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Dwivedi R: Gauss Hypergeometric Function

Gauss Hypergeometric Function

Special Matrix Functions, q-Special Functions

This textbook is relevant to BSc/MSc students interested in mathematical modeling and simulation. It brings together analysis, calculus and numerical methods presented in a single coherent volume. Particular attention is given to engineering mathematics, addressing modeling, analysis, method development, implementation and testing of algorithms, as well as application to actual problems and critical interpretation of the results. The book can be used throughout bachelor programs and parts of masters programs, presenting a comprehensive suite of courses that link formal abstract thinking on the one hand to intuitive model formulation, critical algorithm development and interpretation of results on the other hand. The books contains numerous examples of practical applications from physics, technology, biology and chemistry. It also contains an introduction to Matlab and C for algorithm development and computational analysis.&nbsp;Software and solutions to selected problems are included.

Mathematical Modeling and Simulation

This will be the 7th book in the author's 'Lectures on ...' book series, and the first aimed at graduate-level readers(two additional graduate texts are in preparation). Primarily intended for physics graduate students, the book is accessible to advanced undergraduates and will appeal to students with a background in statistics and a keen interest in quantum physics. By the end of this book, readers will be well-prepared for working on research projects that require the drawing of inference from the noisy data collected in quantum experiments, as epitomized by quantum state estimation.The book begins with chapters on the basics of estimation theory and the basics of quantum theory. This includes, in particular, the roles played by the frequentist methods of statistics, which are crucial when planning an experiment, and the Bayesian methods, which are the tools for drawing inference from the actual data gathered. A central concept is that of optimal error regions that supplement the point estimators ('best guesses') with the analogs of error bars in the high-dimensional parameter space; there is, in particular, the plausible region which comprises all point estimators supported by the data.Practical applications require the evaluation of high-dimensional integrals with the aid of Monte Carlo integration. For that, one needs to draw samples of quantum states from the relevant distributions, namely the priors and posteriors of Bayesian methodology. The book discusses the algorithms well-suited for this kind of sampling, which is central to the processing of real-life data.The book illustrates all concepts with pertinent examples and offers numerous exerciseswhich the readers can practice and perfect their skills with. The presentation is detailed and does not skip technical steps, which makes the book particularly valuable for self-studying readers and as textbook adopted by lecturers teaching courses on this or related topics. While the book is based on lecture notes developed for the author's courses on quantum state estimation at NUS and BIT, this book also offers a comprehensive account of the concepts and methods developed in the author's group at CQT and presents this material in textbook form for the first time.

Lectures On Quantum State Estimation

IEEE Press Series on Power and Energy Systems

Everything we know about the power system, whether for control, or planning, or billing, is the result of a measurement, so the measurements ought to be good. The authors of Measuring the Grid: Mysteries Explained pull no punches in showing how bad today's measurements are, and how to make them better. Misunderstandings about important power system quantities, especially reactive power, apparent power, and phasors, are pervasive. The first four chapters provide foundational information about measurement generally not taught to power engineers. Although power engineers expect their measurements to be "scientific", these chapters explain why some of the most critical power system measurements are distinctly non-scientific and not fit for purpose. In the next four chapters, the most important and most misunderstood measurements are scrutinized more closely. Particular attention is paid to reactive power and to the phasor measurement unit. Although the book discusses serious issues, a little light humor makes for easy reading. Additional topics discussed include: <ul> <li>Two fundamentally different kinds of measurement exist; most of the measurements in the power system are of the non-scientific variety</li> <li>Power theories, such as those of Budeanu and Fryze, are shown to be inevitably wrong; measurement theory resolves the mysteries</li> <li>The number of degrees of freedom of a system is an incisive tool for resolving key questions about the nature of measurements</li> <li>Opportunities for further research</li> <li>An introduction to the important topic of measurement uncertainty</li> </ul> Measuring the Grid: Mysteries Explained fills a significant knowledge gap for all students in programs of study related to power systems. It is also valuable for practicing engineers working in the manufacturing and utility industries.

Mysteries Explained

Measuring the Electric Grid

With Satellite Connectivity and Artificial Intelligence

5G LTE Narrowband Internet of Things

Handbook of Electronic Structure Theory provides a much-needed learning resource that collects and demonstrates the various key methods involved in electronic structure theory, the feasibility and reliability of electronic structure calculations and their applications using computational chemistry, with a particular focus on the most modern and recent problems which are poorly covered in existing, largely outdated book literature. This handbook is designed with early career researcher learning in mind by aiming to provide a careful, structured, coherent, measured, and incremental presentation of the subject matter as well as appropriate problems and worked tutorial examples. Elements like summary boxes, worked examples, and downloadable data sets make this a holistic guide to the topic for learners from different backgrounds who require a deeper understanding of electronic structure theory. Part I one of the book focuses on the critical core theories, before Part II moves on to some of the most important recent developments and their potential future directions, including key topics such as the electronic excited states and the harnessing of machine learning. Finally, Part III then collects a range of key case study examples of applications such as for biomolecules, in spectroscopy, or for use in catalysis amongst others. Handbook of Electronic Structure Theory is written primarily for masters, PhD, and postdoctoral students in theoretical and computational chemistry as well as experimental researchers wishing to apply quantum chemical methods in a critical way. The book will also have significant relevance to those studying and teaching in the adjacent fields of computational physics, materials science, and astrochemistry, who are making use of electronic structure methods. It is also likely to be of interest to chemists working on designing new materials and compounds targeting industrial and environmental applications such as catalysis, energy harvesting or green chemistry.

Methods and Applications

Handbook of Electronic Structure Theory

If there were no Coulomb interaction among electrons, it would be relatively straightforward to solve the many-electron Schrödinger equation. It is, however, precisely this interaction that is at the heart of numerous fascinating phenomena in condensed matter physics such as superconductivity, Kondo physics, magnetism, etc. Due to the large number of electrons in a material being of the order of Avogadro's number, it is at present - and perhaps in the foreseeable future - not feasible or even desirable to solve the Schrödinger equation to obtain the many-electron wavefunction. Fortunately, a large number of important physical properties can be calculated without explicit knowledge of the wavefunction.

Two of the most important formalisms for dealing with the many-electron problem which avoid a direct use of the many-electron wavefunction are the Green function and the density functional theory. Within the Kohn-Sham scheme the latter is used to calculate ground-state properties whereas the former for excitation spectra. The book presents the fundamentals of these two theories in detail with essential many-body tools, such as the occupation number representation and Grassmann algebra developed from scratch. Prior knowledge of many-body theory is not a prerequisite so that it is readable for final-year undergraduates and graduate students in physics and chemistry as well as researchers in the field of electronic structure and many-body theory. The book includes in the last chapter an exposition of a density-functional path for determining the Green function, a new formalism recently proposed by the author. The book should be a valuable companion for those embarking in the field of many-electron physics.

Elements Of Green Function And Density Functional Theory

Intended for graduate and advanced undergraduate students, this textbook is a thoroughly modern introduction to and a self-contained treatise on the theoretical and mathematical fundamentals of General Relativity. The chapters are organized into three parts, with the first covering Maxwell's theory of electromagnetism, the relativistic Kepler problem, and the systematics of the underlying geometry, with the more abstract notion of the fibre bundle relegated to the Appendix. The second part begins with a derivation of the Einstein equations and leads to topics such as cosmology, black holes, causal structures, and action principles. The third part covers the canonical formulation of field theory in general and General Relativity in particular, leading to the concept of the total energy in General Relativity and quantum phenomena with event horizons. The book minimizes historical references, focuses on modern tools, examples, and applications, and emphasizes the commonalities between relativistic gravity and gauge theory.

Gravitation for Theorists

Dynamics and Astrophysics of Galaxies

The Navier-Stokes equations - modeling the motion of viscous, incompressible Newtonian fluids - have been capturing the attention of an increasing number of mathematicians over the years and has now become one of the most intensely studied subjects in applied analysis. This project is dedicated to a complete and updated mathematical analysis of fundamental topics related to these equations. Every subject will be analyzed using different approaches. The main ideas behind them as well as their differences will also be emphasized and discussed. The book aims at being self-contained, however, it will also be supported by a vast bibliography for further reading.

Gauss Hypergeometric Function

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