11404nam 2200613 a 450 991095763330332120251116181920.01-62417-078-1(CKB)2550000001043628(EBL)3021718(SSID)ssj0000880416(PQKBManifestationID)12429473(PQKBTitleCode)TC0000880416(PQKBWorkID)10895178(PQKB)11256498(MiAaPQ)EBC3021718(Au-PeEL)EBL3021718(CaPaEBR)ebr10683458(OCoLC)923666746(BIP)27523957(EXLCZ)99255000000104362820101021d2010 uy 0engur|n|---|||||txtccrComputational mathematics theory, methods and applications /Peter G. Chareton, editor1st ed.New York Nova Science Publishersc20101 online resource (459 p.)Computational mathematics and analysis seriesDescription based upon print version of record.1-60876-271-8 Includes bibliographical references and index.Intro -- COMPUTATIONAL MATHEMATICS: THEORY, METHODS AND APPLICATIONS -- COMPUTATIONAL MATHEMATICS: THEORY, METHODS AND APPLICATIONS -- CONTENTS -- PREFACE -- ANALYTICAL AND NUMERICAL METHODS IN THE LINEAR STABILITY STUDY OF IDEAL FLOWS ON A SPHERE -- ABSTRACT -- 1. INTRODUCTION -- 2. HILBERT SPACES AND GEOMETRIC STRUCTURE OF SMOOTH FUNCTIONS ON A SPHERE -- 3. INTEGRAL FORMULAS RELATED TO THE JACOBIAN -- Lemma 1 -- 4. STEADY BVE SOLUTIONS ON A ROTATING SPHERE -- 5. CONSERVATION LAW FOR PERTURBATIONS TO LP FLOWS AND RH WAVES -- Theorem 1 -- 6. CONSERVATION LAW FOR INFINITESIMAL PERTURBATIONS TO WV WAVES AND MODONS -- Theorem 2 -- 7. UNIFIED CONSERVATION LAW FOR DISTURBANCES OF BE SOLUTIONS -- 8. INSTABILITY CONDITIONS FOR LP FLOWS, RH WAVES, WV WAVES AND MODONS -- Theorem 3 -- Example 1 -- Example 2 -- Example 3 -- Theorem 4 -- 9. PECULIARITIES OF INSTABILITY CONDITIONS FOR WV WAVES AND MODONS -- 10. ESTIMATES OF THE MAXIMUM GROWTH RATE OF UNSTABLE MODES -- Theorem 5 -- Theorem 6 -- 11. ORTHOGONALITY OF UNSTABLE MODES TO THE BASIC FLOW (BVE SOLUTION) -- Theorem 7 -- Corollary 1 -- Corollary 2 -- 12. NUMERICAL EXPERIMENTS -- Experiment 1 -- Experiment 2 -- Experiment 3 -- Experiment 4 -- 13. CONCLUSIONS -- ACKNOWLEDGMENTS -- REFERENCES -- REVIEWED BY -- PURE AND MIXED MATHEMATICS IN THE WORK OF LEONHARD EULER -- ABSTRACT -- 1. INTRODUCTION -- 2. THE RISE OF THE CONCEPT OF FUNCTIONS -- 3. ORDINARY DIFFERENTIAL EQUATIONS -- 4. DIFFERENTIATION AND INTEGRATION OF FUNCTIONS OF TWO VARIABLES -- 5. PARTIAL DIFFERENTIAL EQUATION -- 6. INFINITE POLYNOMIALS AND SERIES -- 7. MECHANICS -- 8. THE CALCULUS OF VARIATIONS AND THE PRINCIPLE OF THE LEAST ACTION -- 9. OTHER RESULTS IN MIXED MATHEMATICS -- REFERENCES -- APPLICATIONS OF COMPUTATIONAL GEOMETRY TO PROBLEMS OF POLITICAL COMPETITION -- ABSTRACT -- 1. INTRODUCTION.2. GEOMETRICAL SEARCH FOR OPTIMUM POSITIONS IN THE GAME WITH RESTRICTIONS: USE OF THE OPINION SURVEYS -- 2.1. The Opinion Surveys -- 2.1.1. Public Opinion and Politics Fiscal Survey Nº 2615 of the CIS -- 2.2. The Algorithm and the Simulation -- 2.2.1. A Graphic Approximation of the Algorithm -- 2.3. Simulation with an Example of the National Politics (Spain) -- 2.3.1. Algorithm Implementation -- 2.3.2. Results -- 2.4. Conclusions -- 3. GEOMETRICAL STUDY OF EQUILIBRIUM POSITIONS IN THE GAME WITH RESTRICTIONS -- 3.1. The Model -- 3.2. Equilibrium with Restrictions -- 3.2.1. Existence Conditions -- 3.2.2. Examples -- 3.3. Conclusions -- APPENDIX A: DEVELOPMENT OF THE ALGORITHM -- REFERENCES -- COHERENCE - HOMOTOPIES OF HIGHER ORDER -- INTRODUCTION -- 1. COHERENT SYSTEMS AND COHERENT MAPS -- Theorem 1.1 -- Theorem 1.2 -- Theorem 1.3 -- Theorem 1.4 -- 2. LEVEL COHERENT CATEGORY -- Theorem 2.1 -- Theorem 2.2 -- Theorem 2.3 -- Theorem 2.4 -- Theorem 2.5 -- Theorem 2.6 -- Theorem 2.7 -- Theorem 2.8 -- 3. COHERENT SHIFT AND COHERENT CATEGORY -- Proposition 3.1 -- Proposition 3.2. -- Theorem 3.1 -- Theorem 3.2 -- Theorem 3.3 -- Theorem 3.4 -- 4. RELATIONS OF COHERENT CATEGORIES -- Theorem 4.1 -- Theorem 4.2 -- APPENDIX: STRICT ORDERING VS ORDERING FOR DIRECTED SETS -- Theorem 1 -- Theorem 2 -- Theorem 3 -- REFERENCES -- STABLE MFS-BASED SOLUTION TO SINGULAR AND NON-SINGULAR INVERSE PROBLEMS FOR TWO-DIMENSIONAL HELMHOLTZ-TYPE EQUATIONS -- Abstract -- 1Introduction -- 2MathematicalFormulationoftheInverseProblems -- 3SingularSolutionsfortheTwo-DimensionalHelmholtz-TypeOperator -- 4SingularInverseProblem:SingularitySubtractionTechnique -- 5StandardandModifiedMethodsofFundamentalSolutions -- 6Regularization -- 6.1TheTikhonovRegularizationMethod -- 6.2TheL-CurveMethod -- 7NumericalResults -- 7.1AccuracyErrors -- 7.2Non-SingularInverseProblems -- 7.2.1Examples.7.2.2EffectoftheTRM -- 7.2.3ChoiceoftheOptimalRegularizationParameter -- 7.2.4NumericalStabilityoftheMethod -- 7.2.5NumericalConvergenceoftheMethod -- 7.3SingularInverseProblems -- 7.3.1Examples -- 7.3.2EffectoftheSST -- 7.3.3EffectoftheTRM -- 7.3.4ChoiceoftheOptimalRegularizationParameter -- 7.3.5NumericalStabilityoftheMethod -- 8Conclusion -- References -- VANDERMONDE SYSTEMS: THEORY AND APPLICATIONS -- 1Introduction -- 2PolynomialInterpolation -- 2.1LagrangeandNewtonform -- 2.2Lebesgueconstant -- 2.2.1Lebesgueconstantforequidistantnodes -- 2.3TheBj¨orckandPereyraalgorithm -- 3APropertyoftheElementarySymmetricFunctions -- 4PolynomialApproximationwithGauss-LobattoPoints -- 4.0.1Theinterpolationproblem -- 4.0.2Theleast-squaresproblem:explicitMoore-Penrosepseudo-inverseformula -- 4.0.3Theleast-squaresproblem:discreteorthogonalpolynomials -- 4.0.4Numericalproperties -- References -- A COMPARATIVE STUDY OF DIFFERENT SEMILOCAL CONVERGENCE RESULTS APPLIED TO KEPLER'S EQUATION -- Abstract -- 1Introduction -- 2Kantorovich'sTheoryAppliedtoKepler'sEquation -- 3Smale'sa-TheoryAppliedtoKepler'sEquation -- 4Conclusion -- References -- DISCRETE MAXIMUM PRINCIPLES FOR FEM SOLUTIONS OF NONLINEAR ELLIPTIC SYSTEMS -- Abstract -- 1Introduction -- 2DiscreteMaximumPrinciplesinDifferentSettings -- 2.1Algebraicbackgroundandthe'matrixmaximumprinciple' -- 2.2SomemotivationfortheDMP -- 2.2.1Linearequationsandcontinuousmaximumprinciples -- 2.2.2TheDMPforasinglenonlinearellipticequation -- 2.3GeometricpropertiestoensuretheDMP -- 2.4AnalgebraicDMPinHilbertspace -- 2.4.1Formulationoftheoperatorequation -- 2.4.2Galerkintypediscretization -- 2.4.3Maximumprinciplefortheabstractdiscretizedproblem -- 3DiscreteMaximumPrinciplesforEllipticReaction-DiffusionTypeSystems -- 3.1Systemswithnonlinearcoefficients -- 3.1.1Formulationoftheproblem -- 3.1.2Finiteelementdiscretization.3.1.3Discretemaximumprincipleforsystemswithnonlinearcoefficients -- 3.2Systemswithgeneralreactiontermsofsublineargrowth -- 3.3Systemswithgeneralreactiontermsofsuperlineargrowth -- 3.4Sufficientconditionsandtheirgeometricmeaning -- 4DiscreteMaximumPrinciplesforEllipticSystemsIncludingFirstOrderTerms -- 4.1Nonsymmetricsystemswithnonlinearreactioncoefficients -- 4.2Nonsymmetricsystemswithsublinearreactionterms -- 4.3Nonsymmetricsystemswithsuperlinearreactionterms -- 4.4Nonsymmetricsystemswithnonlinearconvectioncoefficients -- 5Somereal-lifeexamples -- 5.1Reaction-diffusionsystemsinchemistry -- 5.2Linearellipticsystems -- 5.3Nonsymmetrictransportsystems -- Acknowledgments -- References -- NUMERICAL CONFORMAL MAPPINGS FOR WAVEGUIDES -- Abstract -- 1Introduction -- 2WaveScatteringinTwo-DimensionalWaveguides -- 2.1Theoriginalproblem -- 2.2TheBuildingBlockMethod -- 2.4Solvingtheresultingproblem -- 3ConformalMappingMethods -- 3.1ModifiedSchwarz-Christoffelmappingsforpolygonswithroundedcor-ners -- 3.2Approximatecurvefactors -- 3.3TheOuterPolygonMethod -- 3.4Usingthegeodesicalgorithmforchannels -- 4Conclusion -- References -- COMPUTATIONAL STUDY OF THE 3D AFFINE TRANSFORMATION -- 1Introduction -- 2Definitionofthe3-PointProblem -- 3NumericalSolutions -- 3.1GeneralpolynomialsolverbasedonnumericalGroebnerbasisandeigen-systemmethod -- 3.2Globalminimization -- 3.3HomotopySolution -- 4SymbolicSolutions -- 4.1Dixon'sResultant:BasicConcepts -- 4.2ConstructionofDixonResultant -- Cayley'sformulationofB´ezout'smethod -- Example -- Dixon'sgeneralizationoftheCayley-B´ezout'smethod -- Example -- 4.3ImprovedDixonresultant-Kapur,SaxenaandYangmethod -- 4.4HeuristicmethodstoacceleratetheDixonresultant -- 4.5Earlydiscoveryoffactors:theEDFmethod -- Example -- 4.6ApplicationoftheEDFmethod -- 4.7ApplicationofReducedGroebnerbasis -- 4.8Computationofotherparameters.5DefinitionoftheN-PointProblem -- 6SolutionoftheOverdeterminedModel -- 6.1DirectNumericalSolutionviaGlobalMinimization -- 6.2Newton-RaphsonwithDeflation -- Example -- 6.3ExtendedgeneralProcrustesalgorithm -- 7TheDeterminedModel -- 8NumericalSolutionoftheDeterminedModel -- 9ComplexityStudyoftheAlgorithms -- 10TheProperSelectionofthe3PointsforInitialGuessValues -- 11Conclusions -- Acknowledgments -- References -- DISTANCES BASED ON NEIGHBORHOOD SEQUENCES IN THE TRIANGULAR GRID -- Abstract -- 1Introduction -- 1.1Abriefhistoryofdigitalgeometry -- 2BasicDefinitionsandNotations -- 3TheShortestPaths -- 4ConditionforMetricDistances -- 5ComputingtheDistance -- 6DigitalCircles -- 7Conclusion -- References -- A STREAM IN THE STUDY ON NORMALITY OF S-PRODUCTS -- Abstract -- I.S-ProductsandInfiniteProducts -- 1Introduction -- 2ProductsofCompactFactors -- 3TheDefinitionofS-Products -- 4S-ProductsofMetricSpaces -- II.S-ProductswithCountableTightness -- 5TightnessandProducts -- 6S-ProductsofParacompactp-Spaces -- 7GeneralizedMetricSpaces -- 8S-ProductsofGeneralizedMetricSpaces -- 9S-ProductsofParacompactC-ScatteredSpaces -- 10Non-NormalityofS-Products -- III.S-ProductswithoutCountableTightness -- 11CollectionwiseNormalityofS-Products -- 12CountableParacompactnessofS-Products -- 13TheShrinkingPropertyofS-Products -- 14Non-NormalityofS-Products,Revisited -- IV.RectangularProducts -- 15RectangularProductsandCoveringDimension -- 16ProductsofMetricSpaces -- 17ProductsofGeneralizedMetricSpaces -- 18NormalCoversofProducts -- References -- THE COMPLETION OF FUZZY METRIC SPACES AND OF OTHER RELATED STRUCTURES -- Abstract -- 1IntroductionandPreliminaries -- 2TheCompletionofFuzzyMetricSpaces -- 3TheCompletionofStrongFuzzyMetricSpacesandofNon-ArchimedeanFuzzyMetricSpaces -- 4TheCompletionofFuzzyMetricGroups -- 5TheCompletionofIntuitionisticFuzzyMetricSpaces -- Acknowledgments.References.Chareton gathers the latest research in this study of computational mathematics. He highlights such topics as coherence-homotopies of higher order, Vandermonde systems, numerical conformal mappings for waveguides, commutativity formulas for fundamental group entropy, the completion of fuzzy metric spaces and more.Computational mathematics and analysis series.Numerical analysisData processingNumerical analysisData processing.518.0285Chareton Peter G1867536MiAaPQMiAaPQMiAaPQBOOK9910957633303321Computational mathematics4475154UNINA