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Michael F Shlesinger: Why Not Nonlinear
Algebra: Math, Science, Applications And

Why Not Nonlinear Algebra: Math, Science, Applications And Funding

De Gruyter Studies in Mathematics

Orthogonal Polynomials

This book covers a broad range of questions related to the importance of cell geometry in many areas, including nuclear positioning, chromosome dynamics, cytoskeletal remodeling, tissue patterning, cell-matrix and multicellular contacts. It also addresses medical implications, from its implication in the development of tumors to its role in fibrosis. Together, the chapters in this book will highlight current knowledge and modern approaches to investigating the biophysical design principles underlying key biological functions, with the overall goal of elucidating the connections between cell geometry and nuclear mechanics.

This book covers a broad range of questions related to the importance of cell geometry in many areas, including nuclear positioning, chromosome dynamics, cytoskeletal remodeling, tissue patterning, cell-matrix and multicellular contacts. It also addresses medical implications, from its implication in the development of tumors to its role in fibrosis. Together, the chapters in this book will highlight current knowledge and modern approaches to investigating the biophysical design principles underlying key biological functions, with the overall goal of elucidating the connections between cell geometry and nuclear mechanics.

Cell Geometry

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.

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

Progress In Data Science

Ubiquitous Laplacian: An Introduction To Numerical Pdes With Applications In Data Science

Quantitative Biology

Quantum Communication and Cryptography introduces readers to the theory of quantum cryptography, with a focus will on quantum key distribution (QKD) and more advanced quantum cryptographic protocols beyond QKD. It contains a brief introduction to the field of modern cryptography that is needed to fully appreciate and understand how quantum cryptographic systems are proven secure, and how they can be safely used in combination with current day classical systems. Readers are then introduced to quantum key distribution (QKD) - perhaps the most celebrated, and currently the most practical, of quantum cryptographic techniques. Basic protocols are described, and security proofs are given, providing readers with the knowledge needed to understand how QKD protocols are proven secure using modern, state- of-the-art definitions of security. Following this, more advanced QKD protocols are discussed, along with alternative quantum and classical methods to improve QKD performance. Finally, alternative quantum cryptographic protocols are covered, along with a discussion on some of the practical considerations of quantum secure communication technology. Throughout, protocols are described in a clear and consistent manner that still provides comprehensive, theoretical proofs and methods.

Quantum Communication and Cryptography

De Gruyter Studies in Mathematical Physics

Mirror symmetry is one of the most exciting ideas in mathematics to emerge in the last two decades. It was introduced in physics as a duality between superconformal field theories. This book discusses this rapidly developing aspect of string theory.

Laurent Polynomials in Mirror Symmetry

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

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

Oxford Graduate Texts

Quasi-adiabatic theory has applications across disciplines, from quantum computing and cosmology to materials science and atomic physics. This textbook provides, for the first time, a comprehensive introduction to quasi-adiabatic effects. In modern physics, the term "adiabatic" refers to the slow evolution limit. Nonadiabatic transitions are well understood also. Conversely, quasi-adiabatic theory pertains to a systematically developed theory revealing numerous time-dependent evolutions in physics that, while slow, are not genuinely adiabatic. It is rich in effects that can be understood even in models with complex many-body interactions. Examples from research in quantum computing, phase transitions, ultra-cold atoms, and quantum control are used throughout to illustrate these effects. Quasi-Adiabatic Effects: Introduction to Geometric Phases and Landau-Zener Transitions is aimed at students at graduate level and beyond, who are interested in quantum and classical mechanics, as well as complex analysis. The book seeks to fill a gap in the literature by providing an accessible introduction to both geometric phases and nonadiabatic transitions at a level sufficient to consider numerous applications. Some of the processes found here are discussed for the first time in a textbook format, including the Dykhne formula (Chapter 8) and multistate Landau-Zener theory (Chapter 11). This unique material makes Quasi-Adiabatic Effects a novel and important addition to the textbook literature of several topics encountered in modern research. Throughout the book, students will find discussions and complex analysis of these processes as well as problems to solve (with solutions also provided). The problems help refresh several elementary techniques which will become progressively useful throughout the chapters.

Introduction to Geometric Phases and Landau-Zener Transitions

Quasi-Adiabatic Effects

Spin Fluids And Defect Dynamics: A Common Aspect Of Spinor Condensates And Polarization Optics

Handbook of MRI Pulse Sequences, Second Edition includes 92 self-contained sections, with each section focusing on a single subject. A new section on detailing the advanced pulse sequence techniques covers a variety of basic and advanced image reconstruction methods. The extensive topic coverage and cross-referencing makes this book ideal for beginners learning the building blocks of MRI pulse sequence design, as well as for experienced professionals who are seeking deeper knowledge of a particular technique. This book is among the most important medical imaging techniques available today. Each of these scanners is capable of running many different "pulse sequences." These sequences are governed by physics and engineering principles and implemented by software programs that control the MRI hardware.

Handbook of MRI Pulse Sequences

Why Not Nonlinear Algebra: Math, Science, Applications And Funding

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