Advances in Applied Mathematical Analysis and Applications

312 Pages·2020·24.662 MB·English

by  Mangey Ram, Tadashi Dohi

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ADVANCES IN APPLIED
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V River Publishers Series in Mathematical and Engineering Sciences
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MATHEMATICAL ANALYSIS N
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YS ADVANCES IN APPLIED
AND APPLICATIONS S I
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A MATHEMATICAL ANALYSIS
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AIE AND APPLICATIONS
Mangey Ram and Tadashi Dohi (Editors)
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In recent years, applied mathematics has been used in all novel disciplines A
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of scientific development. Advances in Applied Mathematical Analysis and TIE Mangey Ram and Tadashi Dohi (Editors)
Applications summarizes interdisciplinary work within the field of applied OM
mathematics. NA
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The topics discussed in the book include:
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• S imilarity Solutions of Spherical Shock Waves in a Self-Gravitating L
Ideal Gas
• D ual Solutions for Finite Element Analysis of Unsteady
Hydromagnetic Stagnation Point Flow of Cu – Water Nanofluid
Generated by Stretching Sheet
• M ultiparametric Modeling of Carbon Cycle in Temperate Wetlands M
for Regional Climate Change Analysis Using Satellite Data a
• An Intelligent Neuro Fuzzy System for Pattern Classification n
g
• F uzzy Inventory Model with Demand, Deterioration and Inflation: e
y
A Comparative Study Through NGTFN and CNTFN
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• Summability and Its Application for the Stability of the System a
m
• Design of Manufacturing, Control, and Automation Systems

• SEIR – Application for Crop Through Water and Soil Texture a
n
• Advances in Radial Basis Functions d
• M odeling for Time Period of Natural Frequency for T
Non-Homogeneous Square Plate with Variable Thickness a
d
and Temperature Effect a
s
• A Study on Metric Fixed Point Theorems Satisfying Integral Type h
Contractions i
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• O bjective Function – in Radiometric Studies – Application to AGRS o
Surveys Associated with Radon h
i

• Modeling Kernel Function in Blackbody Radiation Inversion (
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t
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)

River Publishers River River Publishers
Advances in Applied Mathematical
Analysis and Applications
RIVER PUBLISHERS SERIES IN MATHEMATICAL
AND ENGINEERING SCIENCES
SeriesEditors:
TADASHIDOHI ALIAKBARMONTAZERHAGHIGHI
HiroshimaUniversity PrairieViewTexasA&MUniversity
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MANGEYRAM
GraphicEraUniversity
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Advances in Applied Mathematical
Analysis and Applications
Editors
Mangey Ram
GraphicEraDeemedtobeUniversity
India
Tadashi Dohi
HiroshimaUniversity
Japan
River Publishers
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Contents
Preface xiii
Acknowledgements xv
ListofContributors xvii
ListofFigures xxi
ListofTables xxv
ListofAbbreviations xxvii
1 SimilaritySolutionsofSphericalShockWavesina
Self-GravitatingIdealGas 1
AsthaChauhanandRajanArora
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 FormulationofProblem . . . . . . . . . . . . . . . . . . . 3
1.3 SimilarityAnalysis . . . . . . . . . . . . . . . . . . . . . . 5
1.4 SimilaritySolutions . . . . . . . . . . . . . . . . . . . . . 8
1.5 ImplodingShocks . . . . . . . . . . . . . . . . . . . . . . 13
1.6 ResultsandDiscussion . . . . . . . . . . . . . . . . . . . . 15
1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 19
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 DualSolutionsforFiniteElementAnalysisofUnsteady
HydromagneticStagnationPointFlowofCu–WaterNanofluid
GeneratedbyStretchingSheet 23
SantoshChaudharyandKMKanika
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 FormulationoftheProblem . . . . . . . . . . . . . . . . . 26
v
vi Contents
2.3 SimilarityTransformation . . . . . . . . . . . . . . . . . . 28
2.4 LocalSkinFrictionandLocalNusseltNumber . . . . . . . 29
2.5 MethodofSolution . . . . . . . . . . . . . . . . . . . . . . 29
2.6 MethodValidation . . . . . . . . . . . . . . . . . . . . . . 32
2.7 NumericalResultsandDiscussion . . . . . . . . . . . . . . 32
2.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 46
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3 MultiparametricModelingofCarbonCycleinTemperate
WetlandsforRegionalClimateChangeAnalysisUsing
SatelliteData 51
AnnaKozlova,LesiaElistratova,YuriyV.Kostyuchenko,
AlexandrApostolovandIgorArtemenko
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2 OntheMethodologyofEmissionAnalysis . . . . . . . . . 54
3.2.1 GeneralizedApproach . . . . . . . . . . . . . . . . 54
3.2.2 OntheUncertaintyControl . . . . . . . . . . . . . 56
3.3 ModelingoftheCarbonCycle . . . . . . . . . . . . . . . . 57
3.3.1 KeyModelVariablesandParameters . . . . . . . . 57
3.3.2 From Local to Global Methane Cycle Modeling:
VariablesandParameters . . . . . . . . . . . . . . 61
3.3.3 UncertaintyAnalysisintheCarbonModels . . . . . 65
3.3.4 On the Local Models Integration into the Global
Models:AMethodology . . . . . . . . . . . . . . . 66
3.4 SatelliteToolsandDatafortheCarbonCycleControl . . . 72
3.4.1 SatelliteToolsforGHGMonitoring . . . . . . . . . 72
3.4.2 Satellite Tools for Plant Productivity and Carbon
StockAssessment . . . . . . . . . . . . . . . . . . 73
3.4.3 SatelliteToolsforUncertaintyAssessmentinCrops
Productivity . . . . . . . . . . . . . . . . . . . . . 75
3.5 ApproachtoEmissionAssessmentandControl . . . . . . . 79
3.5.1 Stochastic Tools for Decision Making in Carbon
EmissionsControl . . . . . . . . . . . . . . . . . . 80
3.6 Results of Multiparametric Modeling of Methane Cycle in
Temperate Wetlands in View of Regional Climate Change
UsingSatelliteData . . . . . . . . . . . . . . . . . . . . . 82
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 87
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Contents vii
4 AnIntelligentNeuroFuzzySystemforPatternClassification 95
AbduMasanawaSagirandSarathaSathasivam
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2 ArtificialNeuralNetworksApproach . . . . . . . . . . . . 97
4.3 StatisticalApproach . . . . . . . . . . . . . . . . . . . . . 97
4.4 DesignofanIntelligentNeuroFuzzySystem . . . . . . . . 97
4.5 HybridLearningAlgorithmofProposedMethod . . . . . . 98
4.6 ForwardPass . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.7 BackwardPass . . . . . . . . . . . . . . . . . . . . . . . . 100
4.7.1 Rules’IndexVector . . . . . . . . . . . . . . . . . 101
4.8 SimulationResults . . . . . . . . . . . . . . . . . . . . . . 104
4.9 GraphsofPerformanceErrorVsNo.ofIterations . . . . . . 106
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5 FuzzyInventoryModelwithDemand,Deterioration
andInflation:AComparativeStudyThrough
NGTFNandCNTFN 113
MagfuraPervinandSankarKumarRoy
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.2 PreliminaryConcept . . . . . . . . . . . . . . . . . . . . . 115
5.3 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.4 MathematicalModel . . . . . . . . . . . . . . . . . . . . . 118
5.5 FormulationofFuzzyMathematicalModel . . . . . . . . . 121
5.6 NumericalExample . . . . . . . . . . . . . . . . . . . . . 129
5.7 SensitivityAnalysis . . . . . . . . . . . . . . . . . . . . . 130
5.8 ConcludingRemarksandFutureStudies . . . . . . . . . . . 130
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6 SummabilityandItsApplicationfortheStability
oftheSystem 139
SmitaSonkerandAlkaMunjal
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.2 SummabilityProcess . . . . . . . . . . . . . . . . . . . . . 141
6.3 TypesofSummability . . . . . . . . . . . . . . . . . . . . 142
6.3.1 OrdinarySummability . . . . . . . . . . . . . . . . 142
6.3.2 StrongSummability . . . . . . . . . . . . . . . . . 142
6.3.3 AbsoluteSummability . . . . . . . . . . . . . . . . 143
6.4 RegularityofaSummabilityProcess . . . . . . . . . . . . . 143
6.5 Silverman-ToeplitzTheorem . . . . . . . . . . . . . . . . . 143
viii Contents
6.6 ApplicationofAbsoluteSummableFactorforStability . . . 144
6.6.1 Stability of the Frequency Response of the Moving
AverageSystem . . . . . . . . . . . . . . . . . . . 144
6.6.2 StabilityoftheFrequencyResponseofthe
OscillatingImpulseSystem . . . . . . . . . . . . . 147
6.6.3 StabilityoftheFrequencyResponseofthe
ExponentialSystem . . . . . . . . . . . . . . . . . 150
6.6.3.1 Stabilityoffrequencyresponseofthe
exponentialsystemupto
n=0,1,2,...,88 . . . . . . . . . . . . . 151
6.6.3.2 Stabilityoffrequencyresponseofthe
exponentialsystemupto
n=0,1,2,...,176 . . . . . . . . . . . . 153
6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 156
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7 DesignofManufacturing,Control,andAutomation
Systems 159
MohitPant,MohitSood,AeshwaryaDixitandSahilGarg
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.2 StepsinDesignofManufacturingSystems . . . . . . . . . 161
7.3 TypesofManufacturing . . . . . . . . . . . . . . . . . . . 162
7.4 AdditiveManufacturing(AM) . . . . . . . . . . . . . . . . 162
7.4.1 DesignofAdditiveManufacturingSystem . . . . . 163
7.4.2 SubtractiveTypeManufacturing . . . . . . . . . . . 163
7.4.3 MachiningProcessinSubtractiveManufacturing . . 164
7.4.4 CuttingToolsforSubtractiveManufacturing . . . . 165
7.5 RapidPrototyping . . . . . . . . . . . . . . . . . . . . . . 166
7.5.1 AdvantagesandDisadvantagesofRapid
Prototyping . . . . . . . . . . . . . . . . . . . . . 166
7.5.2 TypesofRapidPrototypes . . . . . . . . . . . . . . 167
7.6 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.6.1 FeedbackinControlSystem . . . . . . . . . . . . . 172
7.7 Automation . . . . . . . . . . . . . . . . . . . . . . . . . . 173
7.7.1 ApplicationofAutomationinIndustries . . . . . . 174
7.7.2 TypeofAutomationSystem . . . . . . . . . . . . . 174
7.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 175
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Contents ix
8 SEIR–ApplicationforCropThroughWaterandSoilTexture 179
NitaH.Shah,EktaN.Jayswal,MokshaH.Satia
andForamA.Thakkar
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8.1.1 DynamicalSystem . . . . . . . . . . . . . . . . . . 179
8.1.2 DynamicsofCropusingFertileSoil . . . . . . . . 180
8.2 MathematicalModeling . . . . . . . . . . . . . . . . . . . 181
8.3 StabilityAnalysis . . . . . . . . . . . . . . . . . . . . . . . 184
8.3.1 LocalStability . . . . . . . . . . . . . . . . . . . . 184
8.3.2 GlobalStability . . . . . . . . . . . . . . . . . . . 185
8.4 NumericalSimulation . . . . . . . . . . . . . . . . . . . . 186
8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 189
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
9 AdvancesinRadialBasisFunctions 193
GeetaAroraandGurpreetSinghBhatia
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 193
9.2 RequirementofMesh-freeMethods . . . . . . . . . . . . . 194
9.3 RadialBasisFunction . . . . . . . . . . . . . . . . . . . . 195
9.4 PropertiesofRadialBasisFunctions . . . . . . . . . . . . . 195
9.5 DevelopmentsinRadialBasisFunctions. . . . . . . . . . . 196
9.6 ShapeParameters . . . . . . . . . . . . . . . . . . . . . . . 196
9.7 RBFInterpolation . . . . . . . . . . . . . . . . . . . . . . 198
9.8 SolutionofDifferentialEquation . . . . . . . . . . . . . . . 200
9.8.1 KansaMethod . . . . . . . . . . . . . . . . . . . . 200
9.8.2 SymmetricCollocationMethod . . . . . . . . . . . 201
9.8.3 RBF-pseudospectralApproach . . . . . . . . . . . 201
9.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
10 ModelingforTimePeriodofNaturalFrequency
forNon-HomogeneousSquarePlatewithVariable
ThicknessandTemperatureEffect 209
ReetaBhardwaj,NaveenManiandAmitSharma
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 209
10.2 LiteratureSurvey . . . . . . . . . . . . . . . . . . . . . . . 210
10.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
10.4 ConstructionofProblem . . . . . . . . . . . . . . . . . . . 214
10.5 SolutionofProblem . . . . . . . . . . . . . . . . . . . . . 216