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Stochastics, Control and Robotics

Stochastics, Control and Robotics

Harish Parthasarathy

Taylor Francis Ltd
2021
sidottu
This book discusses various problems in stochastic Processes, Control Theory, Electromagnetics, Classical and Quantum Field Theory & Quantum Stochastics. The problems are chosen to motivate the interested reader to learn more about these subjects from other standard sources. Stochastic Process theory is applied to the study of differential equations of mechanics subject to external noise. Some issues in general relativity like Geodesic motion, field theory in curved space time etc. are discussed via isolated problems. The more recent quantum stochastic process theory as formulated by R.L. Hudson and K. R. Parathasarathy is discussed. This provides a non commutative operator theoretic version of stochastic process theory. V.P. Belavkin's approach to quantum filtering based on non demolition measurements and Hudson Parathasarathy calculus has been discussed in detail. Quantum versions of the simple exclusion model in Markov process theory have been included. 3D Robots carring a current density interacting with an external Klein- Gordon or Electromagnetic field has been given some attention. The readers will after going through this book, be ready to carry out independent research in classical and quantum field theory and stochastic processes as applied to practical problems. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.
Quantum Mechanics

Quantum Mechanics

Harish Parthasarathy

Taylor Francis Ltd
2021
sidottu
This book covers the entire span of quantum mechanics whose developments have taken place during the early part of the twentieth century up till the present day. We start with the Rutherford-Bohr model of the atom followed by Schrodinger's wave mechanics with its application to the solution of calculating the energy spectrum of a particle in a box, the harmonic oscillator and finally the hydrogen atom. Heisenberg's matrix mechanics and its duality with Schrodinger's wave mechanics, quantum mechanics in the interaction picture. Dirac's relativistic theory of the electron exhibiting the spin of the electron as a relativistic effect when it interacts with an external electromagnetic field. Feynman's path integral approach to non-relativistic quantum mechanics with is a marvellous intuitive interpretation as a sum over paths and how classical mechanics is obtained from its limit as Planck' constant tends to zero, methods for computing the spectra of the Dirac Hamiltonian in a radial potential, quantum field theory as developed by Feynman, Schwinger, Tomonaga and Dyson for describing the interaction between electrons, positrons, and photons via propagators using both the operator theoretic expansions and Feynman's path integral. We also introduce time independent and time dependent perturbation theory in quantum mechanics with applications to quantum gate design for quantum computers forming a major part of the research conducted by the author's research group, Quantum noise introduced into the Schrodinger and Dirac's equation based on the Hudson-Parthasarathy quantum stochastic calculus in Boson Fock space, scattering theory and wave operators with applications to quantum gate design, some aspects of second quantization like the interpretation of Boson Fock space in terms of harmonic oscillator algebras and the BCS theory of superconductivity, Wigner-Mackey-Frobenius theory of induced representations of a group with applications to Wigner's theory of particle classification, Dirac's equation in a gravitational field and Yang-Mills non-Abelian gauge theories with application to the construction of unified quantum field theories and finally, the more recent theory of super-symmetry which is a Boson-Fermion unification theory. We have discussed the statistics of Boson's, Fermions and Maxwell-Boltzmann based on entropy maximization. The book is written in problem-solution format and it would be of use to physicists and engineers interested respectively in developing unified field theories and in the design of quantum gates.Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.
Technological Innovations for Effective Pandemic Response
This reference text discusses the potential of efficient R&D management during times of pandemic crisis and how it can provide time-bound real-life deliverables to ward-off the contamination-linked vulnerability aspects of social interaction.It discusses important topics including mechanical ventilator with oxygen enrichment, hospital waste management facility, hospital care assistive robotic devices, implementation of smart manufacturing, special purpose machines, micro machining, 3D printing, disposal of plastic waste utilizing high temperature plasma, automatic biomass briquetting plant, and fully automatic biodiesel plant.Features: Discusses novel technological innovations developed especially to effectively counter pandemics such as COVID 19. Explores how R&D modelling of technology can be interspersed with socio-economic values. Covers how innovative technological solutions can be developed as per the situational requisites and deployed in the least possible time to make maximum impact. Discusses industrial manufacturing and automation techniques. The text will be useful for graduate students, and academic researchers working in diverse areas such as mechanical engineering, industrial engineering, production engineering, manufacturing science, and automobile engineering. It covers influences of Pandemics on water and sanitation services, floating capsule-based biofilm reactor (FCBBR) methodology, and innovative segregation of waste through a mechanized model.
Technological Innovations for Effective Pandemic Response
This reference text discusses the potential of efficient R&D management during times of pandemic crisis and how it can provide time-bound real-life deliverables to ward-off the contamination-linked vulnerability aspects of social interaction.It discusses important topics including mechanical ventilator with oxygen enrichment, hospital waste management facility, hospital care assistive robotic devices, implementation of smart manufacturing, special purpose machines, micro machining, 3D printing, disposal of plastic waste utilizing high temperature plasma, automatic biomass briquetting plant, and fully automatic biodiesel plant.Features: Discusses novel technological innovations developed especially to effectively counter pandemics such as COVID 19. Explores how R&D modelling of technology can be interspersed with socio-economic values. Covers how innovative technological solutions can be developed as per the situational requisites and deployed in the least possible time to make maximum impact. Discusses industrial manufacturing and automation techniques. The text will be useful for graduate students, and academic researchers working in diverse areas such as mechanical engineering, industrial engineering, production engineering, manufacturing science, and automobile engineering. It covers influences of Pandemics on water and sanitation services, floating capsule-based biofilm reactor (FCBBR) methodology, and innovative segregation of waste through a mechanized model.
Supersymmetry and Superstring Theory with Engineering Applications
This book introduces the vast subject of supersymmetry along with many specific examples of engineering applications, for example:The design of quantum unitary gates using supersymmetric actionsBosonic and Fermionic noise in quantum systems using the Hudson-Parthasarathy quantum stochastic calculusSuperstring theory applied to the quantum mechanics of neurons and supersymmetric quantum filtering theory which can, for example, be used to filter out the noise in a cavity resonator electromagnetic field produced by the presence electrons and positrons in a bath surrounding itSimplified versions of super-Yang-Mills theory with gauge and gaugino fields, both transforming under the adjoint representation of the gauge group and elementary super-gravity models have also been introducedAll through the book, emphasis is laid upon exploiting the supersymmetry existing in the nature of Boson-Fermion exchange in designing engineering systems like quantum computers and analyzing the performance of systems in the presence of supersymmetric quantum noise.
Supersymmetry and Superstring Theory with Engineering Applications
This book introduces the vast subject of supersymmetry along with many specific examples of engineering applications, for example:The design of quantum unitary gates using supersymmetric actionsBosonic and Fermionic noise in quantum systems using the Hudson-Parthasarathy quantum stochastic calculusSuperstring theory applied to the quantum mechanics of neurons and supersymmetric quantum filtering theory which can, for example, be used to filter out the noise in a cavity resonator electromagnetic field produced by the presence electrons and positrons in a bath surrounding itSimplified versions of super-Yang-Mills theory with gauge and gaugino fields, both transforming under the adjoint representation of the gauge group and elementary super-gravity models have also been introducedAll through the book, emphasis is laid upon exploiting the supersymmetry existing in the nature of Boson-Fermion exchange in designing engineering systems like quantum computers and analyzing the performance of systems in the presence of supersymmetric quantum noise.
Select Topics in Signal Analysis

Select Topics in Signal Analysis

Harish Parthasarathy

TAYLOR FRANCIS LTD
2022
sidottu
This book developed from a course given by the author to undergraduate and postgraduate students. It takes up Matrix Theory, Antenna Theory, and Probability Theory in detail.The first chapter on matrix theory discusses in reasonable depth the theory of Lie Algebras leading upto Cartan’s Classification Theory. It also discusses some basic elements of Functional Analysis and Operator Theory in infinite dimensional Banach and Hilbert spaces. The second chapter discusses Basic Probability Theory and the topics discussed find applications to Stochastic Filtering Theory for differential equations driven by white Gaussian noise. The third chapter is on Antenna Theory with a focus on Modern Quantum Antenna Theory.The book will be a valuable resource to students and early career researchers in the field of Mathametical Physics.
Select Topics in Signal Analysis

Select Topics in Signal Analysis

Harish Parthasarathy

TAYLOR FRANCIS LTD
2024
nidottu
This book developed from a course given by the author to undergraduate and postgraduate students. It takes up Matrix Theory, Antenna Theory, and Probability Theory in detail.The first chapter on matrix theory discusses in reasonable depth the theory of Lie Algebras leading upto Cartan’s Classification Theory. It also discusses some basic elements of Functional Analysis and Operator Theory in infinite dimensional Banach and Hilbert spaces. The second chapter discusses Basic Probability Theory and the topics discussed find applications to Stochastic Filtering Theory for differential equations driven by white Gaussian noise. The third chapter is on Antenna Theory with a focus on Modern Quantum Antenna Theory.The book will be a valuable resource to students and early career researchers in the field of Mathametical Physics.
Electromagnetics, Control and Robotics

Electromagnetics, Control and Robotics

Harish Parthasarathy

TAYLOR FRANCIS LTD
2022
sidottu
This book covers a variety of problems, and offers solutions to some, in:Statistical state and parameter estimation in nonlinear stochastic dynamical system in both the classical and quantum scenariosPropagation of electromagnetic waves in a plasma as described by the Boltzmann Kinetic Transport EquationClassical and Quantum General RelativityIt will be of use to Engineering undergraduate students interested in analysing the motion of robots subject to random perturbation, and also to research scientists working in Quantum Filtering.
Advanced Probability and Statistics

Advanced Probability and Statistics

Harish Parthasarathy

TAYLOR FRANCIS LTD
2022
sidottu
This book surveys some of the important research work carried out by Indian scientists in the field of pure and applied probability, quantum probability, quantum scattering theory, group representation theory and general relativity. It reviews the axiomatic foundations of probability theory by A.N. Kolmogorov and how the Indian school of probabilists and statisticians used this theory effectively to study a host of applied probability and statistics problems like parameter estimation, convergence of a sequence of probability distributions, and martingale characterization of diffusions.It will be an important resource to students and researchers of Physics and Engineering, especially those working with Advanced Probability and Statistics.
Advanced Classical and Quantum Probability Theory with Quantum Field Theory Applications
This book is based on three undergraduate and postgraduate courses taught by the author on Matrix theory, Probability theory and Antenna theory over the past several years.It discusses Matrix theory, Probability theory and Antenna theory with solved problems. It will be useful to undergraduate and postgraduate students of Electronics and Communications Engineering.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).
Advanced Classical and Quantum Probability Theory with Quantum Field Theory Applications
This book is based on three undergraduate and postgraduate courses taught by the author on Matrix theory, Probability theory and Antenna theory over the past several years.It discusses Matrix theory, Probability theory and Antenna theory with solved problems. It will be useful to undergraduate and postgraduate students of Electronics and Communications Engineering.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).
Advanced Probability and Statistics

Advanced Probability and Statistics

Harish Parthasarathy

TAYLOR FRANCIS LTD
2022
sidottu
The chapters in this book deal with:Basic formulation of waveguide cavity resonator equations especially when the cross sections of the guides and resonators have arbitrary shapes. The focus is on expressing the total field energy within such a cavity resonator as a quadratic form in the complex coefficients that determine the modal expansions of the electromagnetic fieldThe reviews of basic statistical signal processing covering linear models, fast algorithms for estimating the parameters in such linear models, applications of group representation theory to image processing problems especially the representations of the permutation groups and induced representation theory applied to image processing problems involving the three dimensional Euclidean motion groupThe Hartree-Fock equations for approximately solving the two electron atomic problem taking spin-orbit magnetic field interactions into account has been discussed. In the limit as the lattice tends to a continuum, the convergence of the stochastic differential equations governing interacting particles on the lattice to a hydrodynamic scaling limitIt will be useful to undergraduate and postgraduate students with courses on transmission lines and waveguides, and statistical signal processing.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).
Advanced Probability and Statistics

Advanced Probability and Statistics

Harish Parthasarathy

TAYLOR FRANCIS LTD
2024
nidottu
The chapters in this book deal with:Basic formulation of waveguide cavity resonator equations especially when the cross sections of the guides and resonators have arbitrary shapes. The focus is on expressing the total field energy within such a cavity resonator as a quadratic form in the complex coefficients that determine the modal expansions of the electromagnetic fieldThe reviews of basic statistical signal processing covering linear models, fast algorithms for estimating the parameters in such linear models, applications of group representation theory to image processing problems especially the representations of the permutation groups and induced representation theory applied to image processing problems involving the three dimensional Euclidean motion groupThe Hartree-Fock equations for approximately solving the two electron atomic problem taking spin-orbit magnetic field interactions into account has been discussed. In the limit as the lattice tends to a continuum, the convergence of the stochastic differential equations governing interacting particles on the lattice to a hydrodynamic scaling limitIt will be useful to undergraduate and postgraduate students with courses on transmission lines and waveguides, and statistical signal processing.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).
Classical and Quantum Information Theory for the Physicist

Classical and Quantum Information Theory for the Physicist

Harish Parthasarathy

TAYLOR FRANCIS LTD
2022
sidottu
This book deals with certain important problems in Classical and Quantum Information Theory Quantum Information Theory, A Selection of Matrix Inequalities Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings Wigner-distributions in Quantum Mechanics Quantization of Classical Field Theories Statistical Signal Processing Quantum Field Theory, Quantum Statistics, Gravity, Stochastic Fields and Information Problems in Information TheoryIt will be very helpful for students of Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).
Classical and Quantum Information Theory for the Physicist

Classical and Quantum Information Theory for the Physicist

Harish Parthasarathy

TAYLOR FRANCIS LTD
2024
nidottu
This book deals with certain important problems in Classical and Quantum Information Theory Quantum Information Theory, A Selection of Matrix Inequalities Stochastic Filtering Theory Applied to Electromagnetic Fields and Strings Wigner-distributions in Quantum Mechanics Quantization of Classical Field Theories Statistical Signal Processing Quantum Field Theory, Quantum Statistics, Gravity, Stochastic Fields and Information Problems in Information TheoryIt will be very helpful for students of Undergraduate and Postgraduate Courses in Electronics, Communication and Signal Processing.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).
Stochastic Processes in Classical and Quantum Physics and Engineering
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems, electromagnetics, statistical signal processing, quantum information theory, quantum neural network theory, quantum filtering theory, quantum electrodynamics, quantum general relativity, string theory, problems in biology and classical and quantum fluid dynamics. The selection of the problems has been based on courses taught by the author to undergraduates and postgraduates in Electronics and Communications Engineering.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).
Stochastic Processes in Classical and Quantum Physics and Engineering
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems, electromagnetics, statistical signal processing, quantum information theory, quantum neural network theory, quantum filtering theory, quantum electrodynamics, quantum general relativity, string theory, problems in biology and classical and quantum fluid dynamics. The selection of the problems has been based on courses taught by the author to undergraduates and postgraduates in Electronics and Communications Engineering.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan).
Large Deviations Applied to Classical and Quantum Field Theory
This book deals with a variety of problems in Physics and Engineering where the large deviation principle of probability finds application. Large deviations is a branch of probability theory dealing with approximate computation of the probabilities of rare events. It contains applications of the LDP to pattern recognition problems like analysis of the performance of the EM algorithm for optimal parameter estimation in the presence of weak noise, analysis and control of non-Abelian gauge fields in the presence of noise, and quantum gravity wherein we are concerned with perturbation to the quadratic component of the Einstein-Hilbert Hamiltonian caused by higher order nonlinear terms in the position fields and their effect on the Gibbs statistics and consequently quantum probabilities of events computed using the quantum Gibbs state. The reader will also find in this book applications of LDP to quantum filtering theory as developed by Belavkin based on the celebrated Hudson-Parthasarathy quantum stochastic calculus.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).
Large Deviations Applied to Classical and Quantum Field Theory
This book deals with a variety of problems in Physics and Engineering where the large deviation principle of probability finds application. Large deviations is a branch of probability theory dealing with approximate computation of the probabilities of rare events. It contains applications of the LDP to pattern recognition problems like analysis of the performance of the EM algorithm for optimal parameter estimation in the presence of weak noise, analysis and control of non-Abelian gauge fields in the presence of noise, and quantum gravity wherein we are concerned with perturbation to the quadratic component of the Einstein-Hilbert Hamiltonian caused by higher order nonlinear terms in the position fields and their effect on the Gibbs statistics and consequently quantum probabilities of events computed using the quantum Gibbs state. The reader will also find in this book applications of LDP to quantum filtering theory as developed by Belavkin based on the celebrated Hudson-Parthasarathy quantum stochastic calculus.Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan and Bhutan).