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 -- 2.3TheBjörckandPereyraalgorithm -- 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'sformulationofBézout'smethod -- Example -- Dixon'sgeneralizationoftheCayley-Bézout'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.