This contemporary first course focuses on concepts and ideas of Measure Theory, highlighting the theoretical side of the subject. Its primary intention is to introduce Measure Theory to a new generation of students, whether in mathematics or in one of the sciences, by offering them on the one hand a text with complete, rigorous and detailed proofs--sketchy proofs have been a perpetual complaint, as demonstrated in the many Amazon reader reviews critical of authors who "omit 'trivial' steps" and "make not-so-obvious 'it is obvious' remarks." On the other hand, Kubrusly offers a unique collection of fully hinted problems. On the other hand, Kubrusly offers a unique collection of fully hinted problems. The author invites the readers to take an active part in the theory construction, thereby offering them a real chance to acquire a firmer grasp on the theory they helped to build. These problems, at the end of each chapter, comprise complements and extensions of the theory, further examples and counterexamples, or auxiliary results. They are an integral part of the main text, which sets them apart from the traditional classroom or homework exercises.
JARGON BUSTER:
measure theory
Measure theory investigates the conditions under which integration can take place.
It considers various ways in which the "size" of a set can be estimated.
This topic is studied in pure mathematics programs but the theory is also foundational for students of statistics and probability, engineering, and financial engineering.
Key Features
* Designed with a minimum of prerequisites (intro analysis, and for Ch 5, linear algebra)
* Includes 140 classical measure-theory problems
* Carefully crafted to present essential elements of the theory in compact form

The book consists of high-quality papers presented at the International Conference on Computational Science and Applications (ICCSA 2019), held at Maharashtra Institute of Technology World Peace University, Pune, India, from 7 to 9 August 2019. It covers the latest innovations and developments in information and communication technology, discussing topics such as soft computing and intelligent systems, web of sensor networks, drone operating systems, web of sensor networks, wearable smart sensors, automated guided vehicles and many more.

This book describes the variety of direct and indirect population size estimation (PSE) methods available along with their strengths and weaknesses. Direct estimation methods, such as enumeration and mapping, involve contact with members of hard-to-reach groups. Indirect methods have practical appeal because they require no contact with members of hard-to-reach groups. One indirect method in particular, network scale-up (NSU), has several strengths over other PSE methods: It can be applied at a province/country level, it can estimate size of several hard-to-reach population in a single study, and it is implemented with members of the general population rather than members of hard-to-reach groups. The book discusses methods to collect, analyze, and adjust results and presents methods to triangulate and finalize PSEs.

This book concerns issues related to biomathematics, medicine, or cybernetics as practiced by engineers. Considered population dynamics models are still in the interest of researchers, and even this interest is increasing, especially now in the time of SARS-CoV-2 coronavirus pandemic, when models are intensively studied in order to help predict its behaviour within human population. The structures of population dynamics models and practical methods of finding their solutions are discussed. Finally, the hypothesis of the existence of non-trivial ergodic properties of the model of erythropoietic response dynamics formulated by A. Lasota in the form of delay differential equation with unimodal feedback is analysed. The research can be compared with actual medical data, as well as shows that the structures of population models can reflect the dynamic structures of reality.

This book illustrates the powerful interplay between topological, algebraic and complex analytical methods, within the field of integrable systems, by addressing several theoretical and practical aspects. Contemporary integrability results, discovered in the last few decades, are used within different areas of mathematics and physics. Integrable Systems incorporates numerous concrete examples and exercises, and covers a wealth of essential material, using a concise yet instructive approach. This book is intended for a broad audience, ranging from mathematicians and physicists to students pursuing graduate, Masters or further degrees in mathematics and mathematical physics. It also serves as an excellent guide to more advanced and detailed reading in this fundamental area of both classical and contemporary mathematics.

This book contains high-quality papers presented at the First International Forum on Financial Mathematics and Financial Technology. With the rapid development of FinTech, the in-depth integration between mathematics, finance and advanced technology is the general trend. This book focuses on selected aspects of the current and upcoming trends in FinTech. In detail, the included scientific papers focus on financial mathematics and FinTech, presenting the innovative mathematical models and state-of-the-art technologies such as deep learning, with the aim to improve our financial analysis and decision-making and enhance the quality of financial services and risk control. The variety of the papers delivers added value for both scholars and practitioners where they will find perfect integration of elegant mathematical models and up-to-date data mining technologies in financial market analysis.

Mathematical Problems for Chemistry Students has been compiled and written (a) to help chemistry
students in their mathematical studies by providing them with mathematical problems really occurring in chemistry (b) to help practising chemists to activate their applied mathematical skills and (c) to introduce students and specialists
of the chemistry-related fields (physicists, mathematicians, biologists, etc.) into
the world of the chemical applications.
Some problems of the collection are mathematical reformulations of those in the standard textbooks of chemistry, others were taken from theoretical chemistry journals. All major fields of chemistry are covered, and each problem is given a solution.
This problem collection is intended for beginners and users at an intermediate level. It can be used as a companion to virtually all textbooks dealing with scientific and engineering mathematics or specifically mathematics for chemists.
* Covers a wide range of applications of the most essential tools in applied mathematics
* A new approach to a number of classical textbook-problems
* A number of non-classical problems are included

The maturity of BEM over the last few decades has resulted in a substantial number of industrial applications of the method; this demonstrates its accuracy, robustness and ease of use. The range of applications still needs to be widened, taking into account the potentialities of the Mesh Reduction techniques in general. Theoretical developments and new formulations have been reported over the last few decades, helping to expand the range of boundary elements and other mesh reduction methods (BEM/MRM) applications as well as the type of modelled materials in response to the requirements of contemporary industrial and professional environments. As design, analysis and manufacture become more integrated, the chances are that software users will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily within the aforementioned integrated process. The papers included were presented at the 44th International Conference on Boundary Elements and other Mesh Reduction Methods and report advances in techniques that reduce or eliminate the type of meshes associated with finite elements or finite differences.

This book provides a comprehensive overview of statistical descriptions of turbulent flows. Its main objectives are to point out why ordinary perturbative treatments of the Navier-Stokes equation have been rather futile, and to present recent advances in non-perturbative treatments, e.g., the instanton method and a stochastic interpretation of turbulent energy transfer. After a brief introduction to the basic equations of turbulent fluid motion, the book outlines a probabilistic treatment of the Navier-Stokes equation and chiefly focuses on the emergence of a multi-point hierarchy and the notion of the closure problem of turbulence. Furthermore, empirically observed multiscaling features and their impact on possible closure methods are discussed, and each is put into the context of its original field of use, e.g., the renormalization group method is addressed in relation to the theory of critical phenomena. The intended readership consists of physicists and engineers who want to get acquainted with the prevalent concepts and methods in this research area.

This book describes the advanced stability theories for magnetically confined fusion plasmas, especially in tokamaks. As the fusion plasma sciences advance, the gap between the textbooks and cutting-edge researches gradually develops.

This book brings together papers presented at the International Conference on Artificial Intelligence in China (ChinaAI) 2019, which provided a venue for disseminating the latest advances and discussing the interactions and links between the various subfields of AI. Addressing topics that cover virtually all aspects of AI and the latest developments in China, the book is chiefly intended for undergraduate and graduate students in Electrical Engineering, Computer Science, and Mathematics, for researchers and engineers from academia and industry, and for government employees (e.g. at the NSF, DOD, and DOE).

This book focuses on gyro-free inertial navigation technology, which is used to measure not only linear motion parameters but also angular rates. Since no gyroscopes are used, the key technologies, such as initial alignment, attitude resolution, and error calibration, are very different than those used in traditional methods. Discussing each key technology in gyro-free inertial navigation system (GFINS) manufacture in a separate chapter, the book features easy-to-understand, detailed illustrations, to allow all those involved in inertial navigation to gain a better grasp of GFINS manufacture, including accelerometer setting principles; initial alignment; quaternion-based, attitude resolution algorithms; and accelerometer de-noise methods.

The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems.
- New Views for Difficult Problems
- Novel Ideas and Concepts
- Hilbert's 16th Problem
- Normal Forms in Polynomial Hamiltonian Systems
- Grazing Flow in Non-smooth Dynamical Systems
- Stochastic and Fuzzy Nonlinear Dynamical Systems
- Fuzzy Bifurcation
- Parametrical, Nonlinear Systems
- Mode Interactions in nonlinear dynamical systems

This book is devoted to an important branch of the dynamical systems theory: the study of the fine (fractal) structure of Poincare recurrences -instants of time when the system almost repeats its initial state. The authors were able to write an entirely self-contained text including many insights and examples, as well as providing complete details of proofs. The only prerequisites are a basic knowledge of analysis and topology. Thus this book can serve as a graduate text or self-study guide for courses in applied mathematics or nonlinear dynamics (in the natural sciences). Moreover, the book can be used by specialists in applied nonlinear dynamics following the way in the book. The authors applied the mathematical theory developed in the book to two important problems: distribution of Poincare recurrences for nonpurely chaotic Hamiltonian systems and indication of synchronization regimes in coupled chaotic individual systems.

* Portions of the book were published in an article that won the title "month's new hot paper in the field of Mathematics" in May 2004
* Rigorous mathematical theory is combined with important physical applications
* Presents rules for immediate action to study mathematical models of real systems
* Contains standard theorems of dynamical systems theory

This book provides an in-depth analysis of the current evolutionary machine learning techniques. Discussing the most highly regarded methods for classification, clustering, regression, and prediction, it includes techniques such as support vector machines, extreme learning machines, evolutionary feature selection, artificial neural networks including feed-forward neural networks, multi-layer perceptron, probabilistic neural networks, self-optimizing neural networks, radial basis function networks, recurrent neural networks, spiking neural networks, neuro-fuzzy networks, modular neural networks, physical neural networks, and deep neural networks. The book provides essential definitions, literature reviews, and the training algorithms for machine learning using classical and modern nature-inspired techniques. It also investigates the pros and cons of classical training algorithms. It features a range of proven and recent nature-inspired algorithms used to train different types of artificial neural networks, including genetic algorithm, ant colony optimization, particle swarm optimization, grey wolf optimizer, whale optimization algorithm, ant lion optimizer, moth flame algorithm, dragonfly algorithm, salp swarm algorithm, multi-verse optimizer, and sine cosine algorithm. The book also covers applications of the improved artificial neural networks to solve classification, clustering, prediction and regression problems in diverse fields.

This book presents the state of the art in the relatively new field of dynamic economic modelling with regime switches. The contributions, written by prominent scholars in the field, focus on dynamic decision problems with regime changes in underlying dynamics or objectives. Such changes can be externally driven or internally induced by decisions. Utilising the most advanced mathematical methods in optimal control and dynamic game theory, the authors address a broad range of topics, including capital accumulation, innovations, financial decisions, population economics, environmental and resource economics, institutional change and the dynamics of addiction. Given its scope, the book will appeal to all scholars interested in mathematical and quantitative economics.

Recent advances in scientific computing have caused the field of aerodynamics to change at a rapid pace, simplifying the design cycle of aerospace vehicles enormously - this book takes the readers from core concepts of aerodynamics to recent research, using studies and real-life scenarios to explain problems and their solutions. This book presents in detail the important concepts in computational aerodynamics and aeroacoustics taking readers from the fundamentals of fluid flow and aerodynamics to a more in-depth analysis of acoustic waves, aeroacoustics, computational modelling and processing. This book will be of use to students in multiple branches of engineering, physics and applied mathematics. Additionally, the book can also be used as a text in professional development courses for industry engineers and as a self-help reference for active researchers in both academia and the industry.

Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.

This PhD thesis is dedicated to a subfield of elementary particle physics called "Flavour Physics". The Standard Model of Particle Physics (SM) has been confirmed by thousands of experimental measurements with a high precision. But the SM leaves important questions open, like what is the nature of dark matter or what is the origin of the matter-antimatter asymmetry in the Universe. By comparing high precision Standard Model calculations with extremely precise measurements, one can find the first glimpses of the physics beyond the SM - currently we see the first hints of a potential breakdown of the SM in flavour observables. This can then be compared with purely theoretical considerations about new physics models, known as model building. Both precision calculations and model building are extremely specialised fields and this outstanding thesis contributes significantly to both topics within the field of Flavour Physics and sheds new light on the observed anomalies.

This PhD thesis documents two of the highest-profile searches for supersymmetry performed at the ATLAS experiment using up to 80/fb of proton-proton collision data at a center-of-mass energy of 13 TeV delivered by the Large Hadron Collider (LHC) during its Run 2 (2015-2018). The signals of interest feature a high multiplicity of jets originating from the hadronisation of b-quarks and large missing transverse momentum, which constitutes one of the most promising final state signatures for discovery of new phenomena at the LHC. The first search is focused on the strong production of a pair of gluinos, with each gluino decaying into a neutralino and a top-antitop-quark pair or a bottom-antibottom-quark pair. The second search targets the pair production of higgsinos, with each higgsino decaying into a gravitino and a Higgs boson, which in turn is required to decay into a bottom-antibottom-quark pair. Both searches employ state-of-the-art experimental techniques and analysis strategies at the LHC, resulting in some of the most restrictive bounds available to date on the masses of the gluino,neutralino, and higgsino in the context of the models explored.

This book provides novel concepts and techniques for air traffic management (ATM) and communications, navigation, and surveillance (CNS) systems. The book consists of selected papers from the 6th ENRI International Workshop on ATM/CNS (EIWAC2019) held in Tokyo in October 2019, the theme of which was "Exploring Ideas for World Aviation Challenges". Included are key topics to realize safer and more efficient skies in the future, linked to the integrated conference theme consisting of long-term visions based on presentations from various fields. The book is dedicated not only to researchers, academicians, and university students, but also to engineers in the industry, air navigation service providers (ANSPs), and regulators of aviation.

This is the first English translation of Launhardt's Mathematische Begrundung der Volkswirtschaftslehre (1885), a major contribution to neoclassical economic theory which contains many important and original analyses. This edition will provide the basis for a re-evaluation of Launhardt's outstanding, but undervalued, contribution to economics. Taking the neoclassical emphasis on exchange as the central economic problem, Laundardt begins with a thorough treatment of the pure exchange model, then goes on to extend the treatment to the production of goods and the supply of labour, with a sophisticated general equilibrium perspective. It contains important analyses of savings and the role of capital goods, as well as an outstanding study of transport and the location of industry. Launhardt's book can, with justice, with be described as the first comprehensive treatise on welfare economics. Mathematical Principles of Economics will prove stimulating reading for economic theorists as well as those interested in the history of economics thought.

This book brings together ideas from experts in cognitive science, mathematics, and mathematics education to discuss these issues and to present research on how mathematics and its learning and teaching are evolving in the Information Age. Given the ever-broadening trends in Artificial Intelligence and the processing of information generally, the aim is to assess their implications for how math is evolving and how math should now be taught to a generation that has been reared in the Information Age. It will also look at the ever-spreading assumption that human intelligence may not be unique-an idea that dovetails with current philosophies of mind such as posthumanism and transhumanism. The role of technology in human evolution has become critical in the contemporary world. Therefore, a subgoal of this book is to illuminate how humans now use their sophisticated technologies to chart cognitive and social progress. Given the interdisciplinary nature of the chapters, this will be of interest to all kinds of readers, from mathematicians themselves working increasingly with computer scientists, to cognitive scientists who carry out research on mathematics cognition and teachers of mathematics in a classroom.