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El. knyga: Mathematical Methods in Interdisciplinary Sciences [Wiley Online]

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  • Formatas: 464 pages
  • Išleidimo metai: 01-Sep-2020
  • Leidėjas: John Wiley & Sons Inc
  • ISBN-10: 1119585643
  • ISBN-13: 9781119585640
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  • Wiley Online
  • Kaina: 136,34 €*
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Mathematical Methods in Interdisciplinary SciencesDidesnis paveikslėlis
  • Formatas: 464 pages
  • Išleidimo metai: 01-Sep-2020
  • Leidėjas: John Wiley & Sons Inc
  • ISBN-10: 1119585643
  • ISBN-13: 9781119585640
Kitos knygos pagal šią temą:
Wiley Online E-booksMore info about Wiley Online
Partnerių interneto svetainė: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119585640
"This book examines the interface between mathematics and applied sciences. The editor examines the present and future needs for the interaction between various science and engineering areas. This edited book brings together the cutting-edge research on mathematics, combining various fields of science and engineering. The book begins with an introduction to computing and modeling. Next, computation and modeling trends are covered, along with chapters on structural static and vibration problems, heat conduction and diffusion problems, and fluid dynamics problems. Soft computing and machine intelligence based modeling are also discussed, along with bio medical problems. The book concludes with a chapter on modeling in mining, electrical, electronics, and chemical problems. This book is a reference for students and researchers in various fields of engineering such as computer, mechanical, civil, aerospace, electrical, and chemical, as well as and other sciences such as applied mathematics, physics, chemistry, and life sciences"--

Brings mathematics to bear on your real-world, scientific problems

Mathematical Methods in Interdisciplinary Sciences provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics.

The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include:

  • Structural static and vibration problems
  • Heat conduction and diffusion problems
  • Fluid dynamics problems

The book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.

Notes on Contributors xv
Preface xxv
Acknowledgments xxvii
1 Connectionist Learning Models for Application Problems Involving Differential and Integral Equations
1(22)
Susmita Mall
Sumit Kumar Jeswal
Snehashish Chakraverty
1.1 Introduction
1(5)
1.1.1 Artificial Neural Network
1(1)
1.1.2 Types of Neural Networks
1(1)
1.1.3 Learning in Neural Network
2(1)
1.1.4 Activation Function
2(1)
1.1.4.1 Sigmoidal Function
3(1)
1.1.5 Advantages of Neural Network
3(1)
1.1.6 Functional Link Artificial Neural Network (FLANN)
3(1)
1.1.7 Differential Equations (DEs)
4(1)
1.1.8 Integral Equation
5(1)
1.1.8.1 Fredholm Integral Equation of First Kind
5(1)
1.1.8.2 Fredholm Integral Equation of Second Kind
5(1)
1.1.8.3 Volterra Integral Equation of First Kind
5(1)
1.1.8.4 Volterra Integral Equation of Second Kind
5(1)
1.1.8.5 Linear Fredholm Integral Equation System of Second Kind
6(1)
1.2 Methodology for Differential Equations
6(3)
1.2.1 FLANN-Based General Formulation of Differential Equations
6(1)
1.2.1.1 Second-Order Initial Value Problem
6(1)
1.2.1.2 Second-Order Boundary Value Problem
7(1)
1.2.2 Proposed Laguerre Neural Network (LgNN) for Differential Equations
7(1)
1.2.2.1 Architecture of Single-Layer LgNN Model
7(1)
1.2.2.2 Training Algorithm of Laguerre Neural Network (LgNN)
8(1)
1.2.2.3 Gradient Computation of LgNN
9(1)
1.3 Methodology for Solving a System of Fredholm Integral Equations of Second Kind
9(2)
1.3.1 Algorithm
10(1)
1.4 Numerical Examples and Discussion
11(9)
1.4.1 Differential Equations and Applications
11(5)
1.4.2 Integral Equations
16(4)
1.5 Conclusion
20(1)
References
20(3)
2 Deep Learning in Population Genetics: Prediction and Explanation of Selection of a Population
23(10)
Romila Ghosh
Satyakama Paul
2.1 Introduction
23(1)
2.2 Literature Review
23(2)
2.3 Dataset Description
25(1)
2.3.1 Selection and Its Importance
25(1)
2.4 Objective
26(1)
2.5 Relevant Theory, Results, and Discussions
27(3)
2.5.1 automl
27(1)
2.5.2 Hypertuning the Best Model
28(2)
2.6 Conclusion
30(1)
References
30(3)
3 A Survey of Classification Techniques in Speech Emotion Recognition
33(16)
Tanmoy Roy
Tshilidzi Marwala
Snehashish Chakraverty
3.1 Introduction
33(1)
3.2 Emotional Speech Databases
33(1)
3.3 SER Features
34(1)
3.4 Classification Techniques
35(6)
3.4.1 Hidden Markov Model
36(1)
3.4.1.1 Difficulties in Using HMM for SER
37(1)
3.4.2 Gaussian Mixture Model
37(1)
3.4.2.1 Difficulties in Using GMM for SER
38(1)
3.4.3 Support Vector Machine
38(1)
3.4.3.1 Difficulties with SVM
39(1)
3.4.4 Deep Learning
39(2)
3.4.4.1 Drawbacks of Using Deep Learning for SER
41(1)
3.5 Difficulties in SER Studies
41(1)
3.6 Conclusion
41(1)
References
42(7)
4 Mathematical Methods in Deep Learning
49(14)
Srinivasa Manikant Upadhyayula
Kannan Venkataramanan
4.1 Deep Learning Using Neural Networks
49(1)
4.2 Introduction to Neural Networks
49(6)
4.2.1 Artificial Neural Network (ANN)
50(2)
4.2.1.1 Activation Function
52(1)
4.2.1.2 Logistic Sigmoid Activation Function
52(1)
4.2.1.3 tanh or Hyperbolic Tangent Activation Function
53(1)
4.2.1.4 ReLU (Rectified Linear Unit) Activation Function
54(1)
4.3 Other Activation Functions (Variant Forms of ReLU)
55(1)
4.3.1 Smooth ReLU
55(1)
4.3.2 Noisy ReLU
55(1)
4.3.3 Leaky ReLU
55(1)
4.3.4 Parametric ReLU
56(1)
4.3.5 Training and Optimizing a Neural Network Model
56(1)
4.4 Backpropagation Algorithm
56(3)
4.5 Performance and Accuracy
59(1)
4.6 Results and Observation
59(2)
References
61(2)
5 Multimodal Data Representation and Processing Based on Algebraic System of Aggregates
63(36)
Yevgeniya Sulema
Etienne Kerre
5.1 Introduction
63(1)
5.2 Basic Statements of ASA
64(1)
5.3 Operations on Aggregates and Multi-images
65(7)
5.4 Relations and Digital Intervals
72(3)
5.5 Data Synchronization
75(17)
5.6 Fuzzy Synchronization
92(4)
5.7 Conclusion
96(1)
References
96(3)
6 Nonprobabilistic Analysis of Thermal and Chemical Diffusion Problems with Uncertain Bounded Parameters
99(16)
Sukanta Nayak
Tharasi Dilleswar Rao
Snehashish Chakraverty
6.1 Introduction
99(1)
6.2 Preliminaries
99(3)
6.2.1 Interval Arithmetic
99(1)
6.2.2 Fuzzy Number and Fuzzy Arithmetic
100(1)
6.2.3 Parametric Representation of Fuzzy Number
101(1)
6.2.4 Finite Difference Schemes for PDEs
102(1)
6.3 Finite Element Formulation for Tapered Fin
102(3)
6.4 Radon Diffusion and Its Mechanism
105(2)
6.5 Radon Diffusion Mechanism with TFN Parameters
107(5)
6.5.1 EFDM to Radon Diffusion Mechanism with TFN Parameters
108(4)
6.6 Conclusion
112(1)
References
112(3)
7 Arbitrary Order Differential Equations with Fuzzy Parameters
115(10)
Tofigh Altahviranloo
Soheil Salahshour
7.1 Introduction
115(1)
1.2 Preliminaries
115(1)
7.3 Arbitrary Order Integral and Derivative for Fuzzy-Valued Functions
116(2)
7.4 Generalized Fuzzy Laplace Transform with Respect to Another Function
118(4)
References
122(3)
8 Fluid Dynamics Problems in Uncertain Environment
125(20)
Perumandla Karunakar
Uddhaba Biswal
Snehashish Chakraverty
8.1 Introduction
125(1)
8.2 Preliminaries
126(1)
8.2.1 Fuzzy Set
126(1)
8.2.2 Fuzzy Number
126(1)
8.2.3 5-Cut
127(1)
8.2.4 Parametric Approach
127(1)
8.3 Problem Formulation
127(2)
8.4 Methodology
129(2)
8.4.1 Homotopy Perturbation Method
129(1)
8.4.2 Homotopy Perturbation Transform Method
130(1)
8.5 Application of HPM and HPTM
131(5)
8.5.1 Application of HPM to Jeffery-Hamel Problem
131(3)
8.5.2 Application of HPTM to Coupled Whitham-Broer-Kaup Equations
134(2)
8.6 Results and Discussion
136(6)
8.7 Conclusion
142(1)
References
142(3)
9 Fuzzy Rough Set Theory-Based Feature Selection: A Review
145(22)
Tanmoy Som
Shivam Shreevastava
Anoop Kumar Tiwari
Shivani Singh
9.1 Introduction
145(1)
9.2 Preliminaries
146(3)
9.2.1 Rough Set Theory
146(1)
9.2.1.1 Rough Set
146(1)
9.2.1.2 Rough Set-Based Feature Selection
147(1)
9.2.2 Fuzzy Set Theory
147(1)
9.2.2.1 Fuzzy Tolerance Relation
148(1)
9.2.2.2 Fuzzy Rough Set Theory
149(1)
9.2.2.3 Degree of Dependency-Based Fuzzy Rough Attribute Reduction
149(1)
9.2.2 A Discernibility Matrix-Based Fuzzy Rough Attribute Reduction
149(1)
9.3 Fuzzy Rough Set-Based Attribute Reduction
149(5)
9.3.1 Degree of Dependency-Based Approaches
150(4)
9.3.2 Discernibility Matrix-Based Approaches
154(1)
9.4 Approaches for Semisupervised and Unsupervised Decision Systems
154(4)
9.5 Decision Systems with Missing Values
158(1)
9.6 Applications in Classification, Rule Extraction, and Other Application Areas
158(1)
9.7 Limitations of Fuzzy Rough Set Theory
159(1)
9.8 Conclusion
160(1)
References
160(7)
10 Universal Intervals: Towards a Dependency-Aware Interval Algebra
167(48)
Hend Dawood
Yasser Dawood
10.1 Introduction
167(2)
10.2 The Need for Interval Computations
169(1)
10.3 On Some Algebraic and Logical Fundamentals
170(4)
10.4 Classical Intervals and the Dependency Problem
174(2)
10.5 Interval Dependency: A Logical Treatment
176(8)
10.5.1 Quantification Dependence and Skolemization
177(2)
10.5.2 A Formalization of the Notion of Interval Dependency
179(5)
10.6 Interval Enclosures Under Functional Dependence
184(2)
10.7 Parametric Intervals: How Far They Can Go
186(6)
10.7.1 Parametric Interval Operations: From Endpoints to Convex Subsets
186(2)
10.7.2 On the Structure of Parametric Intervals: Are They Properly Founded?
188(4)
10.8 Universal Intervals: An Interval Algebra with a Dependency Predicate
192(9)
10.8.1 Universal Intervals, Rational Functions, and Predicates
193(3)
10.8.2 The Arithmetic of Universal Intervals
196(5)
10.9 The S-Field Algebra of Universal Intervals
201(8)
10.10 Guaranteed Bounds or Best Approximation or Both?
209(1)
Supplementary Materials
210(1)
Acknowledgments
211(1)
References
211(4)
11 Affine-Contractor Approach to Handle Nonlinear Dynamical Problems in Uncertain Environment
215(24)
Nisha Rani Mahato
Saudamini Rout
Snehashish Chakraverty
11.1 Introduction
215(2)
11.2 Classical Interval Arithmetic
217(2)
11.2.1 Intervals
217(1)
11.2.2 Set Operations of Interval System
217(1)
11.2.3 Standard Interval Computations
218(1)
11.2.4 Algebraic Properties of Interval
219(1)
11.3 Interval Dependency Problem
219(1)
11.4 Affine Arithmetic
220(3)
11.4.1 Conversion Between Interval and Affine Arithmetic
220(1)
11.4.2 Affine Operations
221(2)
11.5 Contractor
223(2)
11.5.1 SIVIA
223(2)
11.6 Proposed Methodology
225(5)
11.7 Numerical Examples
230(6)
11.7.1 Nonlinear Oscillators
230(1)
11.7.1.1 Unforced Nonlinear Differential Equation
230(2)
11.7.1.2 Forced Nonlinear Differential Equation
232(1)
11.7.2 Other Dynamic Problem
233(1)
11.7.2.1 Nonhomogeneous Lane-Emden Equation
233(3)
11.8 Conclusion
236(1)
References
236(3)
12 Dynamic Behavior of Nanobeam Using Strain Gradient Model
239(14)
Subrat Kumar Jena
Rajarama Mohan Jena
Snehashish Chakraverty
12.1 Introduction
239(1)
12.2 Mathematical Formulation of the Proposed Model
240(1)
12.3 Review of the Differential Transform Method (DTM)
241(1)
12.4 Application of DTM on Dynamic Behavior Analysis
242(2)
12.5 Numerical Results and Discussion
244(4)
12.5.1 Validation and Convergence
244(1)
12.5.2 Effect of the Small-Scale Parameter
245(2)
12.5.3 Effect of Length-Scale Parameter
247(1)
12.6 Conclusion
248(1)
Acknowledgment
249(1)
References
250(3)
13 Structural Static and Vibration Problems
253(20)
M. Amin Changizi
Ion Stiharu
13.1 Introduction
253(1)
13.2 One-parameter Groups
254(1)
13.3 Infinitesimal Transformation
254(1)
13.4 Canonical Coordinates
254(1)
13.5 Algorithm for Lie Symmetry Point
255(1)
13.6 Reduction of the Order of the ODE
255(1)
13.7 Solution of First-Order ODE with Lie Symmetry
255(1)
13.8 Identification
256(2)
13.9 Vibration of a Microcantilever Beam Subjected to Uniform Electrostatic Field
258(1)
13.10 Contact Form for the Equation
259(1)
13.11 Reducing in the Order of the Nonlinear ODE Representing the Vibration of a Microcantilever Beam Under Electrostatic Field
260(1)
13.12 Nonlinear Pull-in Voltage
261(5)
13.13 Nonlinear Analysis of Pull-in Voltage of Twin Microcantilever Beams
266(2)
13.14 Nonlinear Analysis of Pull-in Voltage of Twin Microcantilever Beams of Different Thicknesses
268(4)
References
272(1)
14 Generalized Differential and Integral Quadrature: Theory and Applications
273(70)
Francesco Tornabene
Rossana Dimitri
14.1 Introduction
273(1)
14.2 Differential Quadrature
274(3)
14.2.1 Genesis of the Differential Quadrature Method
274(1)
14.2.2 Differential Quadrature Law
275(2)
14.3 General View on Differential Quadrature
277(33)
14.3.1 Basis Functions
278(3)
14.3.1.1 Lagrange Polynomials
281(1)
14.3.1.2 Trigonometric Lagrange Polynomials
282(1)
14.3.1.3 Classic Orthogonal Polynomials
282(9)
14.3.1.4 Monomial Functions
291(1)
14.3.1.5 Exponential Functions
291(1)
14.3.1.6 Bernstein Polynomials
291(1)
14.3.1.7 Fourier Functions
292(1)
14.3.1.8 Bessel Polynomials
292(1)
14.3.1.9 Boubaker Polynomials
292(1)
14.3.2 Grid Distributions
293(1)
14.3.2.1 Coordinate Transformation
293(1)
14.3.2.2 5-Point Distribution
293(1)
14.3.2.3 Stretching Formulation
293(1)
14.3.2.4 Several Types of Discretization
293(4)
14.3.3 Numerical Applications: Differential Quadrature
297(13)
14.4 Generalized Integral Quadrature
310(14)
14.4.1 Generalized Taylor-Based Integral Quadrature
312(2)
14.4.2 Classic Integral Quadrature Methods
314(1)
14.4.2.1 Trapezoidal Rule with Uniform Discretization
314(1)
14.4.2.2 Simpson's Method (One-third Rule) with Uniform Discretization
314(1)
14.4.2.3 Chebyshev-Gauss Method (Chebyshev of the First Kind)
314(1)
14.4.2.4 Chebyshev-Gauss Method (Chebyshev of the Second Kind)
314(1)
14.4.2.5 Chebyshev-Gauss Method (Chebyshev of the Third Kind)
315(1)
14.4.2.6 Chebyshev-Gauss Method (Chebyshev of the Fourth Kind)
315(1)
14.4.2.7 Chebyshev-Gauss-Radau Method (Chebyshev of the First Kind)
315(1)
14.4.2.8 Chebyshev-Gauss-Lobatto Method (Chebyshev of the First Kind)
315(1)
14.4.2.9 Gauss-Legendre or Legendre-Gauss Method
315(1)
14.4.2.10 Gauss-Legendre-Radau or Legendre-Gauss-Radau Method
315(1)
14.4.2.11 Gauss-Legendre-Lobatto or Legendre-Gauss-Lobatto Method
316(1)
14.4.3 Numerical Applications: Integral Quadrature
316(4)
14.4.4 Numerical Applications: Taylor-Based Integral Quadrature
320(4)
14.5 General View: The Two-Dimensional Case
324(16)
References
340(3)
15 Brain Activity Reconstruction by Finding a Source Parameter in an Inverse Problem
343(26)
Amir H. Hadian-Rasanan
Jamal Amani Rad
15.1 Introduction
343(3)
15.1.1 Statement of the Problem
344(1)
15.1.2 Brief Review of Other Methods Existing in the Literature
345(1)
15.2 Methodology
346(7)
15.2.1 Weighted Residual Methods and Collocation Algorithm
346(3)
15.2.2 Function Approximation Using Chebyshev Polynomials
349(4)
15.3 Implementation
353(1)
15.4 Numerical Results and Discussion
354(11)
15.4.1 Test Problem 1
355(2)
15.4.2 Test Problem 2
357(1)
15.4.3 Test Problem 3
358(1)
15.4.4 Test Problem 4
359(3)
15.4.5 Test Problem 5
362(3)
15.5 Conclusion
365(1)
References
365(4)
16 Optimal Resource Allocation in Controlling Infectious Diseases
369(22)
A.C. Mahasinghe
S.S.N. Perera
K.K.W.H. Erandi
16.1 Introduction
369(1)
16.2 Mobility-Based Resource Distribution
370(6)
16.2.1 Distribution of National Resources
370(1)
16.2.2 Transmission Dynamics
371(1)
16.2.2.1 Compartment Models
371(1)
16.2.2.2 SI Model
371(1)
16.2.2.3 Exact Solution
371(1)
16.2.2.4 Transmission Rate and Potential
372(1)
16.2.3 Nonlinear Problem Formulation
373(1)
16.2.3.1 Piecewise Linear Reformulation
374(1)
16.2.3.2 Computational Experience
374(2)
16.3 Connection-Strength Minimization
376(3)
16.3.1 Network Model
376(1)
16.3.1.1 Disease Transmission Potential
376(1)
16.3.1.2 An Example
376(1)
16.3.2 Nonlinear Problem Formulation
377(1)
16.3.2.1 Connection Strength Measure
377(1)
16.3.2.2 Piecewise Linear Approximation
378(1)
16.3.2.3 Computational Experience
379(1)
16.4 Risk Minimization
379(7)
16.4.1 Novel Strategies for Individuals
379(1)
16.4.1.1 Epidemiological Isolation
380(1)
16.4.1.2 Identifying Objectives
380(1)
16.4.2 Minimizing the High-Risk Population
381(1)
16.4.2.1 An Example
381(1)
16.4.2.2 Model Formulation
382(1)
16.4.2.3 Linear Integer Program
383(1)
16.4.2.4 Computational Experience
383(1)
16.4.3 Minimizing the Total Risk
384(1)
16.4.4 Goal Programming Approach
384(2)
16.5 Conclusion
386(1)
References
387(4)
17 Artificial Intelligence and Autonomous Car
391(22)
Merve Antiirk
Sirma Yavuz
Tofigh Allahviranloo
17.1 Introduction
391(1)
17.2 What Is Artificial Intelligence?
391(1)
17.3 Natural Language Processing
391(2)
17.4 Robotics
393(2)
17.4.1 Classification by Axes
393(1)
17.4.1.1 Axis Concept in Robot Manipulators
393(1)
17.4.2 Classification of Robots by Coordinate Systems
394(1)
17.4.3 Other Robotic Classifications
394(1)
17.5 Image Processing
395(2)
17.5.1 Artificial Intelligence in Image Processing
395(1)
17.5.2 Image Processing Techniques
395(1)
17.5.2.1 Image Preprocessing and Enhancement
396(1)
17.5.2.2 Image Segmentation
396(1)
17.5.2.3 Feature Extraction
396(1)
17.5.2.4 Image Classification
396(1)
17.5.3 Artificial Intelligence Support in Digital Image Processing
397(1)
17.5.3.1 Creating a Cancer Treatment Plan
397(1)
17.5.3.2 Skin Cancer Diagnosis
397(1)
17.6 Problem Solving
397(2)
17.6.1 Problem-solving Process
397(2)
17.7 Optimization
399(1)
17.7.1 Optimization Techniques in Artificial Intelligence
399(1)
17.8 Autonomous Systems
400(10)
17.8.1 History of Autonomous System
400(1)
17.8.2 What Is an Autonomous Car?
401(1)
17.8.3 Literature of Autonomous Car
402(3)
17.8.4 How Does an Autonomous Car Work?
405(1)
17.8.5 Concept of Self-driving Car
406(1)
17.8.5.1 Image Classification
407(1)
17.8.5.2 Object Tracking
407(1)
17.8.5.3 Lane Detection
408(1)
17.8.5.4 Introduction to Deep Learning
408(1)
17.8.6 Evaluation
409(1)
17.9 Conclusion
410(1)
References
410(3)
18 Different Techniques to Solve Monotone Inclusion Problems
413(20)
Tanmoy Som
Pankaj Gautam
Avinash Dixit
D. R. Sahu
18.1 Introduction
413(2)
18.2 Preliminaries 4J4
18.3 Proximal Point Algorithm
415(1)
18.4 Splitting Algorithms
415(3)
18.4.1 Douglas-Rachford Splitting Algorithm
416(1)
18.4.2 Forward-Backward Algorithm
416(2)
18.5 Inertial Methods
418(11)
18.5.1 Inertial Proximal Point Algorithm
419(2)
18.5.2 Splitting Inertial Proximal Point Algorithm
421(1)
18.5.3 Inertial Douglas-Rachford Splitting Algorithm
421(1)
18.5.4 Pock and Lorenz's Variable Metric Forward-Backward Algorithm
422(6)
18.5.5 Numerical Example
428(1)
18.6 Numerical Experiments
429(1)
References
430(3)
Index 433
PROFESSOR SNEHASHISH CHAKRAVERTY, is working in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha, India as a Senior (Higher Administrative Grade) Professor. Prior to this he was with CSIR-Central Building Research Institute, Roorkee, India. Prof. Chakraverty received his Ph. D. from University of Roorkee (now IIT Roorkee). There after he did his post-doctoral research at Institute of Sound and Vibration Research (ISVR), University of Southampton, U.K. and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He has authored/co-authored 20 books, published 356 research papers in journals and conferences. Prof. Chakraverty is the Chief Editor of "International Journal of Fuzzy Computation and Modelling" (IJFCM), Inderscience Publisher, Switzerland (http://www.inderscience.com/ijfcm) and Associate Editor of "Computational Methods in Structural Engineering, Frontiers in Built Environment". He has been the President of the Section of Mathematical sciences (including Statistics) of "Indian Science Congress" (2015-2016) and was the Vice President – "Orissa Mathematical Society" (2011-2013). Prof. Chakraverty is recipient of prestigious awards viz. Indian National Science Academy (INSA) nomination under International Collaboration/Bilateral Exchange Program, Platinum Jubilee ISCA Lecture Award (2014), CSIR Young Scientist (1997), BOYSCAST (DST), UCOST Young Scientist (2007, 2008), Golden Jubilee Director's (CBRI) Award (2001), Roorkee University Gold Medals (1987, 1988) etc. His present research area includes Differential Equations (Ordinary, Partial and Fractional), Numerical Analysis and Computational Methods, Structural Dynamics (FGM, Nano) and Fluid Dynamics, Mathematical Modeling and Uncertainty Modeling, Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy, Interval and Affine Computations).
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