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Number Fields
Number Fields is a textbook for algebraic number theory. It grew out of lecture notes of master courses taught by the author at Radboud University, the Netherlands, over a period of more than four decades. It is self-contained in the sense that it uses only mathematics of a bachelor level, including some Galois theory. Part I of the book contains topics in basic algebraic number theory as they may be presented in a beginning master course on algebraic number theory. It includes the classification of abelian number fields by groups of Dirichlet characters. Class field theory is treated in Part II: the more advanced theory of abelian extensions of number fields in general. Full proofs of its m...
Nanoplasmonics
Nanoplasmonics is a young topic of research, which is part of nanophotonics and nano-optics. Nanoplasmonics concerns to the investigation of electron oscillations in metallic nanostructures and nanoparticles. Surface plasmons have optical properties, which are very interesting. For instance, surface plasmons have the unique capacity to confine light at the nanoscale. Moreover, surface plasmons are very sensitive to the surrounding medium and the properties of the materials on which they propagate. In addition to the above, the surface plasmon resonances can be controlled by adjusting the size, shape, periodicity, and materials' nature. All these optical properties can enable a great number of applications, such as biosensors, optical modulators, photodetectors, and photovoltaic devices. This book is intended for a broad audience and provides an overview of some of the fundamental knowledges and applications of nanoplasmonics.
Progress in Optics
A volume in the Progress in Optics series, the papers in this book cover a range of topics, including: anamorphic beam shaping for laser and diffuse light; ultra-fast all-optical switching in optical networks; generation of dark hollow beams and their application; and two-photon lasers.
Principles of Optics
The 60th anniversary edition of this classic and unrivalled optics reference work includes a special foreword by Sir Peter Knight.
Field-Theoretic Simulations in Soft Matter and Quantum Fluids
This monograph provides an introduction to field-theoretic simulations in classical soft matter and Bose quantum fluids. The method represents a new class of molecular computer simulation in which continuous fields, rather than particle coordinates, are sampled and evolved. Field-theoretic simulations are capable of analysing the properties of systems that are challenging for traditional simulation techniques, including dense phases of high molecular weight polymers, self-assembling fluids, and quantum fluids at finite temperature. The monograph details analytical methods for converting classical and quantum many-body problems to equilibrium field theory models with a molecular basis. Numerical methods are described that enable efficient, accurate, and scalable simulations of such models on modern computer hardware, including graphics processing units (GPUs). Extensions to non-equilibrium systems are discussed, along with an introduction to advanced field-theoretic simulation techniques including free energy estimation, alternative ensembles, coarse-graining, and variable cell methods.
Mathematical Physiology
Divided into two volumes, the book begins with a pedagogical presentation of some of the basic theory, with chapters on biochemical reactions, diffusion, excitability, wave propagation and cellular homeostasis. The second, more extensive part discusses particular physiological systems, with chapters on calcium dynamics, bursting oscillations and secretion, cardiac cells, muscles, intercellular communication, the circulatory system, the immune system, wound healing, the respiratory system, the visual system, hormone physiology, renal physiology, digestion, the visual system and hearing. New chapters on Calcium Dynamics, Neuroendocrine Cells and Regulation of Cell Function have been included. ...
Mathematical Foundations of Imaging, Tomography and Wavefield Inversion
Inverse problems are of interest and importance across many branches of physics, mathematics, engineering and medical imaging. In this text, the foundations of imaging and wavefield inversion are presented in a clear and systematic way. The necessary theory is gradually developed throughout the book, progressing from simple wave equation based models to vector wave models. By combining theory with numerous MATLAB based examples, the author promotes a complete understanding of the material and establishes a basis for real world applications. Key topics of discussion include the derivation of solutions to the inhomogeneous and homogeneous Helmholtz equations using Green function techniques; the propagation and scattering of waves in homogeneous and inhomogeneous backgrounds; and the concept of field time reversal. Bridging the gap between mathematics and physics, this multidisciplinary book will appeal to graduate students and researchers alike. Additional resources including MATLAB codes and solutions are available online at www.cambridge.org/9780521119740.
Phase Conjugation in a Layer of Nonlinear Material
Optical phase conjugation, or time reversal, of an optical wave front is an important technique to correct distortions in electromagnetic waves which are built up during propagation through a medium. The authors have studied theoretically optical phase conjugation through four-wave mixing in a slab of non-linear material. When two strong counter-propagating laser beams irradiate a non-linear crystal, the third-order susceptibility is activated, and can couple to an external weak probe field. A four-wave mixing process then generates a phase-conjugated or time-reversed replica of this incident probe field. They investigated the mechanism of the production of phase-conjugated radiation in such...
Framework for Analysis and Identification of Nonlinear Distributed Parameter Systems using Bayesian Uncertainty Quantification based on Generalized Polynomial Chaos
In this work, the Uncertainty Quantification (UQ) approaches combined systematically to analyze and identify systems. The generalized Polynomial Chaos (gPC) expansion is applied to reduce the computational effort. The framework using gPC based on Bayesian UQ proposed in this work is capable of analyzing the system systematically and reducing the disagreement between the model predictions and the measurements of the real processes to fulfill user defined performance criteria.
Algebra
This graduate-level text is intended for initial courses in algebra that begin with first principles but proceed at a faster pace than undergraduate-level courses. It employs presentations and proofs that are accessible to students, and it provides numerous concrete examples. Exercises appear throughout the text, clarifying concepts as they arise; additional exercises, varying widely in difficulty, are included at the ends of the chapters. Subjects include groups, rings, fields and Galois theory, modules, and structure of rings and algebras. Further topics encompass infinite Abelian groups, transcendental field extensions, representations and characters of finite groups, Galois groups, and additional areas. Based on many years of classroom experience, this self-contained treatment breathes new life into abstract concepts.
