This classic text provides an excellent introduction to a new and rapidly developing field of research. Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.

This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series -convergence operators -hypercyclic set of linear operators Analytic operators in Bela Szoekefalvi-Nagy's sense Bases of the perturbed operator T( ) Frame of the perturbed operator T( ) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory

In any linear system, the input and the output are connected by means of a linear operator. When the input can be notionally represented by a function that is null valued everywhere except at a specific location in spacetime, the corresponding output is called the Green function in field theories. Dyadic Green functions are commonplace in electromagnetics, because both the input and the output are vector functions of space and time. This book provides a survey of the state-of-the-art knowledge of infinite space dyadic Green functions.

This book provides practical applications of doubly classified models by using R syntax to generate the models. It also presents these models in symbolic tables so as to cater to those who are not mathematically inclined, while numerous examples throughout the book illustrate the concepts and their applications. For those who are not aware of this modeling approach, it serves as a good starting point to acquire a basic understanding of doubly classified models. It is also a valuable resource for academics, postgraduate students, undergraduates, data analysts and researchers who are interested in examining square contingency tables.

This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.

Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. It is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This book is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in this volume can hardly be found.

The book comprehensively covers the various aspects of risk modeling and analysis in technological contexts. It pursues a systems approach to modeling risk and reliability concerns in engineering, and covers the key concepts of risk analysis and mathematical tools used to assess and account for risk in engineering problems. The relevance of incorporating risk-based structures in design and operations is also stressed, with special emphasis on the human factor and behavioral risks. The book uses the nuclear plant, an extremely complex and high-precision engineering environment, as an example to develop the concepts discussed. The core mechanical, electronic and physical aspects of such a complex system offer an excellent platform for analyzing and creating risk-based models. The book also provides real-time case studies in a separate section to demonstrate the use of this approach. There are many limitations when it comes to applications of risk-based approaches to engineering problems. The book is structured and written in a way that addresses these key gap areas to help optimize the overall methodology. This book serves as a textbook for graduate and advanced undergraduate courses on risk and reliability in engineering. It can also be used outside the classroom for professional development courses aimed at practicing engineers or as an introduction to risk-based engineering for professionals, researchers, and students interested in the field.

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques.

This book is a survey of the research work done by the author over the last 15 years, in collaboration with various eminent mathematicians and climate scientists on the subject of tropical convection and convectively coupled waves. In the areas of climate modelling and climate change science, tropical dynamics and tropical rainfall are among the biggest uncertainties of future projections. This not only puts at risk billions of human beings who populate the tropical continents but it is also of central importance for climate predictions on the global scale. This book aims to introduce the non-expert readers in mathematics and theoretical physics to this fascinating topic in order to attract interest into this difficult and exciting research area. The general thyme revolves around the use of new deterministic and stochastic multi-cloud models for tropical convection and convectively coupled waves. It draws modelling ideas from various areas of mathematics and physics and used in conjunction with state-of-the-art satellite and in-situ observations and detailed numerical simulations. After a review of preliminary material on tropical dynamics and moist thermodynamics, including recent discoveries based on satellite observations as well as Markov chains, the book immerses the reader into the area of models for convection and tropical waves. It begins with basic concepts of linear stability analysis and ends with the use of these models to improve the state-of-the-art global climate models. The book also contains a fair amount of exercises that makes it suitable as a textbook complement on the subject.

Chemistry, physics and biology are by their nature genuinely difficult. Mathematics, however, is man-made, and therefore not as complicated. Two ideas form the basis for this book: 1) to use ordinary mathematics to describe the simplicity in the structure of mathematics and 2) to develop new branches of mathematics to describe natural sciences.

Mathematics can be described as the addition, subtraction or multiplication of planes. Using the exponential scale the authors show that the addition of planes gives the polyhedra, or any solid. The substraction of planes gives saddles. The multiplication of planes gives the general saddle equations and the multispirals. The equation of symmetry is derived, which contains the exponential scale with its functions for solids, the complex exponentials with the nodal surfaces, and the GD (Gauss Distribution) mathematics with finite periodicity.

Piece by piece, the authors have found mathematical functions for the geometrical descriptions of chemical structures and the structure building operations. Using the mathematics for dilatation; twins, trillings, fourlings and sixlings are made, and using GD mathematics these are made periodic. This description of a structure is the nature of mathematics itself. Crystal structures and 3D mathematics are synonyms. Mathematics are used to describe rod packings, Olympic rings and defects in solids. Giant molecules such as cubosomes, the DNA double helix, and certain building blocks in protein structures are also described mathematically.

The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be studied in time intervals that include an extremely large number of periods. As is known, these equations cannot be solved efficiently using conventional methods. A further study of novel geometric integrators has become increasingly important in recent years. The objective of this monograph is to explore further geometric integrators for highly oscillatory problems that can be formulated as systems of ordinary and partial differential equations. Facing challenging scientific computational problems, this book presents some new perspectives of the subject matter based on theoretical derivations and mathematical analysis, and provides high-performance numerical simulations. In order to show the long-time numerical behaviour of the simulation, all the integrators presented in this monograph have been tested and verified on highly oscillatory systems from a wide range of applications in the field of science and engineering. They are more efficient than existing schemes in the literature for differential equations that have highly oscillatory solutions. This book is useful to researchers, teachers, students and engineers who are interested in Geometric Integrators and their long-time behaviour analysis for differential equations with highly oscillatory solutions.

This book offers a complete guide to designing Linear Fresnel Reflector Systems for concentrating solar radiation. It includes theoretical analyses, computational tools and mathematical formulae to facilitate the development, design, construction and application of these systems. In addition, the book presents a concise yet thorough treatment of the theory behind these systems, and provides useful and efficient calculation procedures that can be used to model and develop their practical applications. Along with the theoretical analyses provided in the book, the physical background is explained using mathematical formulae, illustrations, graphs and tables. Methods are presented for solving the non-linear mathematical systems that describe a significant variety of cases. In addition, MATLAB codes are supplied (both in the text and online). Consequently, readers interested in applying the methodology presented here will have all the source codes at hand, allowing them to easily expand on them by introducing appropriate modifications for their respective design configuration. Given its scope, the book will be of interest to engineers and researchers, who can use their scientific background to help them develop more energy-efficient Linear Fresnel Reflector systems. It will also appeal to students studying these systems for the first time, as it supplies a comprehensive overview of their theoretical analysis and applications.

This book sets out to give a rigorous mathematical description of the greenhouse effect through the theory of infrared atmospheric emission. In contrast to traditional climatological analysis, this approach eschews empirical relations in favour of a strict thermodynamical derivation, based on data from NASA and from the HITRAN spectroscopy database. The results highlight new aspects of the role of clouds in the greenhouse effect.

Ulam Stability of Operators presents a modern, unified, and systematic approach to the field. Focusing on the stability of functional equations across single variable, difference equations, differential equations, and integral equations, the book collects, compares, unifies, complements, generalizes, and updates key results. Whenever suitable, open problems are stated in corresponding areas. The book is of interest to researchers in operator theory, difference and functional equations and inequalities, differential and integral equations.

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ? N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein's special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas.

For courses in Business Mathematics. Focuses on current issues, real companies, and pragmatic business scenarios Business Mathematics by Clendenen and Salzman teaches students the mathematical skills they need for success in business, emphasizing mastery of business concepts and scenarios that require a mathematical solution. With a strong focus on current issues, real companies, and pragmatic business scenarios, the authors cover the full spectrum of basic business math, placing every concept in context with relevant examples. Along with an updated MyLab (TM) Math course, the 14th Edition has been significantly revised to modernize the text, improve discussions, and make the material more meaningful to students. This revision is packed with data, examples, graphs, photographs, and case studies that demonstrate the material's relevance as it teaches students to interpret data and information. A global perspective is emphasized through examples and exercises that highlight issues in other countries. Also available with MyLab Math By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information. If you would like to purchase both the physical text and MyLab Math, search for: 0135195969 / 9780135195963 Business Mathematics Plus MyLab Math with Pearson eText - Access Card Package Package consists of: 0134693329 / 9780134693323 Business Mathematics, 14e 0134836235 / 9780134836232 MyLab Math with Pearson eText - Access Card - for Business Mathematics, 14/e

A combinatorial method is developed in this book to explore the mysteries of chaos, which has became a topic of science since 1975. Using tools from theoretical computer science, formal languages and automata, the complexity of symbolic behaviors of dynamical systems is classified and analysed thoroughly. This book is mainly devoted to explanation of this method and apply it to one-dimensional dynamical systems, including the circle and interval maps, which are typical in exhibiting complex behavior through simple iterated calculations. The knowledge for reading it is self-contained in the book.

This is an introduction to basic music technology, including acoustics for sound production and analysis, Fourier, frequency modulation, wavelets, and physical modeling and a classification of musical instruments and sound spaces for tuning and counterpoint. The acoustical theory is applied to its implementation in analogue and digital technology, including a detailed discussion of Fast Fourier Transform and MP3 compression. Beyond acoustics, the book discusses important symbolic sound event representation and software as typically realized by MIDI and denotator formalisms. The concluding chapters deal with globalization of music on the Internet, referring to iTunes, Spotify and similar environments. The book will be valuable for students of music, music informatics, and sound engineering.

The best laboratory math text on the market for almost 20 years, this title covers both the general principles of mathematics and specific equations, formulas, and calculations used for laboratory testing. It provides simple, easily understood explanations of calculations commonly used in clinical and biological laboratories. Contains more than 1000 practice problems.

This state of the art book takes an applications based approach to teaching mathematics to engineering and applied sciences students. The book lays emphasis on associating mathematical concepts with their physical counterparts, training students of engineering in mathematics to help them learn how things work. The book covers the concepts of number systems, algebra equations and calculus through discussions on mathematics and physics, discussing their intertwined history in a chronological order. The book includes examples, homework problems, and exercises. This book can be used to teach a first course in engineering mathematics or as a refresher on basic mathematical physics. Besides serving as core textbook, this book will also appeal to undergraduate students with cross-disciplinary interests as a supplementary text or reader.

Here is an accurate and readable translation of a seminal article by Henri Poincare that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincare applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations' solutions, such as orbital resonances and horseshoe orbits. Poincare wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.

This monograph is centered on mathematical modeling, innovative numerical algorithms and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art phase-field fracture models are complemented with prototype explanations and rigorous numerical analysis. These developments are embedded into a carefully designed balance between scientific computing aspects and numerical modeling of nonstationary coupled variational inequality systems. Therein, a focus is on nonlinear solvers, goal-oriented error estimation, predictor-corrector adaptivity, and interface conditions. Engineering applications show the potential for tackling practical problems within the fields of solid mechanics, porous media, and fluidstructure interaction.

This book offers a didactic and a self-contained treatment of the physics of liquid and flowing matter with a statistical mechanics approach. Experimental and theoretical methods that were developed to study fluids are now frequently applied to a number of more complex systems generically referred to as soft matter. As for simple liquids, also for complex fluids it is important to understand how their macroscopic behavior is determined by the interactions between the component units. Moreover, in recent years new and relevant insights have emerged from the study of anomalous phases and metastable states of matter. In addition to the traditional topics concerning fluids in normal conditions, the authors of this book discuss recent developments in the field of disordered systems in condensed and soft matter. In particular they emphasize computer simulation techniques that are used in the study of soft matter and the theories and study of slow glassy dynamics. For these reasons the book includes a specific chapter about metastability, supercooled liquids and glass transition. The book is written for graduate students and active researchers in the field.

The first World Meeting for Women in Mathematics - (WM)(2) - was a satellite event of the International Congress of Mathematicians (ICM) 2018 in Rio de Janeiro. With a focus on Latin America, the first (WM)(2) brought together mathematicians from all over the world to celebrate women mathematicians, and also to reflect on gender issues in mathematics, challenges, initiatives, and perspectives for the future. Its activities were complemented by a panel discussion organized by the Committee for Women in Mathematics (CWM) of the International Mathematical Union (IMU) inside the ICM 2018 entitled "The gender gap in mathematical and natural sciences from a historical perspective". This historical proceedings book, organized by CWM in coordination with the Association for Women in Mathematics, records the first (WM)(2) and the CWM panel discussion at ICM 2018. The first part of the volume includes a report of activities with pictures of the first (WM)(2) and a tribute to Maryam Mirzakhani, the first woman to be awarded the Fields medal. It also comprises survey research papers from invited lecturers, which provide panoramic views of different fields in pure and applied mathematics. The second part of the book contains articles from the panelists of the CWM panel discussion, which consider the historical context of the gender gap in mathematics. It includes an analysis of women lecturers in the ICM since its inception. This book is dedicated to the memory of Maryam Mirzakhani.