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Davidson P: Waves

Waves

An Introduction for Physicists and Engineers

Selected Topics

Quantum Modelling of Economic and Financial Systems

Mathematics and Biomedical Engineering in Medicine, Physiology and Health Sciences is a visionary book, whose purpose is to demonstrate how fundamental mathematics and biomedical engineering can be incorporated into physiology, medicine, and health sciences teaching, research, and clinical practice to make these disciplines more quantitative and computational, and hence more explanatory and informative. The book also provides more quantitative formulation of medical procedures, towards supporting the growing field of precision medicine.

Mathematics and Biomedical Engineering in Medicine, Physiology and Health Sciences

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chemistry, with a particular focus on the most modern and recent problems which are poorly covered in existing, largely outdated book literature.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

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

An Elementary Introduction Emphasizing Applications

Stochastic Calculus

On the Trail of Extraterrestrial Treasures and the Secrets Inside Them

The Meteorite Hunters

For Doctoral Level Physics

A First Graduate Course in Quantum Field Theory

Geomechanics Research

This book provides a basis to interpret acoustic emission (AE) as damage processes in stressed rock, with applications to stress measurements, size effects, source mechanisms, and fracture mechanics. Basic features of an AE monitoring system will be covered, with some background on the sensor, pre-amplifier, and data acquisition. Several examples of AE monitoring will include both lab and field applications ranging from element testing to hydraulic fracturing. Intended for geologists, geophysicists and mining, petroleum and civil engineers dealing with rock stress and rock damage processes.

Rock stress and rock damaging are some of the main obstacles encountered when designing and constructing engineering projects with rock. This book will provide a basis to interpret acoustic emission (AE) as damage processes in stressed rock, with applications to stress measurements, size effects, source mechanisms, and fracture mechanics. The nature of rock will be described as a crystalline solid with voids in the form of small cracks and pores called damage, and AE will be explained as energy released as a result of increase in damage. Basic features of an AE monitoring system will be covered, with some background on the sensor, pre-amplifier, and data acquisition. Waveform analyses will include source locations through a geometric interpretation and a numerical algorithm, which will be available through the authors’ web sites. Fault plane solutions and moment tensor analysis will be presented for a quantitative evaluation of micromechanisms of rock failure under tension and shear. Several examples of AE monitoring will include both lab and field applications ranging from element testing to hydraulic fracturing. Intended for geologists, geophysicists and mining, petroleum and civil engineers dealing with rock stress and rock damage processes.

Microcracking in Rock as Acoustic Emission

This book is the first one that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. They develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.

Neural networks and neural dynamics are powerful approaches for the online solution of mathematical problems arising in many areas of science, engineering, and business. Compared with conventional gradient neural networks that only deal with static problems of constant coefficient matrices and vectors, the authors’ new method called zeroing dynamics solves time-varying problems. Zeroing Dynamics, Gradient Dynamics, and Newton Iterations is the first book that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The book brings together research in the developing fields of neural networks, neural dynamics, computer mathematics, numerical algorithms, time-varying computation and optimization, simulation and modeling, analog and digital hardware, and fractals.The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. Readers will discover how novel theoretical results have been successfully applied to many practical problems. The authors develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.

Zeroing Dynamics, Gradient Dynamics, and Newton Iterations

Astronomy and astrophysics library

This book is based in part on classroom tested lectures related to the first stars (Pop III stars), but also draws from the author's review articles of the main physical principles involved. The book will thus combine pedagogical introductory chapters with more advanced ones to survey the cutting-edge advances from the frontier of research.The formation of Pop III stars and galaxies is one of the great outstanding challenges in modern astrophysics and cosmology. The first stars are likely key drivers for early cosmic evolution and will be at the center of attention over the next decade. The best available space and ground-based telescopes like the Hubble Space Telescope probe the Universe to high redshifts and provide us with tantalizing hints; but they cannot yet directly detect the first generation of stars and the formation of the first galaxies. This is left as key science for future telescopes like the James Webb Space Telescope.The book covers the theory of first star formation, the relation between first stars and dark matter, their impact on cosmology, their observational signatures, the transition to normal star formation as well as the assembly of the first galaxies. It will prepare advanced students and researchers entering the field for interpreting observational findings and their cosmological implications.

This book is based in part on classroom tested lectures related to the first stars (Pop III stars), but also draws from the author's review articles of the main physical principles involved. The book will thus combine pedagogical introductory chapters with more advanced ones to survey the cutting-edge advances from the frontier of research.The formation of Pop III stars and galaxies is one of the great outstanding challenges in modern astrophysics and cosmology. The first stars are likely key drivers for early cosmic evolution and will be at the center of attention over the next decade. The best available space and ground-based telescopes like the Hubble Space Telescope probe the Universe to high redshifts and provide us with tantalizing hints; but they cannot yet directly detect the first generation of stars and the formation of the first galaxies. This is left as key science for future telescopes like the James Webb Space Telescope.The book covers the theoryof first star formation, the relation between first stars and dark matter, their impact on cosmology, their observational signatures, the transition to normal star formation as well as the assembly of the first galaxies. It will prepare advanced students and researchers entering the field for interpreting observational findings and their cosmological implications.

The First Stars

While the field of Deep Learning has been advancing at frightening speeds during the last ten years, we do not have a plausible theoretical explanation of its success yet. One can safely say that Deep Learning works, but nobody really understands why. Nevertheless, starting around five years before now, a decent number of theoretical papers specifically concerning neural nets started to emerge at top machine learning venues. This makes us think that the core of Deep Learning theory has already started to crystallize.The goal of the present book is to present these core concepts of Deep Learning theory to readers so that they could directly dive into recent papers of this area. For this purpose, each chapter elaborates a simple model or a classical result in details first and then discusses possible generalizations and more recent developments of the same idea.We have to warn the reader that the present book is not a mathematical manuscript. Not all results here are stated as formal theorems and not all theorems are provided with complete and rigorous proofs. Many of the theorems of the book are proven up to some technical lemmas, while for some there is only a proof sketch. This conforms with the main idea of the book: present and illustrate concepts rather than reproduce all the results.The book, in its present form, covers the following topics: uniform generalization bounds, PAC-bayesian generalization bounds, double descent phenomena, infinitely-wide networks, implicit bias of gradient descent, loss landscape, gradient descent convergence guarantees, and initialization strategies.

Elements Of Deep Learning Theory

Series in Astronomy and Astrophysics

This book focuses on observing magnetic fields in order to understand their role in star and planet formation. Polarimetry observers will gain a better understanding of all the various techniques, especially those beyond what they themselves use. Theorists will gain an understanding of exactly what one can infer from the observational data, including both the limitations and the power of the different techniques. Readers not actively involved in star formation research will gain a clear understanding of the possible roles played by magnetic fields and the current state of the observational field. The book provides a foundation for future research in this field.

This book focuses on observing magnetic fields in order to understand their role in star and planet formation. Polarimetry observers will gain a better understanding of all the various techniques, especially those beyond what they themselves use. Theorists will gain an understanding of exactly what one can infer from the observational data, including both the limitations and the power of the different techniques. Readers not actively involved in star formation research will gain a clear understanding of the possible roles played by magnetic fields and the current state of the observational field. The book provides a foundation for future research in this field.

Observations and Implications

Magnetic Fields in Regions of Star Formation

Volume II

Cryptocurrency Forensics and Investigation using Open Source Intelligence Techniques (OSINT)

Waves

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