80th Birthday Festschrift in Honor of K. Babu Joseph

Foreword by P. P. Divakaran
Foreword by M. Lakshmanan
Preface
A Tribute to Prof. K. Babu Joseph on His 80th Birthday
Contents
Contributors
Cosmology
A Non-empty Bouncing Milne Model  for the Universe
	1 Introduction
	2 Eternal Coasting Models of the Universe
		2.1 Cosmological Problems
		2.2 Milne\'s Coasting Model
		2.3 Non-empty Eternal Coasting Model
		2.4 Other Coasting Models
	3 Complex Extension of the Milne Model
		3.1 Wheeler–DeWitt Equation
		3.2 Negative Energy Density
	4 Discussion
	References
Cosmic Acceleration and Dark Energy
	1 Introduction
	2 The New Effective Equation of State Parameter
	3 Results
	4 Conclusion
	References
Signature of the Quantum Gravity  on the CMB
	1 Introduction
	2 Inflation and Power Spectra
	3 Tensor Power Spectrum
	4 Effective Theory and Inflation
		4.1 Quantum Gravity Effect on the Chaotic Inflation
	5 Quantum Gravity Effect on the BB Mode Angular Spectrum of CMB
	6 Conclusion
	References
High Energy Physics and Gravitation
Aspects of Schrödinger Picture Formalism
	1 Introduction
	2 Scalar Field Quantization
	3 Basic Formalism
	4 Example of Non-interacting Scalar Field
	5 Example of Φ4 Field
	6 Effective Action for φ6 Model
	7 Static Effective Potential
	8 Renormalization
	9 Conclusions
	References
On Gravity: Remembrance of the Association Between a Guru and His Student/Colleague
	1 Introduction
	2 A Very Brief History of Association Between Prof. Babu Joseph and Prof. Sabir
	3 On Gravity
		3.1 Searching for Quantum Version of Gravity
		3.2 Reformulation of Gravity in Flat Space Using Gauge Field Theory—A Remarkable Contribution by KBJ  and MS
	4 Conclusion
	References
Mathematical Physics
q-Oscillators and a q-deformed Debye Model for Lattice Heat Capacity
	1 Introduction
		1.1 Quantum Groups and non-commutative Spaces
		1.2 q-Deformed Numbers and q-Differential Calculus
		1.3 suq(2) Algebra
		1.4 q-Harmonic Oscillator
	2 q-Oscillator Debye Model for Lattice Heat Capacity
	3 q-Anharmonic Oscillator (q-AO) with quartic Interaction
	4 Conclusion
	References
Quantum Groups, q-Oscillators and q-Deformed Quantum Mechanics
	1 Quantum Groups
		1.1 Introduction
		1.2 Quantum Group as a Key to New Physics
		1.3 Formal Definition of a Quantum Group
		1.4 Lie Algebraic Approach
		1.5 Non-commutative Differential Geometric Approach
	2 Elements of q-Analysis
	3 q-Deformed Oscillators
	4 q-Deformed Quantum Mechanics
		4.1 General Formulation of q-Quantum Mechanics
		4.2 q-Deformation of the Schrödinger Equation
		4.3 Physical Implications of q-Deformation
	5 Conclusion
	References
Mandelbrot Set and Fermat\'s Last Theorem
	1 Mandlebrot Set
	2 Fermat\'s Last Theorem
		2.1 Topological Fields
		2.2 Finite Fields
		2.3 Elliptic Curves
	3 FLT on the Mandelbrot Set
	References
Nonlinear Dynamics
Soliton Propagation Through Photorefractive Media
	1 Introduction
	2 The Soliton and Its History
	3 Optical Solitons
	4 Nonlinear Schrödinger Equation (NLSE) and Optical Solitons
	5 Coupled Nonlinear Schrödinger Equation (CNLSE)
	6 Photorefractive Solitons
	7 Two-Beam Coupling Using Solitons
	8 Conclusion
	References
Neurons and Near-Death Spikes
	1 Introduction
	2 Spatiotemporal Activities of a Pulse-Coupled Biological Neural Network (PCNN)
		2.1 Izhikevich Model of Neuron
		2.2 Entropy of Network
		2.3 Influence of Chaotic Neurons
		2.4 Bursting Synchronization (B)
		2.5 Influence of Inhibitory Neurons
	3 Lévy Noise-Induced Near-Death Spikes and Phase Transitions
		3.1 Bursting Synchronization in the Presence of Noise
		3.2 Behaviour of the Network When Neurons are Chaotic
		3.3 Average Firing Rate (F)
		3.4 Average Firing Rate with the Chaotic Neurons  in the Network
		3.5 Variations of Neuron Firing with α
	4 Conclusion and Discussion
	References
Machine Learning and the Bigdata Paradigm
	1 Introduction
		1.1 Adaptive Transfer Function
		1.2 The Difference Boosting Neural Network
	2 Conclusion
	References
Dynamics of Nonlinear Systems: Integrable and Chaotic Solutions
	1 Introduction
	2 Integrable Systems
		2.1 Perturbed Nonlinear Schrödinger Equation
	3 Propagation of Solitons Through 2D Lattice
		3.1 Deduction of the Nonlinear Equations for Wave Propagation Through 2D Lattice
		3.2 Integrability Studies of KP and mKP Equations
		3.3 Solitary Wave Solutions
	4 Modelling of Nonlinear Waveguide for Optical Soliton Propagation
		4.1 Planar Waveguides
		4.2 Optical Solitons and NLSE
	5 Chaos Theory—An Introduction
		5.1 Lorentz System
	6 Conclusion
	References