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This book focuses on bulk and nanostructure crystals, and specifically discusses possible crystal lattices, their reciprocal lattices, and the Bragg relation for determining crystal structure. It describes band theory in independent electron approximation using the usual perturbation quantum theory, as well as how the internal electric field of the lattice periodic potential affects degenerate states at the Brillouin zone boundaries by using the Stark effect, which leads to energy bands separated by energy gaps. The book also discusses low-dimensional systems and nanostructures using the free electron model and tight binding model. The band structure and wave function of graphene, graphene nanoribbons, single-wall carbon nanotubes, and double-wall carbon nanotubes are obtained. Additionally, nanostructure vibrations are discussed.This text is for graduate and undergraduate students, as well as researchers who are interested in working on different condensed matter physics subjects. We use simple methods to introduce and explain the initial concepts of crystal structure physics to undergraduate students.

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Advances in Functional Analysis and Operator Theory, held July 18–22, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The papers reflect the modern interplay between differential equations, functional analysis, operator algebras, and their applications from the dynamics to quantum groups to number theory. Among the topics discussed are the Sturm-Liouville and boundary value problems, axioms of quantum mechanics, $C^{•}$-algebras and symbolic dynamics, von Neumann algebras and low-dimensional topology, quantum permutation groups, the Jordan algebras, and the Kadison–Singer transforms.

This book is based on lectures given at Harvard University during the academic year 1960–1961. The presentation assumes knowledge of the elements of modern algebra (groups, vector spaces, etc.) and point-set topology and some elementary analysis. Rather than giving all the basic information or touching upon every topic in the field, this work treats various selected topics in differential geometry. The author concisely addresses standard material and spreads exercises throughout the text. his reprint has two additions to the original volume: a paper written jointly with V. Guillemin at the beginning of a period of intense interest in the equivalence problem and a short description from the author on results in the field that occurred between the first and the second printings.

The roots of the modern theories of differential and $q$-difference equations go back in part to an article by George D. Birkhoff, published in 1913, dealing with the three “sister theories” of differential, difference and $q$-difference equations. This book is about $q$-difference equations and focuses on techniques inspired by differential equations, in line with Birkhoff's work, as revived over the last three decades. It follows the approach of the Ramis school, mixing algebraic and analytic methods. While it uses some $q$-calculus and is illustrated by $q$-special functions, these are not its main subjects. After a gentle historical introduction with emphasis on mathematics and a thorough study of basic problems such as elementary $q$-functions, elementary $q$-calculus, and low order equations, a detailed algebraic and analytic study of scalar equations is followed by the usual process of transforming them into systems and back again. The structural algebraic and analytic properties of systems are then described using $q$-difference modules (Newton polygon, filtration by the slopes). The final chapters deal with Fuchsian and irregular equations and systems, including their resolution, classification, Riemann-Hilbert correspondence, and Galois theory. Nine appendices complete the book and aim to help the reader by providing some fundamental yet not universally taught facts. There are 535 exercises of various styles and levels of difficulty. The main prerequisites are general algebra and analysis as taught in the first three years of university. The book will be of interest to expert and non-expert researchers as well as graduate students in mathematics and physics.

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This volume contains the proceedings of the BIRS Workshop'Topics in Multiple Time Scale Dynamics,'held from November 27– December 2, 2022, at the Banff International Research Station, Banff, Alberta, Canada. The area of multiple-scale dynamics is rapidly evolving, marked by significant theoretical breakthroughs and practical applications. The workshop facilitated a convergence of experts from various sub-disciplines, encompassing topics like blow-up techniques for ordinary differential equations (ODEs), singular perturbation theory for stochastic differential equations (SDE), homogenization and averaging, slow-fast maps, numerical approaches, and network dynamics, including their applications in neuroscience and climate science. This volume provides a wide-ranging perspective on the current challenging subjects being explored in the field, including themes such as novel approaches to blowing-up and canard theory in unique contexts, complex multi-scale challenges in PDEs, and the role of stochasticity in multiple-scale systems.

This book provides mechanical engineering students with the theoretical and fundamental basics of the Finite Element (FE) method used in structural mechanics. Students should be able to apply this knowledge to develop FE models and use them to analyze systems both statically and dynamically. The author believes that learning about the Finite Element tool without learning how to build computer codes for it makes it just a theoretical tool, good only for very simple models with very few elements, rather than being useful for practical problems. In most of the chapters of this book, computer codes using MATLAB are presented in order to render the developed models useful for practical applications. Moreover, the book also stresses on the idea that engineers should be able to convert real life problems into simplified models from which one can predict the behavior or the performance of the system.

This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach—emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s—was popularized for the graduate level in the 1940s and 1950s to some degree by the authors'publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.

This book analyses the threats the COVID-19 pandemic poses and the need for managing healthcare resources carefully. Focusing on the impact Lower and middle-income countries experience due to the lack of medical personal, bed in hospitals and medical supplies.In the chapters, non-medical researchers together with epidemiologists contribute studies which aim to improve decision making processes when dealing with pandemic dynamics. The book also presents challenging models for post-pandemic studies and the continuation of post-pandemic treatments. This text develops an analysis of COVID-19 data and provides evidence on the increase of social inequalities with Latin American countries, and particularly on the effect of a new medicament in improving the quality of life of recovered patients with lung damage. This book would be of interest to all medical researchers and academics interested in the effects of both the pandemic and post pandemic fallout.

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia. The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frölicher structures in the formal Kadomtsev–Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras. The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.

Spatio-Temporal Methods in Environmental Epidemiology with R, like its First Edition, explores the interface between environmental epidemiology and spatio-temporal modeling. It links recent developments in spatio-temporal theory with epidemiological applications. Drawing on real-life problems, it shows how recent advances in methodology can assess the health risks associated with environmental hazards. The book's clear guidelines enable the implementation of the methodology and estimation of risks in practice.New additions to the Second Edition include: a thorough exploration of the underlying concepts behind knowledge discovery through data; a new chapter on extracting information from data using R and the tidyverse; additional material on methods for Bayesian computation, including the use of NIMBLE and Stan; new methods for performing spatio-temporal analysis and an updated chapter containing further topics. Throughout the book there are new examples, and the presentation of R code for examples has been extended. Along with these additions, the book now has a GitHub site (https://spacetime-environ.github.io/stepi2) that contains data, code and further worked examples.Features:• Explores the interface between environmental epidemiology and spatio­-temporal modeling• Incorporates examples that show how spatio-temporal methodology can inform societal concerns about the effects of environmental hazards on health• Uses a Bayesian foundation on which to build an integrated approach to spatio-temporal modeling and environmental epidemiology• Discusses data analysis and topics such as data visualization, mapping, wrangling and analysis• Shows how to design networks for monitoring hazardous environmental processes and the ill effects of preferential sampling• Through the listing and application of code, shows the power of R, tidyverse, NIMBLE and Stan and other modern tools in performing complex data analysis and modelingRepresenting a continuing important direction in environmental epidemiology, this book – in full color throughout – underscores the increasing need to consider dependencies in both space and time when modeling epidemiological data. Readers will learn how to identify and model patterns in spatio-temporal data and how to exploit dependencies over space and time to reduce bias and inefficiency when estimating risks to health.

The latest edition in the gold standard of project management case study collections As a critical part of any successful, competitive business, project management sits at the intersection of several functional areas. And in the newly revised Sixth Edition of Project Management Case Studies, world-renowned project management professional Dr. Harold Kerzner delivers practical and in-depth coverage of project management in industries as varied as automotive, healthcare, government, manufacturing, communications, construction, chemical, aerospace, and more. The latest edition of this bestselling book acts as the perfect supplement to any project management textbook or as an aid in the preparation for the PMP certification exam. The author includes new topics, like risk management, information sharing, scope changes, crisis dashboards, and innovation. The Sixth Edition includes ten new case studies and a wide array of updates to existing cases to meet today's industry standards and reflect the unique challenges facing modern project management professionals. This new edition: Features 10 new case studies from LEGO, NorthStar, Berlin Brandenburg Airport, and more Includes over 100 case studies drawn from real companies illustrating successful and poor implementation of project management Provides coverage of broad areas of project management as well as focused content on the automotive, healthcare, government, manufacturing, communications, construction, chemical, and aerospace industries Offers new topics including risk management, information sharing, scope changes, crisis dashboards, and innovation Perfect for students taking courses on project management during their undergraduate degrees and at the graduate level as part of an MBA or graduate engineering program, Project Management Case Studies is also an indispensable resource for consulting and training companies who work with other professionals.Harold Kerzner, PhD, is Senior Executive Director for Project, Program and Portfolio Management at the International Institute of Learning, Inc. (IIL). Dr. Kerzner's impact on the project management industry inspired IIL to establish the Kerzner International Project Manager of the Year Award. IIL also donated $1M to the Project Management Institute Educational Foundation (PMIEF) to establish the Dr. Harold Kerzner Scholarship Fund.

The updated book presents Matlab illustrations on various digital signal processing (DSP) techniques such as random process, time varying wireless system model, and detection and estimation theory used in wireless communication. The book also covers recent wireless techniques like OFDM, massive MIMO techniques, non-orthogonal multiple access, millimeter wave MIMO, full duplex, cognitive radio, co-operating communication, unmanned aerial vehicles etc. This book is suitable for those who are doing basic and applied research in digital signal processing for wireless communication.

This treatise, by one of Russia's leading mathematicians, gives in easily accessible form a coherent account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, electrical engineering, etc. The individual chapters have been kept as far as possible independent of each other, so that the reader acquainted with the contents of Chapter 1 can proceed immediately to the chapters of special interest. This is an excellent textbook. —Zentralblatt MATH

Thelong-anticipated revision of ArtificialIntelligence: A Modern Approach explores the full breadth and depth of the field of artificialintelligence (AI). The 4th Edition brings readers up to date on the latest technologies,presents concepts in a more unified manner, and offers new or expanded coverageof machine learning, deep learning, transfer learning, multi agent systems,robotics, natural language processing, causality, probabilistic programming,privacy, fairness, and safe AI.

Cancer is a complex and heterogeneous (systematic) disease that exhibits high levels of robustness against various therapeutic interventions. Due to the complex, heterogeneous, and evolving nature of cancer, it is essential for a system-oriented view to be adopted in order to understand the pathogenic mechanism of cancer which will eventually lead to the drug discovery and treatment of patients. This book not only provides new insights from system modeling and large scale experimental data, but also will allow the reader to perceive the systematic characteristics of cancer under some micro-environments. Based on the systems biology method and genome-wide high throughput data, the book presents the PPI network, gene regulatory network and epigenetic network as an integrated genetic and epigenetic cellular network of lung cancer, bladder cancer, thyroid cancer, colorectal cancer, and liver cancer to investigate their core signaling pathways of the carcinogenesis process to identify their corresponding significant carcinogenic biomarkers as drug targets for systems drug discovery and design. Consequently, the book presents the design of a multiple-molecule drug that can target these biomarkers for the therapeutic treatment of cancer with fewer side effects.

An in-depth and up-to-date coverage of the areas of statistics at the PhD level. During the recent years, there has been a huge increase in the use of advanced statistical methods in clinical and epidemiological research. Many researchers need an understanding of statistics beyond what is covered in introductory courses. This book is intended as a course textbook in clinical and epidemiological research, as well as a reference book for students or working professionals in health sciences. It gives an in-depth and up-to-date coverage of the areas of statistics which are relevant at the PhD level in clinical and epidemiological research. The book consists of twenty chapters written by twenty-nine authors, all experts in their fields. Each chapter is self-contained and may be read independently according to the needs of the reader. The editors, Marit B. Veierød, Stian Lydersen and Petter Laake, all Professors of Medical Statistics, have extensive experience from teaching medical statistics at the Master and PhD levels, and from clinical and epidemiological research projects. The tables and figures in the book are available for downloading for educational use from the book's website, www.medicalstatistics.no. Contents: 1. Design and analysis (Marit B. Veierød, Stian Lydersen and Petter Laake) 2. Categorical data and contingency tables.. (Stian Lydersen, Morten W. Fagerland and Petter Laake) 3. Logistic regression (David W. Hosmer and Stanley Lemeshow) 4. Linear regression (Morten W. Fagerland, Geir Egil Eide and Petter Laake) 5. Survival analysis (Odd O. Aalen and Marianne Riksheim) 6. Poisson regression (Sven Ove Samuelsen and Marit B. Veierød) 7. Mixed models (Magne Thoresen and Håkon K. Gjessing) 8. Longitudinal analysis (Magne Thoresen) 9. Generalized linear latent and mixed models.. (Anders Skrondal and Sophia Rabe-Hesketh) 10. Measurement error (John P. Buonaccorsi) 11. Power and sample size (Michael Væ

Gain an understanding of how econometrics can answer today's questions in business, policy evaluation and forecasting with Wooldridge's INTRODUCTORY ECONOMETRICS: A MODERN APPROACH, 7E. Unlike traditional texts, this book's practical, yet professional, approach demonstrates how econometrics has moved beyond a set of abstract tools to become genuinely useful for answering questions across a variety of disciplines. The author has organized the book's presentation around the type of data being analyzed with a systematic approach that only introduces assumptions as they are needed. This makes the material easier to understand and, ultimately, leads to better econometric practices. Packed with relevant applications, the text incorporates more than 100 data sets in different formats. Updates introduce the latest developments in the field, including the recent advances in the so-called “causal effects” or “treatment effects,'to provide a complete understanding of the impact and importance of econometrics today.

Eldenburg's Management is an introductory text that focuses on presenting content in an easy to understand way that encourages students to think critically and draw connections between theory and practice. This new seventh edition has a strengthened focus on technology and features have been updated to help students further consolidate their knowledge.This includes various forms of revision materials such as auto-graded knowledge-check questions and self-skill assessment. There is also a broad variety of concise case studies, including new ones with a strategic focus, which enable instructors to have thought-provoking and engaging tutorials. An exciting addition to the interactive e-text are the new ANZ videos that feature a diverse group of management thought-leaders who give insights and ‘tales from the front.'This will provide supplementary content for lectures or serve as pre-work for a flipped classroom.

This book is a unique study of a transition economy, using the little-known case of Belarus, a country “trapped in transition” from state capitalism to market economy. The first of its kind, this book explains how decisions are made by economic authorities and businesses in this developing country. It proves that, in order to boost economic reforms, the Belarusian government needs to rely on the support of the high-income public.

The main aim of the present book is to suggest some improved estimators using auxiliary and attribute information in case of simple random sampling and stratified random sampling and some inventory models related to capacity constraints. This volume is a collection of five papers, written by six co-authors (listed in the order of the papers): Dr. Rajesh Singh, Dr. Sachin Malik, Dr. Florentin Smarandache, Dr. Neeraj Kumar, Mr. Sanjey Kumar & Pallavi Agarwal.

Back by popular demand, we are pleased to reissue this outstanding collection of problems and solutions from the Putnam Competitions covering the years 1938-1964. Problemists the world over, including all past and future Putnam Competitors, will revel in mastering the difficulties posed by this collection of problems from the first 25 William Lowell Putnam Competitions. Solutions to all 347 problems are given. In some cases multiple solutions are included, some which contestants could reasonably be expected to find under examination conditions, and others which are more elegant or utilize more sophisticated techniques. Valuable references and historical comments on many of the problems are presented. The book concludes with four articles on the Putnam competition written by G. Birkhoff, L. E. Bush, L. J. Mordell, and L. M. Kelly which are reprinted from the American Mathematical Monthly. There is great appeal here for all; teachers, students, and all those who love good problems and see them as an entree to beautiful and powerful ideas.

This book will appeal to both practitioners and researchers in industrial and university analytical laboratories, as well as students specializing in analytical spectroscopy and chemometrics. The subjects covered include the advanced principles of calibration (univariate and multivariate) and the estimation of the peak parameters in spectra with overlapping components. This book differs from existing studies on the subject in that it provides easily reproducible computer calculations illustrating its significant theoretical statements. As such, it can also serve as a practical guide to lecturers in analytical spectrometry and chemometrics.

Let $F$ be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations $\mathrm{Gal}(\overline{F}/F) \to \mathrm{PGL}_n(\mathbb{C})$ lift to $\mathrm{GL}_n(\mathbb{C})$. The author takes special interest in the interaction of this result with algebraicity (for automorphic representations) and geometricity (in the sense of Fontaine-Mazur). On the motivic side, the author studies refinements and generalizations of the classical Kuga-Satake construction. Some auxiliary results touch on: possible infinity-types of algebraic automorphic representations; comparison of the automorphic and Galois “Tannakian formalisms” monodromy (independence-of-$\ell$) questions for abstract Galois representations.

There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many of these results and proofs obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, the author provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It can serve as a supplementary text for an undergraduate or graduate algebra course.

The content of this book is somewhat different from that of traditional books on representation theory. First, bearing in mind the needs of physicists, the author has tried to make the exposition as elementary as possible. The need for an elementary exposition has influenced the distribution of the material. The book is divided into three largely independent parts, arranged in order of increasing difficulty. Besides compact Lie groups, groups with other topological structure (“similar” to compact groups in some sense) are considered. Prominent among these are reductive complex Lie groups (including semisimple groups), obtained from compact Lie groups by analytic continuation, and also their real forms (reductive real Lie groups). The theory of finite-dimensional representation for these classes of groups is developed, striving whenever possible to emphasize the “compact origin” of these representations, i.e., their analytic relationship to representations of compact Lie groups. In conclusion, the author briefly presents some aspects of infinite-dimensional representations of semisimple complex Lie algebras and Lie groups.

A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group $SU(2)$, and the hypergeometric function and representations of the group $SL(2,R)$, as well as many other classes of special functions.

Dynamical systems and statistical mechanics have been developing in close interaction during the past decade, and the papers in this book attest to the productiveness of this interaction. The first paper in the collection contains a new result in the theory of quantum chaos, a burgeoning line of inquiry that combines mathematics and physics and is likely in time to produce many new connections and applications. Another paper, related to the renormalization group method for the study of maps of the circle with singularities due to a jump in the derivative, demonstrates that the fixed point of the renormgroup can be sufficiently described in this case. In certain situations, the renormgroup methods work better than the traditional KAM method. Other topics covered include thermodynamic formalism for certain infinite-dimensional dynamical systems, numerical simulation of dynamical systems with hyperbolic behavior, periodic points of holomorphic maps, the theory of random media, statistical properties of the leading eigenvalue in matrix ensembles of large dimension, spectral properties of the one-dimensional Schrödinger operator. This volume will appeal to many readers, as it covers a broad range of topics and presents a view of the some of the frontier research in the Soviet Union today.

Problem solving in mathematics is often thought of as a one way process. For example: take two numbers and multiply them together. However for each problem there is also an inverse problem which runs in the opposite direction: now take a number and find a pair of factors. Such problems are considerably more important, in mathematics and throughout science, than they might first appear. This book concentrates on these inverse problems and how they can be usefully introduced to undergraduate students. A historical introduction sets the scene and gives a cultural context for what the rest of the book. Chapters dealing with inverse problems in calculus, differential equations and linear algebra then follow and the book concludes with suggestions for further reading. Whatever their own field of expertise, this will be an essential purchase for anyone interested in the teaching of mathematics.

The study of natural and social phemomena indicates that the future development of many processes depends not only on their present state, but also on their history. Such processes can be described mathematically by using the machinery of equations with aftereffect. This book is a comprehensive, up-to-date presentation of control theory for hereditary systems of various types. Topics covered include background of the theory of hereditary equations, their applications in modeling real phenomena, optimal control of deterministic and stochastic systems, optimal estimation of systems with delay, and optimal control with uncertainties. The exposition is illustrated by examples, figures, and tables.

Integer solutions for systems of linear inequalities, equations, and congruences are considered along with the construction and theoretical analysis of integer programming algorithms. The complexity of algorithms is analyzed dependent upon two parameters: the dimension, and the maximal modulus of the coefficients describing the conditions of the problem. The analysis is based on a thorough treatment of the qualitative and quantitative aspects of integer programming, in particular on bounds obtained by the author for the number of extreme points. This permits progress in many cases in which the traditional approach—which regards complexity as a function only of the length of the input—leads to a negative result.

This book is dedicated to two problems. The first concerns the description of maximal exponential growth of functions or distributions for which the Cauchy problem is well posed. The description is presented in the language of the behavior of the symbol in a complex domain. The second problem concerns the structure of and explicit formulas for differential operators with large automorphism groups. It is suitable as an advanced graduate text in courses in partial differential equations and the theory of distributions.

Provides the basic as well as advanced knowledge of control systems for textile machines. Basic concepts underlying the electronic controls have been dealt with by the authors in a simple and comprehensive manner considering the requirements of undergraduate and postgraduate students. The authors have meticulously planned the chapters and have covered every relevant topic in a very systematic way. Sufficient examples have been given wherever necessary with clear diagrammatic illustrations. The amalgamation of experiences of industry and academia has helped the authors to write the book in a well-defined manner.

Hilbert $C^•$-modules provide a natural generalization of Hilbert spaces arising when the field of scalars $\mathbf{C}$ is replaced by an arbitrary $C^•$-algebra. The general theory of Hilbert $C^•$-modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool in operator algebras theory, in index theory of elliptic operators, in $K$- and $KK$-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert $C^•$-modules is interesting on its own. The present book is an introduction to the theory of Hilbert $C^•$-modules. The authors explain in detail the basic notions and results of the theory, and provide a number of important examples. Some results related to the authors'research interests are also included. A large part of the book is devoted to structural results (self-duality, reflexivity) and to nonadjointable operators. Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.

The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered, the best known, but by no means the only one, being to medical tomography. The present book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski–Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of $SL(2,\mathbb C)$, integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry.

This is the first introductory book on the theory of prehomogeneous vector spaces, introduced in the 1970s by Mikio Sato. The author was an early and important developer of the theory and continues to be active in the field. This book explains the basic concepts of prehomogeneous vector spaces, the fundamental theorem, the zeta functions associated with prehomogeneous vector spaces and a classification theory of irreducible prehomogeneous vector spaces. This book is written for students, and is appropriate for second-year graduate level and above. However, because it is self-contained, covering algebraic and analytic preliminaries in considerable detail, the content may in fact prove to be accessible to many advanced undergraduate and beginning graduate students. It also provides a useful introduction for working mathematicians who want to learn about prehomogeneous vector spaces.

The main topic of this book is the isoenergetic structure of the Liouville foliation generated by an integrable system with two degrees of freedom and the topological structure of the corresponding Poisson action of the group ${\mathbb R}^2$. This is a first step towards understanding the global dynamics of Hamiltonian systems and applying perturbation methods. Emphasis is placed on the topology of this foliation rather than on analytic representation. In contrast to previously published works in this area, here the authors consistently use the dynamical properties of the action to achieve their results.