewed; they are reasonably
self-contained and pedagogically exposed for a multidisciplinary readership. Con-
tributionsareinvitedonlyandreflectthemostrecentadvances deliveredinahigh
standard,self-containedway.Thegoalsoftheseriesareasfollows:
1. Toenhancemultidisciplinaryunderstandingbetweenthedisciplinesbyshowing
howsomenewadvancesinaparticulardisciplinecanbeofinteresttotheother
discipline or how different disciplines contribute to a better understanding of a
relevantissueattheinterfaceofmathematicsandthesciences
2. Topromotethespiritofinquirysocharacteristicofmathematicsfortheadvances
ofthenatural,physical,andbehavioralsciencesbyfeaturingleadingexpertsand
outstandingpresenters
3. To encourage diversity in the readers’ background and expertise while struc-
turallyfosteringgenuineinterdisciplinaryinteractionsandnetworking
Currentdisciplinaryboundariesdonotencourageeffectiveinteractionsbetween
scientists; researchers from different fields usually occupy different buildings,
publish in journals specific to their field, and attend different scientific meetings.
Existingscientificmeetingsusuallyfallintoeithersmallgatheringsspecializingon
specificquestions,targetingspecificandsmallgroupofscientistsalreadyawareof
eachother’sworkandpotentiallycollaborating,orlargemeetingscoveringawide
field and targeting a diverse group of scientists but usually not allowing specific
interactions to develop due to their large size and a crowded program. Traditional
departmental seminars are becoming so technical as to be largely inaccessible to
anyonewhodidnotcoauthortheresearchbeingpresented.Herecontributorsfocus
onhowtomaketheirworkintelligibleandaccessibletoadiverseaudience,which
intheprocessenforcesmasteryoftheirownfieldofexpertise.
vii
viii Preface
This volume, as the previous ones, strongly advocates multidisciplinarity with
the goal to generate new interdisciplinary approaches, instruments, and models
including new knowledge, transcending scientific boundaries to adopt a more
holistic approach. For instance, it should be acknowledged, following Nobel
LaureateandpresidentoftheUK’sRoyalSocietyofChemistry,ProfessorSirHarry
Kroto, “that the traditional chemistry, physics, biology departmentalised univer-
sity infrastructures—which are now clearly out-of-date and a serious hindrance
to progress—must be replaced by new ones which actively foster the synergy
inherent in multidisciplinarity.” The National Institutes of Health and the Howard
Hughes Medical Institute have strongly recommended that undergraduate biology
education should incorporate mathematics, physics, chemistry, computer science,
andengineeringuntil“interdisciplinarythinkingandworkbecomesecondnature.”
Young physicists and chemists are encouraged to think about the opportunities
waiting for them at the interface with the life sciences. Mathematics is playing
an ever more important role in the physical and life sciences, engineering, and
technology,blurringtheboundariesbetweenscientificdisciplines.
Theseriesistobeareferenceofchoiceforestablishedinterdisciplinaryscientists
andmathematiciansandasourceofinspirationforabroadspectrumofresearchers
and research students, graduate, and postdoctoral fellows; the shared emphasis of
thesecarefullyselectedandrefereedcontributedchaptersisonimportantmethods,
research directions, and applications of analysis including within and beyond
mathematics. As such the volume promotes mathematical sciences, physical and
life sciences, engineering, and technology education, as well as interdisciplinary,
industrial,andacademicgenuinecooperation.
Towardsuchgoals,thefollowingchaptersarefeaturedinthecurrentvolume.
The present volume contains the contributions from the participants of the
conference in honor of Professor Mahouton Norbert Hounkonnou on his 60th
birthdayheldinCotonou,Benin.Itfeaturesthefollowingchapters.
Chapter “Metric Operators, Generalized Hermiticity, and Partial Inner Product
Spaces”, by Jean-Pierre Antoine and Camillo Trapani, analyzes the structure of
metric operators, bounded or unbounded, drawing from recent results on pseudo-
Hermitianquantummechanics.
In chapter “Beyond Frames: Semi-frames and Reproducing Pairs”, Jean-Pierre
AntoineandCamilloTrapanistudysemi-frames(upperandlower)andreproducing
pairswhichgeneratetwoHilbertspacesconjugatesofeachother.
Chapter“OnHilbert-SchmidtOperatorFormulationofNoncommutativeQuan-
tumMechanics”,byIsiakaAremua,EzinviBaloitcha,MahoutonNorbertHounkon-
nou, and Komi Sodoga, investigates a system of charged particle in a constant
magneticfieldasawaytoemphasizetheimportanceofHilbert-Schmidtoperators
intheformulationofnoncommutativequantumtheory.
Inchapter“SymplecticAffineActionandMomentumwithCocycle”,Augustin
BatubengeandWallaceHaziyushowthatasymplecticstructurecanbedefinedon
theorbit,asymplecticmanifold,ofacertainaffineaction.
Preface ix
Chapter “Some Difference Integral Inequalities”, by Gaspard Bangerezako and
Jean-PaulNuwacu,usestheLagrangemethodoflineardifferenceequationoffirst
ordertoestablishdifferentversionsofsomeclassicalintegralinequalities.
Inchapter“TheoreticalandNumericalComparisonsoftheParameterEstimator
of the Fractional Brownian Motion”, Jean-Marc Bardet presents theoretical and
numerical comparisons of the most important methods of parameter estimators of
thefractionalBrownianmotion.
Chapter “MinimalLethalDisturbance forFiniteDimensional Linear Systems”,
by Abdes Samed Bernoussi, Mina Amharref, and Mustapha Ouardouz, considers
theproblemofrobustviabilitygivingsomecharacterizationsoftheviabilityradius
for finite dimensional disturbed linear systems leading to the determination of the
so-calledminimallethaldisturbance.
Inchapter“WalkerOssermanMetricofSignature(3,3)”,AbdoulSalamDiallo,
MouhamadouHassirou,andOusmaneToudouIssainvestigateatorsion-freeaffine
manifold and the related Riemann extension to produce an example of Walker
Ossermanmetricofsignature(3,3).
Chapter“ConformalSymmetryTransformationsandNonlinearMaxwellEqua-
tions”,byGeraldA.Goldin,VladimirM.Shtelen,andStevenDuplij,exploresways
todescribegeneral,nonlinearMaxwellfieldswithconformalsymmetry,makinguse
oftheconformalcompactificationofMinkowskispacetime.
LaureGouba,inchapter“TheYukawaModelinOneSpace-OneTimeDimen-
sions”,revisitstheYukawamodelinonespace-onetimedimensionsshowingitasa
constrainedsystemattheclassicallevelusingtheDiracmethodandreformulating
themodelasaquantumlevelofscalarfieldbyabosonizationprocedure.
Chapter “Towards the Quantum Geometry of Saturated Quantum Uncertainty
Relations: The Case of the (Q,P) Heisenberg Observables”, by Jan Govaerts,
outlines a program to identify geometric structures associated to the manifold
in Hilbert space of the quantum states that saturate the Schrodinger-Robertson
uncertaintyrelationtoaspecificsetofquantumobservablescharacterizingagiven
quantumsystemanditsdynamics.
In chapter “The Role of the Jacobi Last Multiplier in Nonholonomic Systems
and Locally Conformal Symplectic Structure”, Partha Guha studies the geometric
structure of nonholonomic system with almost symplectic structure in relation to
Jacobi’slastmultiplier.
Chapter “Non-perturbative Renormalization Group of a U(1) Tensor Model”,
by Vincent Lahoche and Dine Ousmane Samary, discusses the non-perturbative
renormalizationgroupofaU(1)tensormodel.
RichardKerner,inchapter“TernaryZ andZ GradedAlgebrasandGeneralized
2 3
Color Dynamics”, studies cubic and ternary algebras as a direct generalization of
GrassmannandCliffordalgebraswithZ grading.
3
Using the fuel smuggling trade between Benin and Nigeria as a background,
chapter“Pseudo-SolutionofWeightEquationsinNeuralNetworks:Applicationfor
StatisticalParametersEstimation”,byVincentJ.M.Kiki,VillevoAdanhounme,and
MahoutonNorbertHounkonnou,presentsapseudo-solutiontoweightequationsin
aclassofneuralnetworksusinganalgebraicapproach.