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Advances in Applied Mathematical Analysis and Applications by Mangey Ram and Tadashi Dohi is available for free download in PDF format
Advances in Applied Mathematical Analysis and Applications Contents
Preface xiii
Acknowledgements xv
List of Contributors xvii
List of Figures xxi
List of Tables xxv
List of Abbreviations xxvii
1 Similarity Solutions of Spherical Shock Waves in a
Self-Gravitating Ideal Gas 1
Astha Chauhan and Rajan Arora
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Formulation of Problem . . . . . . . . . . . . . . . . . . . 3
1.3 Similarity Analysis . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Similarity Solutions . . . . . . . . . . . . . . . . . . . . . 8
1.5 Imploding Shocks . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . 15
1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 19
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Dual Solutions for Finite Element Analysis of Unsteady
Hydromagnetic Stagnation Point Flow of Cu – Water Nanofluid
Generated by Stretching Sheet 23
Santosh Chaudhary and KM Kanika
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Formulation of the Problem . . . . . . . . . . . . . . . . . 26
2.3 Similarity Transformation . . . . . . . . . . . . . . . . . . 28
2.4 Local Skin Friction and Local Nusselt Number . . . . . . . 29
2.5 Method of Solution . . . . . . . . . . . . . . . . . . . . . . 29
2.6 Method Validation . . . . . . . . . . . . . . . . . . . . . . 32
2.7 Numerical Results and Discussion . . . . . . . . . . . . . . 32
2.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 46
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3 Multiparametric Modeling of Carbon Cycle in Temperate
Wetlands for Regional Climate Change Analysis Using
Satellite Data 51
Anna Kozlova, Lesia Elistratova, Yuriy V. Kostyuchenko,
Alexandr Apostolov and Igor Artemenko
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2 On the Methodology of Emission Analysis . . . . . . . . . 54
3.2.1 Generalized Approach . . . . . . . . . . . . . . . . 54
3.2.2 On the Uncertainty Control . . . . . . . . . . . . . 56
3.3 Modeling of the Carbon Cycle . . . . . . . . . . . . . . . . 57
3.3.1 Key Model Variables and Parameters . . . . . . . . 57
3.3.2 From Local to Global Methane Cycle Modeling: Variables and Parameters . . . . . . . . . . . . . . 61
3.3.3 Uncertainty Analysis in the Carbon Models . . . . . 65
3.3.4 On the Local Models Integration into the Global
Models: A Methodology . . . . . . . . . . . . . . . 66
3.4 Satellite Tools and Data for the Carbon Cycle Control . . . 72
3.4.1 Satellite Tools for GHG Monitoring . . . . . . . . . 72
3.4.2 Satellite Tools for Plant Productivity and Carbon
Stock Assessment . . . . . . . . . . . . . . . . . . 73
3.4.3 Satellite Tools for Uncertainty Assessment in Crops Productivity . . . . . . . . . . . . . . . . . . . . . 75
3.5 Approach to Emission Assessment and Control . . . . . . . 79
3.5.1 Stochastic Tools for Decision Making in Carbon
Emissions Control . . . . . . . . . . . . . . . . . . 80
3.6 Results of Multiparametric Modeling of Methane Cycle in
Temperate Wetlands in View of Regional Climate Change
Using Satellite Data . . . . . . . . . . . . . . . . . . . . . 82
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 87
References . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 90
4 An Intelligent Neuro Fuzzy System for Pattern Classification 95
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2 Artificial Neural Networks Approach . . . . . . . . . . . . 97
4.3 Statistical Approach . . . . . . . . . . . . . . . . . . . . . 97
4.4 Design of an Intelligent Neuro Fuzzy System . . . . . . . . 97
4.5 Hybrid Learning Algorithm of Proposed Method . . . . . . 98
4.6 Forward Pass . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.7 Backward Pass . . . . . . . . . . . . . . . . . . . . . . . . 100
4.7.1 Rules’ Index Vector . . . . . . . . . . . . . . . . . 101
4.8 Simulation Results . . . . . . . . . . . . . . . . . . . . . . 104
4.9 Graphs of Performance Error Vs No. of Iterations . . . . . . 106
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5 Fuzzy Inventory Model with Demand, Deterioration
and Inflation: A Comparative Study Through
NGTFN and CNTFN 113
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.2 Preliminary Concept . . . . . . . . . . . . . . . . . . . . . 115
5.3 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.4 Mathematical Model . . . . . . . . . . . . . . . . . . . . . 118
5.5 Formulation of Fuzzy Mathematical Model . . . . . . . . . 121
5.6 Numerical Example . . . . . . . . . . . . . . . . . . . . . 129
5.7 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . 130
5.8 Concluding Remarks and Future Studies . . . . . . . . . . . 130
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6 Summability and Its Application for the Stability of the System 139
Smita Sonker and Alka Munjal
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.2 Summability Process . . . . . . . . . . . . . . . . . . . . . 141
6.3 Types of Summability . . . . . . . . . . . . . . . . . . . . 142
6.3.1 Ordinary Summability . . . . . . . . . . . . . . . . 142
6.3.2 Strong Summability . . . . . . . . . . . . . . . . . 142
6.3.3 Absolute Summability . . . . . . . . . . . . . . . . 143
6.4 Regularity of a Summability Process . . . . . . . . . . . . . 143
6.5 Silverman-Toeplitz Theorem . . . . . . . . . . . . . . . . . 143
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6.6 Application of Absolute Summable Factor for Stability . . . 144
6.6.1 Stability of the Frequency Response of the Moving
Average System . . . . . . . . . . . . . . . . . . . 144
6.6.2 Stability of the Frequency Response of the
Oscillating Impulse System . . . . . . . . . . . . . 147
6.6.3 Stability of the Frequency Response of the
Exponential System . . . . . . . . . . . . . . . . . 150
6.6.3.1 Stability of frequency response of the exponential system up to
n = 0, 1, 2,. . . , 88 . . . . . . . . . . . . . 151
6.6.3.2 Stability of frequency response of the exponential system up to
n = 0, 1, 2, . . . , 176 . . . . . . . . . . . . 153
6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 156
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7 Design of Manufacturing, Control, and Automation Systems 159
Mohit Pant, Mohit Sood, Aeshwarya Dixit and Sahil Garg
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.2 Steps in Design of Manufacturing Systems . . . . . . . . . 161
7.3 Types of Manufacturing . . . . . . . . . . . . . . . . . . . 162
7.4 Additive Manufacturing (AM) . . . . . . . . . . . . . . . . 162
7.4.1 Design of Additive Manufacturing System . . . . . 163
7.4.2 Subtractive Type Manufacturing . . . . . . . . . . . 163
7.4.3 Machining Process in Subtractive Manufacturing. . 164
7.4.4 Cutting Tools for Subtractive Manufacturing . . . . 165
7.5 Rapid Prototyping . . . . . . . . . . . . . . . . . . . . . . 166
7.5.1 Advantages and Disadvantages of Rapid
Prototyping . . . . . . . . . . . . . . . . . . . . . 166
7.5.2 Types of Rapid Prototypes . . . . . . . . . . . . . . 167
7.6 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.6.1 Feedback in Control System . . . . . . . . . . . . . 172
7.7 Automation . . . . . . . . . . . . . . . . . . . . . . . . . . 173
7.7.1 Application of Automation in Industries . . . . . . 174
7.7.2 Type of Automation System . . . . . . . . . . . . . 174
7.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 175
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8 SEIR – Application for Crop through Water and Soil Texture 179
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8.1.1 Dynamical System . . . . . . . . . . . . . . . . . . 179
8.1.2 Dynamics of Crop using Fertile Soil . . . . . . . . 180
8.2 Mathematical Modeling . . . . . . . . . . . . . . . . . . . 181
8.3 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . 184
8.3.1 Local Stability . . . . . . . . . . . . . . . . . . . . 184
8.3.2 Global Stability . . . . . . . . . . . . . . . . . . . 185
8.4 Numerical Simulation . . . . . . . . . . . . . . . . . . . . 186
8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 189
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
9 Advances in Radial Basis Functions 193
Geeta Arora and Gurpreet Singh Bhatia
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 193
9.2 Requirement of Mesh-free Methods . . . . . . . . . . . . . 194
9.3 Radial Basis Function . . . . . . . . . . . . . . . . . . . . 195
9.4 Properties of Radial Basis Functions . . . . . . . . . . . . . 195
9.5 Developments in Radial Basis Functions . . . . . . . . . . . 196
9.6 Shape Parameters . . . . . . . . . . . . . . . . . . . . . . . 196
9.7 RBF Interpolation . . . . . . . . . . . . . . . . . . . . . . 198
9.8 Solution of Differential Equation . . . . . . . . . . . . . . . 200
9.8.1 Kansa Method . . . . . . . . . . . . . . . . . . . . 200
9.8.2 Symmetric Collocation Method . . . . . . . . . . . 201
9.8.3 RBF-pseudospectral Approach . . . . . . . . . . . 201
9.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
10 Modeling for Time Period of Natural Frequency for Non-Homogeneous Square Plate with Variable
Thickness and Temperature Effect 209
Reeta Bhardwaj, Naveen Mani and Amit Sharma
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 209
10.2 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . 210
10.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
10.4 Construction of Problem . . . . . . . . . . . . . . . . . . . 214
10.5 Solution of Problem . . . . . . . . . . . . . . . . . . . . . 216
10.6 Numerical Illustration and Discussions . . . . . . . . . . . 218
10.7 Results Comparison . . . . . . . . . . . . . . . . . . . . . 223
10.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 224
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
11 A Study on Metric Fixed Point Theorems Satisfying Integral
Type Contractions 229
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 230
11.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 230
11.3 Fixed Point Theorem Satisfying Weak Integral Type
Rational Contractions . . . . . . . . . . . . . . . . . . . . 234
11.4 (π; φ)− Integral Type Weak Contractions and Fixed-Point
Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
11.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 246
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
12 Objective Function – in Radiometric Studies – Application to AGRS Surveys Associated with Radon 249
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 249
12.2 Ordinary and Weighted Linear Regression Models . . . . . 250
12.3 Computations of Compton Factors . . . . . . . . . . . . . . 252
12.3.1 Study of Variations in Stripping Factors when the
Correlation among Radioelements Exists . . . . . . 253
12.3.2 Estimation of Stripping Factors and their Variations with Flying Heights . . . . . . . . . . . . . . . . . 255
12.4 Objective Function for Study of Random Errors in Stripping
Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 256
12.5 Effects of Airborne Bi24 and Error Bias due to It . . . . . . 258
12.6 Ground and Airborne Experiments . . . . . . . . . . . . . . 259
12.7 Results and Discussion . . . . . . . . . . . . . . . . . . . . 260
12.7.1 Test Area A . . . . . . . . . . . . . . . . . . . . . 260
12.7.2 Test Area B . . . . . . . . . . . . . . . . . . . . . 260
12.7.3 Area of Very High Thorium Concentration . . . . . 261
12.7.4 Area of High Uranium Concentration . . . . . . . . 261
12.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . 261
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
13 Modeling Kernel Function in Blackbody Radiation Inversion 265
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 265
13.2 Nature and Statement of the Problem . . . . . . . . . . . . 266
13.3 Towards a Solution to the Problem . . . . . . . . . . . . . . 269
13.3.1 Reducing Φ(x) Function to Gaussians . . . . . . . . 272
13.3.2 Convolution of Equation (13.4) . . . . . . . . . . . 274
13.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . 276
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Index 277
About the Editors 281