Essays in Mathematics and its Applications: In Honor of Vladimir Arnold

659 Pages·2016·9.65 MB·English

by  Themistocles M. Rassias

Themistocles M. Rassias ·
Panos M. Pardalos Editors
Essays in
Mathematics
and its
Applications
In Honor of Vladimir Arnold
Essays in Mathematics and its Applications

Themistocles M. Rassias • Panos M. Pardalos
Editors
Essays in Mathematics
and its Applications
In Honor of Vladimir Arnold
123
Editors
ThemistoclesM.Rassias PanosM.Pardalos
DepartmentofMathematics UniversityofFlorida
NationalTechnicalUnversityofAthens Gainesville,FL,USA
Athens,Greece
ISBN978-3-319-31336-8 ISBN978-3-319-31338-2 (eBook)
DOI10.1007/978-3-319-31338-2
LibraryofCongressControlNumber:2016941332
©SpringerInternationalPublishingSwitzerland2016
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Preface
EssaysinMathematicsand itsApplications:InHonorofVladimirArnold focuses
onvariousimportantareasofMathematicalresearch.Thecontributedpapershave
beenwrittenbyeminentscientistsandexpertsfromtheinternationalMathematical
community.Thesepapersdeepenourunderstandingofsomeofthecurrentresearch
problemsandtheorieswhichhavetheiroriginorhavebeeninfluencedbyV.Arnold.
The presentation of concepts and methods featured in this volume makes it an
invaluablereferenceforawidereadership.
We are indebted to all of the scientists who contributed to this volume, and we
wouldalsoliketoacknowledgethesuperbassistancethatthestaffofSpringerhas
providedforthispublication.
Athens,Greece ThemistoclesM.Rassias
Gainesville,FL,USA PanosM.Pardalos
v

Contents
A New Way to Compute the Rodrigues Coefficients of
FunctionsoftheLieGroupsofMatrices...................................... 1
DorinAndricaandOanaLilianaChender
QuasimodesinIntegrableSystemsandSemi-ClassicalLimit .............. 25
M.BaldoandF.Raciti
ManifoldsWhichAreComplexandSymplecticButNotKähler........... 49
GiovanniBazzoniandVicenteMuñoz
SolvabilityofaNonclampedFrictionalContactProblemwithAdhesion . 71
O.Chau,D.Goeleven,andR.Oujja
TheKolmogorov-Arnold-Moser (KAM)andNekhoroshev
TheoremswithArbitraryTimeDependence.................................. 89
AlessandroFortunatiandStephenWiggins
IterativeMethodsfortheElastographyInverseProblemof
LocatingTumors ................................................................. 101
B.Jadamba,A.A.Khan,F.Raciti,C.Tammer,andB.Winkler
TransversalityTheorywithApplicationstoDifferentialEquations........ 133
DumitruMotreanuandVioricaVeneraMotreanu
Lattice-likeSubsetsofEuclideanJordanAlgebras .......................... 159
A.B.NémethandS.Z.Németh
Simultaneous Diophantine Approximation: Searching for
AnaloguesofHurwitz’sTheorem .............................................. 181
WernerGeorgNowak
On the Fixed Points of a Hamiltonian Diffeomorphism in
PresenceofFundamentalGroup............................................... 199
KaoruOnoandAndreiPajitnov
vii
viii Contents
SomeGeneralizationsofFixed-PointTheoremsonS-MetricSpaces ...... 229
NihalYılmazÖzgürandNihalTas¸
FunctionalInequalitiesinBanachSpacesandFuzzyBanachSpaces...... 263
ChoonkilPark,JungRyeLee,andThemistoclesM.Rassias
TheMaslovIndexinPDEsGeometry ......................................... 311
AgostinoPrástaro
OntheInfimumofCertainFunctionals....................................... 361
BiagioRicceri
TheAlgebraofGyrogroups:Cayley’sTheorem,Lagrange’s
Theorem,andIsomorphismTheorems........................................ 369
TeerapongSuksumran
MildContinuityPropertiesofRelationsandRelatorsinRelatorSpaces . 439
ÁrpádSzázandAmrZakaria
ContractionMapsinPseudometricStructures............................... 513
MihaiTurinici
NovelToolstoDetermineHyperbolicTriangleCenters ..................... 563
AbrahamAlbertUngar
A New Way to Compute the Rodrigues
Coefficients of Functions of the Lie Groups
of Matrices
DorinAndricaandOanaLilianaChender
Abstract InTheorem1wepresent,inthecasewhentheeigenvaluesofthematrix
arepairwisedistinct,adirectwaytodeterminethegeneralRodriguescoefficientsof
amatrixfunctionforthegenerallineargroupGL.n;R/byreducingtheRodrigues
problem to the system (7). Then, Theorem 2 gives the explicit formulas in terms
of the fundamental symmetric polynomials of the eigenvalues of the matrix. Our
formulas permit to consider also the degenerated cases (i.e., the situations when
therearemultiplicitiesoftheeigenvalues)andtoobtainnicedeterminantformulas.
In the cases n D 2;3;4, the computations are effectively given, and the formulas
arepresentedinclosedform.Themethodisillustratedfortheexponentialmapand
theCayleytransformofthespecialorthogonalgroupSO.n/,whennD2;3;4.
AMSSubjectClassification(2010): 22Exx,22E60,22E70
1 Introduction
The exponential map exp W gl.n;R/ D M .R/ ! GL.n;R/, where GL.n;R/
n
denotestheLiegroupofrealinvertiblen(cid:2)nmatrices,isdefinedby(see,forinstance,
Chevalley[8],MarsdenandRa¸tiu[15],orWarner[22])
X1 1
exp.X/D Xk: (1)
kŠ
kD0
Accordingtothewell-knownHamilton–Cayleytheorem,itfollowsthateverypower
Xk,k(cid:3)n,isalinearcombinationofX0,X1,:::,Xn(cid:2)1;hence,wecanwrite
Xn(cid:2)1
exp.X/D a .X/Xk; (2)
k
kD0
D.Andrica((cid:2))(cid:129)O.L.Chender
DepartmentofMathematics,“Babes¸-Bolyai”University,M.Koga˘lniceanu1,400084
Cluj-Napoca,Romania
e-mail:[email protected];[email protected]
©SpringerInternationalPublishingSwitzerland2016 1
T.M.Rassias,P.M.Pardalos(eds.),EssaysinMathematicsanditsApplications,
DOI10.1007/978-3-319-31338-2_1