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How AI Thinks: How we built it, how it can help us, and how we can control it

by Nigel Toon

THE #2 TIMES BESTSELLER'Artificial intelligence is going to have a massive impact on everyone’s lives... an accessible and sensible read that helps demystify AI' Deborah Meaden, entrepreneur and star of Dragon's Den'Nigel Toon is a visionary leader in the field of artificial intelligence... a must-read' Marc Tremblay, Distinguished Engineer, MicrosoftThose who understand how AI thinks are about to win big.We are used to thinking of computers as being a step up from calculators - very good at storing information, and maybe even at playing a logical game like chess. But up to now they haven't been able to think in ways that are intuitive, or respond to questions as a human might. All that has changed, dramatically, in the past few years.Our search engines are becoming answer engines. Artificial intelligence is already revolutionising sectors from education to healthcare to the creative arts. But how does an AI understand sentiment or context? How does it play and win games that have an almost infinite number of moves? And how can we work with AI to produce insights and innovations that are beyond human capacity, from writing code in an instant to unfolding the elaborate 3D puzzles of proteins?We stand at the brink of a historic change that will disrupt society and at the same time create enormous opportunities for those who understand how AI thinks. Nigel Toon shows how we train AI to train itself, so that it can paint images that have never existed before or converse in any language. In doing so he reveals the strange and fascinating ways that humans think, too, as we learn how to live in a world shared by machine intelligences of our own creation.

How Energy Considerations Have Shaped Our Fundamental Modern Theories of Physics: Theory and Key Historical Moments

by E. B. Manoukian

At long last, with sufficient technical details, emphasizing key historical moments, a book that develops all of fundamental modern theoretical physics from energy considerations in a compact form. Starting with a few electron-volts of atoms in the quantum world at low energies extending up to quantum gravity and beyond to the birth of the Universe, readers will experience the entire spectrum of fundamental modern theoretical physics, with one theory leading to another in an integrated unified manner. Energy considerations lead to the development of special and general relativity, quantum field theory, renormalization theory, modern quantum electrodynamics, electro-weak theory, the standard model of particle physics, grand unified theories, string theory, the current standard model of inflationary big bang theory, and even to the birth of the Higgs field, and in developments of quantum gravity. Unfortunately, due to strong specialization within theirfields, students and many practicing physicists are exposed only to parts of the beautiful story of modern fundamental physics. Here the entire story is told! This is a must-read book for graduate students, advanced undergraduate students, instructors and professionals who are interested in all aspects of fundamental modern theoretical physics and key historical moments in its development.

How to Use SPSS®: A Step-By-Step Guide to Analysis and Interpretation

by Brian C. Cronk

How to Use SPSS® is designed with the novice computer user in mind and for people who have no previous experience using SPSS. Each chapter is divided into short sections that describe the statistic being used, important underlying assumptions, and how to interpret the results and express them in a research report. The book begins with the basics, such as starting SPSS, defining variables, and entering and saving data. It covers all major statistical techniques typically taught in beginning statistics classes, such a descriptive statistics, graphing data, prediction and association, parametric inferential statistics, nonparametric inferential statistics and statistics for test construction. More than 275 screenshots (including sample output) throughout the book show students exactly what to expect as they follow along using SPSS. The book includes a glossary of statistical terms and practice exercises. A complete set of online resources including video tutorials and output files for students, and PowerPoint slides and test bank questions for instructors, make How to Use SPSS® the definitive, field-tested resource for learning SPSS. New to this edition: Fully updated to the reflect SPSS version 29. Every screen shot has been recaptured. New video supplements for all practice exercises. References to significance levels have been updated to reflect the new SPSS output format. Effect size is now shown in output for many procedures and reference to some effect size has been moved from Appendix A to be more integrated into the chapters. Sample results sections now also include effect size where SPSS directly calculates effect size. A new section covering the EXPLORE command has been added to Chapter 3.

How to Use SPSS®: A Step-By-Step Guide to Analysis and Interpretation

by Brian C. Cronk

How to Use SPSS® is designed with the novice computer user in mind and for people who have no previous experience using SPSS. Each chapter is divided into short sections that describe the statistic being used, important underlying assumptions, and how to interpret the results and express them in a research report. The book begins with the basics, such as starting SPSS, defining variables, and entering and saving data. It covers all major statistical techniques typically taught in beginning statistics classes, such a descriptive statistics, graphing data, prediction and association, parametric inferential statistics, nonparametric inferential statistics and statistics for test construction. More than 275 screenshots (including sample output) throughout the book show students exactly what to expect as they follow along using SPSS. The book includes a glossary of statistical terms and practice exercises. A complete set of online resources including video tutorials and output files for students, and PowerPoint slides and test bank questions for instructors, make How to Use SPSS® the definitive, field-tested resource for learning SPSS. New to this edition: Fully updated to the reflect SPSS version 29. Every screen shot has been recaptured. New video supplements for all practice exercises. References to significance levels have been updated to reflect the new SPSS output format. Effect size is now shown in output for many procedures and reference to some effect size has been moved from Appendix A to be more integrated into the chapters. Sample results sections now also include effect size where SPSS directly calculates effect size. A new section covering the EXPLORE command has been added to Chapter 3.

Human and Artificial Rationalities: Second International Conference, HAR 2023, Paris, France, September 19–22, 2023, Proceedings (Lecture Notes in Computer Science #14522)

by Jean Baratgin Baptiste Jacquet Hiroshi Yama

This book constitutes the proceedings of the Second International Conference on Human and Artificial Rationalities, HAR 2023, which took place in Paris, France, in September 2023. The 18 full and 5 short papers included in this book were carefully reviewed and selected from 39 submissions. They were organized in topical sections as follows: Human and artificial thinking; human thinking and reasoning; neuropsychology and interaction; artificial agents and interaction; and applied reasoning. This volume also contains 2 invited talks in full-paper length.

Human Machine Interaction in the Digital Era: Towards Conversational Artificial Intelligence

by J. Dhilipan V. Saravanan R. Agusthiyar

The Human Machine Interaction in the Digital Era (ICHMIDE) 2023 conference aims to address the main issues of concern in the design issues with a particular emphasis on the design and development of interfaces for autonomous robots. Its main objective is to provide an international forum for the dissemination and exchange of up-to-date scientific information on research related to integrated human/machine systems at multiple scales, and includes areas such as human/machine interaction, engineering mathematical models, assistive technologies, system modelling, design, testing and validation. The organization of ICHMS is based on the following Track types: Smart Applications for Digital Era, Computational Mathematical and Electronics, Intelligent Systems in Security and Communication Technologies, Technological Interventions using AI and Machine Learning, Applied Science, and IoT Techniques for Industries.

Human Machine Interaction in the Digital Era: Towards Conversational Artificial Intelligence

by J. Dhilipan V. Saravanan R. Agusthiyar

The Human Machine Interaction in the Digital Era (ICHMIDE) 2023 conference aims to address the main issues of concern in the design issues with a particular emphasis on the design and development of interfaces for autonomous robots. Its main objective is to provide an international forum for the dissemination and exchange of up-to-date scientific information on research related to integrated human/machine systems at multiple scales, and includes areas such as human/machine interaction, engineering mathematical models, assistive technologies, system modelling, design, testing and validation. The organization of ICHMS is based on the following Track types: Smart Applications for Digital Era, Computational Mathematical and Electronics, Intelligent Systems in Security and Communication Technologies, Technological Interventions using AI and Machine Learning, Applied Science, and IoT Techniques for Industries.

IBM SPSS Statistics 29 Step by Step: A Simple Guide and Reference

by Darren George Paul Mallery

IBM SPSS Statistics 29 Step by Step: A Simple Guide and Reference, eighteenth edition, takes a straightforward, step-by-step approach that makes SPSS software clear to beginners and experienced researchers alike.Extensive use of four-color screen shots, clear writing, and step-by-step boxes guide readers through the program. Output for each procedure is explained and illustrated, and every output term is defined. Exercises at the end of each chapter support students by providing additional opportunities to practice using SPSS. This book covers the basics of statistical analysis and addresses more advanced topics such as multidimensional scaling, factor analysis, discriminant analysis, measures of internal consistency, MANOVA (between- and within-subjects), cluster analysis, Log-linear models, logistic regression, and a chapter describing residuals. New to this edition is a new chapter on meta-analysis that describes new SPSS procedures for analyzing effect sizes across studies, and the content has been thoroughly updated in line with the latest version of the SPSS software, SPSS 29. The end sections include a description of data files used in exercises, an exhaustive glossary, suggestions for further reading, and a comprehensive index.Accompanied by updated online instructor’s materials and website data files, this is an essential resource for instructors and students needing a guide to using SPSS in their work, across the social sciences, behavioural sciences, education, and beyond.

IBM SPSS Statistics 29 Step by Step: A Simple Guide and Reference

by Darren George Paul Mallery

IBM SPSS Statistics 29 Step by Step: A Simple Guide and Reference, eighteenth edition, takes a straightforward, step-by-step approach that makes SPSS software clear to beginners and experienced researchers alike.Extensive use of four-color screen shots, clear writing, and step-by-step boxes guide readers through the program. Output for each procedure is explained and illustrated, and every output term is defined. Exercises at the end of each chapter support students by providing additional opportunities to practice using SPSS. This book covers the basics of statistical analysis and addresses more advanced topics such as multidimensional scaling, factor analysis, discriminant analysis, measures of internal consistency, MANOVA (between- and within-subjects), cluster analysis, Log-linear models, logistic regression, and a chapter describing residuals. New to this edition is a new chapter on meta-analysis that describes new SPSS procedures for analyzing effect sizes across studies, and the content has been thoroughly updated in line with the latest version of the SPSS software, SPSS 29. The end sections include a description of data files used in exercises, an exhaustive glossary, suggestions for further reading, and a comprehensive index.Accompanied by updated online instructor’s materials and website data files, this is an essential resource for instructors and students needing a guide to using SPSS in their work, across the social sciences, behavioural sciences, education, and beyond.

Image Analysis and Processing - ICIAP 2023 Workshops: Udine, Italy, September 11–15, 2023, Proceedings, Part II (Lecture Notes in Computer Science #14366)

by Gian Luca Foresti Andrea Fusiello Edwin Hancock

The two-volume set LNCS 14365 and 14366 constitutes the papers of workshops hosted by the 22nd International Conference on Image Analysis and Processing, ICIAP 2023, held in Udine, Italy, in September 2023.In total, 72 workshop papers and 10 industrial poster session papers have been accepted for publication. Part II of the set, volume 14366, contains 41 papers from the following workshops:– Medical Imaging Hub:• Artificial Intelligence and Radiomics in Computer-Aided Diagnosis (AIR-CAD)• Multi-Modal Medical Imaging Processing (M3IP)• Federated Learning in Medical Imaging and Vision (FedMed)– Digital Humanities Hub:• Artificial Intelligence for Digital Humanities (AI4DH)• Fine Art Pattern Extraction and Recognition (FAPER)• Pattern Recognition for Cultural Heritage (PatReCH)• Visual Processing of Digital Manuscripts: Workflows, Pipelines, BestPractices (ViDiScript)

Importance-Informed Reliability Engineering (Springer Series in Reliability Engineering)

by Hongyan Dui Shaomin Wu

This book provides university students and practitioners with a collection of importance measures to design systems with high reliability, maintain them with high availability, and restore them in case of failures. Optimal reliability design, properly system maintenance and resilience management are vital for retaining a high level of system availability. Reliability importance measures, which are used to identify the weakest components from different perspectives, can be used to achieve this goal. The book has seven parts. Chapter 1 introduces the basic concepts. Chapter 2 focuses on importance measures for the system design phase and introduces how the system reliability can be improved with importance measures. Chapters 3 and 4 provide importance measures-related methods for scheduling maintenance policies under different scenarios. Chapter 5 provides importance measures for networks. Chapter 6 proposes importance measures for resilience management. The last chapter, or Chapter 7, illustrates the importance measures with case studies adopted from four types of systems: mechanical systems, energy systems, transport networks, and supply chain networks.

Improper Riemann Integrals

by Ioannis Markos Roussos

The scope of this book is the improper or generalized Riemann integral and infinite sum (series). The reader will study its convergence, principal value, evaluation and application to science and engineering. Improper Riemann integrals and infinite sums are interconnected. In the new edition, the author has involved infinite sums more than he did in the first edition. Apart from having computed and listed a large number of improper integrals and infinite sums, we have also developed the necessary theory and various ways of evaluating them or proving their divergence. Questions, problems and applications involving various improper integrals and infinite sums (series) of numbers emerge in science and application very often. Their complete presentations and all rigorous proofs would require taking the graduate-level courses on these subjects. Here their statements are adjusted to a level students of all levels can understand and use them efficiently as powerful tools in a large list of problems and applications.

Improper Riemann Integrals

by Ioannis Markos Roussos

The scope of this book is the improper or generalized Riemann integral and infinite sum (series). The reader will study its convergence, principal value, evaluation and application to science and engineering. Improper Riemann integrals and infinite sums are interconnected. In the new edition, the author has involved infinite sums more than he did in the first edition. Apart from having computed and listed a large number of improper integrals and infinite sums, we have also developed the necessary theory and various ways of evaluating them or proving their divergence. Questions, problems and applications involving various improper integrals and infinite sums (series) of numbers emerge in science and application very often. Their complete presentations and all rigorous proofs would require taking the graduate-level courses on these subjects. Here their statements are adjusted to a level students of all levels can understand and use them efficiently as powerful tools in a large list of problems and applications.

In the Tradition of Thurston III: Geometry and Dynamics

by Ken’ichi Ohshika Athanase Papadopoulos

William Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The purpose of the present volume and of the other volumes in the same series is to provide a collection of articles that allows the reader to learn the important aspects of Thurston’s heritage. The topics covered in this volume include Kleinian groups, holomorphic motions, earthquakes from the Anti-de Sitter point of view, the Thurston and Weil–Petersson metrics on Teichmüller space, 3-manifolds, geometric structures, dynamics on surfaces, homeomorphism groups of 2-manifolds and the theory of orbifolds.

Incentive Mechanism for Mobile Crowdsensing: A Game-theoretic Approach (SpringerBriefs in Computer Science)

by Youqi Li Fan Li Song Yang Chuan Zhang

Mobile crowdsensing (MCS) is emerging as a novel sensing paradigm in the Internet of Things (IoTs) due to the proliferation of smart devices (e.g., smartphones, wearable devices) in people’s daily lives. These ubiquitous devices provide an opportunity to harness the wisdom of crowds by recruiting mobile users to collectively perform sensing tasks, which largely collect data about a wide range of human activities and the surrounding environment. However, users suffer from resource consumption such as battery, processing power, and storage, which discourages users’ participation. To ensure the participation rate, it is necessary to employ an incentive mechanism to compensate users’ costs such that users are willing to take part in crowdsensing. This book sheds light on the design of incentive mechanisms for MCS in the context of game theory. Particularly, this book presents several game-theoretic models for MCS in different scenarios. In Chapter 1, the authors present an overview of MCS and state the significance of incentive mechanism for MCS. Then, in Chapter 2, 3, 4, and 5, the authors propose a long-term incentive mechanism, a fair incentive mechanism, a collaborative incentive mechanism, and a coopetition-aware incentive mechanism for MCS, respectively. Finally, Chapter 6 summarizes this book and point out the future directions. This book is of particular interest to the readers and researchers in the field of IoT research, especially in the interdisciplinary field of network economics and IoT.

Industry 4.0 Technologies: Volume II - Methods for transition and trends (Environmental Footprints and Eco-design of Products and Processes)

by K. E. K. Vimal Sonu Rajak Vikas Kumar Rahul S. Mor Almoayied Assayed

This book covers topics related to implementation of advanced technologies, such as AI, big data, procurement 4.0, Logistics 4.0 and Lean 4.0, in Industry 4.0 for the manufacturing supply chain. Many applications of Industry 4.0 in the manufacturing supply chain have been presented. The content of this book is useful for students, researchers and professionals in order to implement Industry 4.0 in manufacturing supply chain.

Industry 4.0 Technologies: Volume 1—Theory, Challenges, and Opportunity (Environmental Footprints and Eco-design of Products and Processes)

by K E K Vimal Sonu Rajak Vikas Kumar Rahul S. Mor Almoayied Assayed

This book brings forth the fundamental understanding of the role of Industry 4.0 technologies in sustainable manufacturing supply chain. Readers will get an overview of the challenges, opportunities, and requirements for the implementation of digital technologies and how they can support manufacturing supply chains to be sustainable. The book presents many applications of Industry 4.0 including integration of IoT, AI, Big Data, Blockchain, Procurement 4.0, Logistics 4.0, and Lean 4.0 in different contexts. The book therefore provides a platform for researchers, academicians, and professionals from diverse backgrounds to gain state-of-the-art knowledge for using Industry 4.0 in sustainable manufacturing supply chains. Readers will also be able to identify the practical significance and opportunities for future work directions.

Infinite Group Actions on Polyhedra (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics #77)

by Michael W. Davis

In the past fifteen years, the theory of right-angled Artin groups and special cube complexes has emerged as a central topic in geometric group theory. This monograph provides an account of this theory, along with other modern techniques in geometric group theory. Structured around the theme of group actions on contractible polyhedra, this book explores two prominent methods for constructing such actions: utilizing the group of deck transformations of the universal cover of a nonpositively curved polyhedron and leveraging the theory of simple complexes of groups. The book presents various approaches to obtaining cubical examples through CAT(0) cube complexes, including the polyhedral product construction, hyperbolization procedures, and the Sageev construction. Moreover, it offers a unified presentation of important non-cubical examples, such as Coxeter groups, Artin groups, and groups that act on buildings. Designed as a resource for graduate students and researchers specializing in geometric group theory, this book should also be of high interest to mathematicians in related areas, such as 3-manifolds.

Informatik auf den Punkt gebracht: Informatik für Life Sciences Studierende und andere Nicht-Informatiker

by Boris Tolg

Dieses Lehrbuch richtet sich an Studierende von fachfremden Studiengängen mit Informatikanteilen. Ein besonderer Schwerpunkt liegt dabei auf den sogenannten Lebenswissenschaften, wie Medizintechnik, Rettungsingenieurwesen, Biotechnologie, Umwelttechnik oder Verfahrenstechnik. Das Lehrbuch eignet sich für Leser in Studium und Praxis, die sich einen Einstieg in die Informatik verschaffen wollen. Die Besonderheit dieses Buches liegt in der problembasierten Herangehensweise, sowie der nach verschiedenen Taxonomiestufen konzipierten Übungsaufgaben.

Information-Powered Engines (Springer Theses)

by Tushar Kanti Saha

This book presents the experimental development of an information-powered engine inspired by the famous thought experiment, Maxwell’s demon, to understand its potential to produce energy for practical purposes. The development of an engine based on Maxwell’s demon was for a long time inconceivable, but technological advances have led to novel investigations into theoretical and practical applications. The built information engine consists of a micron-sized glass bead trapped in a tightly focused laser beam. It rectifies the bead's Brownian motion by controlling the laser's position and generates a unidirectional motion against gravity without doing any work, thus converting thermal heat into stored gravitational potential energy. A theoretical model based on a spring-mass system describes the engine's dynamics and was then used to find optimum parameters to improve the engine's performance. Experimentally implementing these optimization strategies led to engine output powers comparable to those measured in biological motors. This book also highlights performance improvements made in the presence of measurement noise and presents important guiding principles to design information engines to operate in non-equilibrium environments. By focusing on practical applications, the book overall aims to broaden the scope of information-engine investigations.

Information Systems: 20th European, Mediterranean, and Middle Eastern Conference, EMCIS 2023, Dubai, United Arab Emirates, December 11-12, 2023, Proceedings, Part I (Lecture Notes in Business Information Processing #501)

by Maria Papadaki Marinos Themistocleous Khalid Al Marri Marwan Al Zarouni

This book constitutes selected papers from the 20th European, Mediterranean, and Middle Eastern Conference, EMCIS 2023, which was held in Dubai, UAE, during December 11-12, 2023. EMCIS covers technical, organizational, business, and social issues in the application of information technology and is dedicated to the definition and establishment of Information Systems (IS) as a discipline of high impact for IS professionals and practitioners. It focuses on approaches that facilitate the identification of innovative research of significant relevance to the IS discipline following sound research methodologies that lead to results of measurable impact. The 43 papers presented in this volume were carefully reviewed and selected from a total of 126 submissions. They were organized in topical sections as follows: Part I: Metaverse; blockchain technology and applications; digital governance; healthcare information systems; artificial intelligence; Part II: Big data and analytics; digital services and social media; innovative research projects; managing information systems; smart cities.

Information Systems: 20th European, Mediterranean, and Middle Eastern Conference, EMCIS 2023, Dubai, United Arab Emirates, December 11-12, 2023, Proceedings, Part II (Lecture Notes in Business Information Processing #502)

by Marinos Themistocleous Khalid Al Marri Maria Papadaki Marwan Al Zarouni

This book constitutes selected papers from the 20th European, Mediterranean, and Middle Eastern Conference, EMCIS 2023, which was held in Dubai, UAE, during December 11-12, 2023. EMCIS covers technical, organizational, business, and social issues in the application of information technology and is dedicated to the definition and establishment of Information Systems (IS) as a discipline of high impact for IS professionals and practitioners. It focuses on approaches that facilitate the identification of innovative research of significant relevance to the IS discipline following sound research methodologies that lead to results of measurable impact. The 43 papers presented in this volume were carefully reviewed and selected from a total of 126 submissions. They were organized in topical sections as follows: Part I: Metaverse; blockchain technology and applications; digital governance; healthcare information systems; artificial intelligence; Part II: Big data and analytics; digital services and social media; innovative research projects; managing information systems; smart cities.

Information Theory for Complex Systems: An Information Perspective on Complexity in Dynamical Systems and Statistical Mechanics (Understanding Complex Systems)

by Kristian Lindgren

This book introduces a comprehensive framework tailored for dissecting complex systems across diverse disciplines. What defines a complex system? How can we harness information to quantify its order, structure, and intricacy? Delving into phenomena from the intricate processes in physical systems to the dynamic behaviours in cellular automata and pattern formation, readers will uncover the profound interplay between physics and information theory. This intricate relationship provides fresh insight into physical phenomena, reimagining them through the lens of information. Notably, the book demystifies how seemingly opposing forces—rising order and increasing disorder—coexist, ultimately shedding light on the second law of thermodynamics as an outcome of deterministic, reversible dynamics beneath the surface. Geared towards graduate students, this book presumes an undergraduate foundation in mathematics and physics, ensuring a deep, engaging exploration for its readers.

Infrared Small Target Detection: Theory, Methods, and Algorithms.

by Hu Zhu Yushan Pan Lizhen Deng Guoxia Xu

Uncover the secrets of cutting-edge research in “Infrared Small Target Detection,” a crucial resource that delves into the dynamic world of infrared imaging and detection algorithms. This comprehensive book is an indispensable gem for the research community, offering a profound introduction to the theory, methods, and algorithms underlying infrared small object detection. As an invaluable guide, this book explores diverse models and categories of infrared small object detection algorithms, providing meticulous descriptions and comparisons of their strengths and limitations. Perfectly tailored for researchers, practitioners, and students with a passion for infrared imaging and detection, this book equips readers with the necessary knowledge to embark on groundbreaking investigations in this field.Readers can particularly be drawn to the book's methods, results, and topics, encompassing diverse categories of infrared small object detection algorithms and their corresponding advantages and disadvantages. The book also imparts foundational knowledge in mathematical morphology, tensor decomposition, and deep learning, enabling readers to grasp the underlying principles of these advanced algorithms. Experience the key benefits of “Infrared Small Target Detection” as readers gain a profound understanding of theory, methods, and algorithms tailored to infrared small object detection. The comprehensive descriptions and comparisons of various algorithm categories empower readers to select the perfect algorithms for their specific applications. Unlock the potential of this groundbreaking resource with a basic understanding of mathematics, statistics, and image processing. Some familiarity with infrared imaging and detection proves advantageous in fully immersing oneself in the wealth of knowledge presented within these pages.

Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik: (AMS-219) (Annals of Mathematics Studies #215)

by Camillo De Lellis Elia Brué Dallas Albritton Maria Colombo Vikram Giri Maximilian Janisch Hyunju Kwon

An essential companion to M. Vishik&’s groundbreaking work in fluid mechanicsThe incompressible Euler equations are a system of partial differential equations introduced by Leonhard Euler more than 250 years ago to describe the motion of an inviscid incompressible fluid. These equations can be derived from the classical conservations laws of mass and momentum under some very idealized assumptions. While they look simple compared to many other equations of mathematical physics, several fundamental mathematical questions about them are still unanswered. One is under which assumptions it can be rigorously proved that they determine the evolution of the fluid once we know its initial state and the forces acting on it. This book addresses a well-known case of this question in two space dimensions. Following the pioneering ideas of M. Vishik, the authors explain in detail the optimality of a celebrated theorem of V. Yudovich from the 1960s, which states that, in the vorticity formulation, the solution is unique if the initial vorticity and the acting force are bounded. In particular, the authors show that Yudovich&’s theorem cannot be generalized to the L^p setting.

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