Energy and power are fundamental concepts in electromagnetism and circuit theory, as well as in optics, signal processing, power engineering, electrical machines, and power electronics. However, in crossing the disciplinary borders, we encounter understanding difficulties due to (1) the many possible mathematical representations of the same physical objects, and (2) the many possible physical interpretations of the same mathematical entities. The monograph proposes a quantum and a relativistic approach to electromagnetic power theory that is based on recent advances in physics and mathematics. The book takes a fresh look at old debates related to the significance of the Poynting theorem and the interpretation of reactive power. Reformulated in the mathematical language of geometric algebra, the new expression of electromagnetic power reflects the laws of conservation of energy-momentum in fields and circuits. The monograph offers a mathematically consistent and a physically coherent interpretation of the power concept and of the mechanism of power transmission at the subatomic (mesoscopic) level. The monograph proves (paraphrasing Heaviside) that there is no finality in the development of a vibrant discipline: power theory.

Recent instances of bioinvasion, such as the emergence of the zebra mussel in the American Great Lakes, generated a demand among marine biologists and ecologists for groundbreaking new references that detail how organisms colonize hard substrates, and how to prevent damaging biomass concentrations. Marine Biofouling: Colonization Processes and Defenses is the English language version of a comprehensive work by eminent Russian scientist Alexander I. Railkin, who details the causes of vast biomass concentrations on submerged hard substrates. He also delivers a quantitative description of colonization processes and provides detailed models for preventing biofouling. This volume expounds on many topics rarely discussed in the frame of one book: types of hard substrate communities; comparison of hard and soft substrate communities; harm caused by micro- and macrofoulers; larval taxes and drift; mechanisms of settlement and attachment of microorganisms, invertebrates, ascidians and macroalgae; the impact of currents; protection from epibionts; industrial biofouling protection; successions on hard substrates; and the recovery of disturbed communities or the self-assembly of communities. The text includes much Russian-language research translated for the first time. Through a thorough examination of substrate organisms and an exploration of preventive methods, this monograph prepares those concerned with marine biology to help protect the self-purifying organisms that keep marine ecosystems healthy and productive.

This book presents a broad and well-structured overview of various non-Fourier heat conduction models. The classical Fourier heat conduction model is valid for most macroscopic problems. However, it fails when the wave nature of the heat propagation becomes dominant and memory or non-local spatial effects become significant; e.g., during ultrafast heating, heat transfer at the nanoscale, in granular and porous materials, at extremely high values of the heat flux, or in heat transfer in biological tissues. The book looks at numerous non-Fourier heat conduction models that incorporate time non-locality for materials with memory, such as hereditary materials, including fractional hereditary materials, and/or spatial non-locality, i.e. materials with a non-homogeneous inner structure. Beginning with an introduction to classical transport theory, including phase-lag, phonon, and thermomass models, the book then looks at various aspects of relativistic and quantum transport, including approaches based on the Landauer formalism as well as the Green-Kubo theory of linear response. Featuring an appendix that provides an introduction to methods in fractional calculus, this book is a valuable resource for any researcher interested in theoretical and numerical aspects of complex, non-trivial heat conduction problems.

Recent instances of bioinvasion, such as the emergence of the zebra mussel in the American Great Lakes, generated a demand among marine biologists and ecologists for groundbreaking new references that detail how organisms colonize hard substrates, and how to prevent damaging biomass concentrations.

Marine Biofouling: Colonization Processes and Defenses is the English language version of a comprehensive work by eminent Russian scientist Alexander I. Railkin, who details the causes of vast biomass concentrations on submerged hard substrates. He also delivers a quantitative description of colonization processes and provides detailed models for preventing biofouling.

This volume expounds on many topics rarely discussed in the frame of one book: types of hard substrate communities; comparison of hard and soft substrate communities; harm caused by micro- and macrofoulers; larval taxes and drift; mechanisms of settlement and attachment of microorganisms, invertebrates, ascidians and macroalgae; the impact of currents; protection from epibionts; industrial biofouling protection; successions on hard substrates; and the recovery of disturbed communities or the self-assembly of communities. The text includes much Russian-language research translated for the first time.

Through a thorough examination of substrate organisms and an exploration of preventive methods, this monograph prepares those concerned with marine biology to help protect the self-purifying organisms that keep marine ecosystems healthy and productive.

Deep and detailed discussions on chemistry, chemical physics, photoelectrochemistry, photophysics, photocatalysis and possible applications of nanostructured semiconductor materials have shown increasing interest in the matter by scientists representing various research areas as well as industrial enterprises. Indeed, solar energy conversion and chemical methods for its realization became very popular again after the "great jump" of renewable energy sources between the middle of the 1970s and the beginning of the 1980s.
Several excellent books have been published over the past years, however, in these books no attempt was made to approach this research area from the point of view of classical chemical physics.
With this book, the editors aim: a) to generate an adequate scope of the modern trends and data obtained during the last years in the area of chemical physics of nanostructured materials, in particular, nanocrystalline semiconductors; b) to select an equal mix of scientists from Western and Eastern countries, all of them experts in their respective research areas; and c) to present to the international scientific community many interesting and important results which have been obtained by former Soviet Union researchers, but are not well known because they had originally been published in Russian books and journals.
This book will be interesting and useful for scientists working in the area of semiconductor nanotechnology, photoelectrochemistry, photocatalysis, photochemistry of water and air purification, as well as for graduate and post-graduate students who are planning to join these research areas.

This book covers the discrete mathematics as it has been established after its emergence since the middle of the last century and its elementary applications to cryptography. It can be used by any individual studying discrete mathematics, finite mathematics, and similar subjects. Any necessary prerequisites are explained and illustrated in the book. As a background of cryptography, the textbook gives an introduction into number theory, coding theory, information theory, that obviously have discrete nature. Designed in a "self-teaching" format, the book includes about 600 problems (with and without solutions) and numerous, practical examples of cryptography. FEATURES Designed in a "self-teaching" format, the book includes about 600 problems (with and without solutions) and numerous examples of cryptography Provides an introduction into number theory, game theory, coding theory, and information theory as background for the coverage of cryptography Covers cryptography topics such as CRT, affine ciphers, hashing functions, substitution ciphers, unbreakable ciphers, Discrete Logarithm Problem (DLP), and more

This book presents various examples of how advanced fluorescence and spectroscopic analytical methods can be used in combination with computer data processing to address different biochemical questions. The main focus is on evolutionary biochemistry and the description of biochemical and metabolic issues; specifically, the use of pulse amplitude modulated fluorescence (PAM) for the functional analysis of the cellular state, as well as results obtained by means of the derivative spectroscopy method characterizing structural reorganization of a cell under the influence of external factors, are discussed. The topics presented here will be of interest to biologists, geneticists, biophysicists and biochemists, as well as experts in analytical chemistry, pharmaceutical chemistry and radio chemistry and radio activation studies with protonen and alpha-particles. It also offers a valuable resource for advanced undergraduate and graduate students in biological, physical and chemical disciplines whose work involves derivative spectrophotometry and PAM-fluorescence.

Continuing the authors' multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts. Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions.

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.

Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis. Volume 2: Linear and Nonlinear Dynamics of Continuous Media continues the multivolume project which endeavors to show how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researchers in applied mathematics, physical sciences, and engineering. It contains an analysis of the three basic types of linear partial differential equations--elliptic, parabolic, and hyperbolic--as well as chapters on first-order nonlinear partial differential equations and conservation laws, and generalized solutions of first-order nonlinear PDEs. Nonlinear wave, growing interface, and Burger's equations, KdV equations, and the equations of gas dynamics and porous media are also covered. The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. Features * Application oriented exposition of distributional (Dirac delta) methods in the theory of partial differential equations. Abstract formalism is keep to a minimum. * Careful and rich selection of examples and problems arising in real-life situations. Complete solutions to all exercises appear at the end of the book. * Clear explanations, motivations, and illustration of all necessary mathematical concepts.

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.

This book presents various examples of how advanced fluorescence and spectroscopic analytical methods can be used in combination with computer data processing to address different biochemical questions. The main focus is on evolutionary biochemistry and the description of biochemical and metabolic issues; specifically, the use of pulse amplitude modulated fluorescence (PAM) for the functional analysis of the cellular state, as well as results obtained by means of the derivative spectroscopy method characterizing structural reorganization of a cell under the influence of external factors, are discussed. The topics presented here will be of interest to biologists, geneticists, biophysicists and biochemists, as well as experts in analytical chemistry, pharmaceutical chemistry and radio chemistry and radio activation studies with protonen and alpha-particles. It also offers a valuable resource for advanced undergraduate and graduate students in biological, physical and chemical disciplines whose work involves derivative spectrophotometry and PAM-fluorescence.

This book provides a multidisciplinary overview to the application of high order derivative spectrophotometry and Electron Spin Resonance (ESR) spectroscopy in biology and ecology. The characteristics of the principle methods as well as the generation of reliable spectra are discussed in general terms allowing the reader to gain an idea of these methods' potentials. Furthermore the authors give an extended overview to the spectroscopic and spectro-photometric analysis of specific biological materials. This volume is a well condensed description of an analytical method and a clear review to its application in biology and related fields and an essential tool for researchers who are new in the field of spectroscopic methods and their applications in the life sciences.

Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis. Volume 2: Linear and Nonlinear Dynamics of Continuous Media continues the multivolume project which endeavors to show how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researchers in applied mathematics, physical sciences, and engineering. It contains an analysis of the three basic types of linear partial differential equations--elliptic, parabolic, and hyperbolic--as well as chapters on first-order nonlinear partial differential equations and conservation laws, and generalized solutions of first-order nonlinear PDEs. Nonlinear wave, growing interface, and Burger's equations, KdV equations, and the equations of gas dynamics and porous media are also covered. The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. Features * Application oriented exposition of distributional (Dirac delta) methods in the theory of partial differential equations. Abstract formalism is keep to a minimum. * Careful and rich selection of examples and problems arising in real-life situations. Complete solutions to all exercises appear at the end of the book. * Clear explanations, motivations, and illustration of all necessary mathematical concepts.

"Nuclear Electrodynamics" quantitatively describes both nuclear electromagnetic properties and processes of the electromagnetic interaction.The main emphasis is on the derivation of basic equations. The book is intended for both theorists and experimentalists specializing in this field. Contents: - Introduction - Electromagnetic Multipole Moments - Interaction Between Nuclei and Electromagnetic Radiation - Electron-Nucleus Interaction (Elastic and Inelastic Scattering) - Electron-Nucleus Interaction (Nuclear Electrodisintegration and Inclusive Processes) - Electromagnetic Interaction between Heavy Charged Particles and Nuclei - References - Subject Index

This book provides a multidisciplinary overview to the application of high order derivative spectrophotometry and Electron Spin Resonance (ESR) spectroscopy in biology and ecology. The characteristics of the principle methods as well as the generation of reliable spectra are discussed in general terms allowing the reader to gain an idea of these methods' potentials. Furthermore the authors give an extended overview to the spectroscopic and spectro-photometric analysis of specific biological materials. This volume is a well condensed description of an analytical method and a clear review to its application in biology and related fields and an essential tool for researchers who are new in the field of spectroscopic methods and their applications in the life sciences.

This book is devoted to the quantitative physical modeling of subduction and subduction-related processes. It presents a coherent description of the modeling method (including similarity criteria, and a novel applied experimental technique), results from model experiments, theoretical analysis of results on the basis of continuum mechanics, and their geodynamic interpretation. Subduction is modeled in general as well as applied to particular regions using both 2-D and 3-D approaches, with both slab-push and slab-pull driving forces. The modeling covers all stages from subduction initiation to death', different regimes of subduction producing back arc extension and compression, blocking of subduction and jumps of subduction zone, arc-continent collision and continental subduction. This work is for geologists and geophysicists interested in geodynamics of the convergent plate boundaries and in mechanics of the lithosphere.

Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.

Molecules and Their Spectroscopic Properties presents a comprehensive collection of geometrical and spectroscopic constants and collisional characteristics for molecules most important in applications, with data on: energy levels, fundamental vibrational frequencies, electron and proton affinities, dipole moments and polarizabilities, ionization potentials and effective cross sections for various elementary processes occurring in laboratory and astrophysical plasmas, chemical processes, and molecular lasers. Besides the tabulated and graphical material, the most important physical notations and fundamental relationships are included, too. The up-to-date reference data presented will be useful for specialists working in molecular spectroscopy, physics of molecular collisions, and laser physics.

The history of physics furnishes many examples of how a simple semiem pirical method, essentially based on intuitive considerations, may prove to be much more successful than a rigorous theoretical approach. A pertinent example is the method of atom-atom potentials, which treats the intermolec ular interactions between polyatomic molecules in terms of pairwise inter actions between their constituent atoms. Despite a few conceptual short comings, the method provides a fairly reliable practical means of handling, on a microscopic level, a wide range of problems that arise in the solid-state physics and chemistry of organic compounds. This monograph is an attempt to generalize the experience gained in the past twenty years in interpreting the static and dynamic properties of organic molecular solids in terms of atom-atom potentials. It embraces nearly all aspects of the application of the method, including an evaluation of cohesive energies, equilibrium crystal structures, phonon spectra, ther modynamic functions, and crystal defects. Many related topics such as the effect of the crystal field on molecular conformation, the determination of crystal structures from raw diffraction data, and the problem of polymor phic transitions are also discussed. We believe that this book will be of use to researchers in solid-state physics, chemistry, crystallography, physical chemistry, and polymer chem istry. It also gives us an opportunity to acknowledge our indebtedness to those who sent us published as well as unpublished information and sugges tions, including A.T. Amos, E.L. Bokhenkov, H. Bonadeo, R.K. Boyd, C.P."

A comprehensive exposition on analytic methods for solving science and engineering problems, written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.

This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

The theory of social choice deals with both the processes and results of col lective decision making. In this book, we explore some issues in the theory of social choice and mechanism design. We examine the premises of this theory, the axiomatic approach, and the mechanism design approach. The main questions are what is collective interest, how is it related to individuals' interests, how should one design social interactions, laws, and in stitutions? These questions are not new. Philosophers, social scientists have indeed pondered upon them for years. And, in fact, the organizational struc tures of many social institutions -courts, parliaments, committees and reg ulatory boards -often lack a sound theoretical base. This is not surprising, as it is, indeed, difficult to provide for a comprehensive formalization of the activities of such organizations. Nevertheless, there has been a definite trend towards providing clear and unambiguous rules for collective decision mak ing. These very rules constitute the body of social choice theory and its main object. The basic problem of social choice We explain here more precisely what a problem of social choice is, what approaches might be used to tackle it, and what kind of solutions it leads to. We introduce a few basic notions in preliminarily fashion and, in doing so, we stress both motivations and explanations."

This book, written by a leader in neural network theory in Russia, uses mathematical methods in combination with complexity theory, nonlinear dynamics and optimization. It details more than 40 years of Soviet and Russian neural network research and presents a systematized methodology of neural networks synthesis. The theory is expansive: covering not just traditional topics such as network architecture but also neural continua in function spaces as well.