This book, featuring a truly interdisciplinary approach, provides an overview of cutting-edge mathematical theories and techniques that promise to play a central role in climate science. It brings together some of the most interesting overview lectures given by the invited speakers at an important workshop held in Rome in 2013 as a part of MPE2013 ("Mathematics of Planet Earth 2013"). The aim of the workshop was to foster the interaction between climate scientists and mathematicians active in various fields linked to climate sciences, such as dynamical systems, partial differential equations, control theory, stochastic systems, and numerical analysis. Mathematics and statistics already play a central role in this area. Likewise, computer science must have a say in the efforts to simulate the Earth's environment on the unprecedented scale of petabytes. In the context of such complexity, new mathematical tools are needed to organize and simplify the approach. The growing importance of data assimilation techniques for climate modeling is amply illustrated in this volume, which also identifies important future challenges.

This book is based on lectures given at the first edition of the Domoschool, the International Alpine School in Mathematics and Physics, held in Domodossola, Italy, in July 2018. It is divided into two parts. Part I consists of four sets of lecture notes. These are extended versions of lectures given at the Domoschool, written by well-known experts in mathematics and physics related to General Relativity. Part II collects talks by selected participants, focusing on research related to General Relativity.

This book is the first part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton's research. Each article is accompanied by comments from an expert on the respective topic, which serves to situate the article in its proper context, to successfully link past, present and hopefully future developments of the theory, and to help readers grasp the extent of Kalton's accomplishments. Kalton's work represents a bridge to the mathematics of tomorrow, and this book will help readers to cross it. Nigel Kalton (1946-2010) was an extraordinary mathematician who made major contributions to an amazingly diverse range of fields over the course of his career.

This book provides a comprehensive introduction to numerical modeling of size effects in metal plasticity. The main classes of strain gradient plasticity formulations are described and efficiently implemented in the context of the finite element method. A robust numerical framework is presented and employed to investigate the role of strain gradients on structural integrity assessment. The results obtained reveal the need of incorporating the influence on geometrically necessary dislocations in the modeling of various damage mechanisms. Large gradients of plastic strain increase dislocation density, promoting strain hardening and elevating crack tip stresses. This stress elevation is quantified under both infinitesimal and finite deformation theories, rationalizing the experimental observation of cleavage fracture in the presence of significant plastic flow. Gradient-enhanced modeling of crack growth resistance, hydrogen diffusion and environmentally assisted cracking highlighted the relevance of an appropriate characterization of the mechanical response at the small scales involved in crack tip deformation. Particularly promising predictions are attained in the field of hydrogen embrittlement. The research has been conducted at the Universities of Cambridge, Oviedo, Luxembourg, and the Technical University of Denmark, in a collaborative effort to understand, model and optimize the mechanical response of engineering materials.

This book outlines a possible future theoretical perspective for systemics, its conceptual morphology and landscape while the Good-Old-Fashioned-Systemics (GOFS) era is still under way. The change from GOFS to future systemics can be represented, as shown in the book title, by the conceptual change from Collective Beings to Quasi-systems. With the current advancements, problems and approaches occurring in contemporary science, systemics are moving beyond the traditional frameworks used in the past. From Collective Beings to Coherent Quasi-Systems outlines a conceptual morphology and landscape for a new theoretical perspective for systemics introducing the concept of Quasi-systems. Advances in domains such as theoretical physics, philosophy of science, cell biology, neuroscience, experimental economics, network science and many others offer new concepts and technical tools to support the creation of a fully transdisciplinary General Theory of Change. This circumstance requires a deep reformulation of systemics, without forgetting the achievements of established conventions. The book is divided into two parts. Part I, examines classic systemic issues from new theoretical perspectives and approaches. A new general unified framework is introduced to help deal with topics such as dynamic structural coherence and Quasi-systems. This new theoretical framework is compared and contrasted with the traditional approaches. Part II focuses on the process of translation into social culture of the theoretical principles, models and approaches introduced in Part I. This translation is urgent in post-industrial societies where emergent processes and problems are still dealt with by using the classical or non-systemic knowledge of the industrial phase.

This thesis reports a rare combination of experiment and theory on the role of geometry in materials science. It is built on two significant findings: that curvature can be used to guide crack paths in a predictive way, and that protected topological order can exist in amorphous materials. In each, the underlying geometry controls the elastic behavior of quasi-2D materials, enabling the control of crack propagation in elastic sheets and the control of unidirectional waves traveling at the boundary of metamaterials. The thesis examines the consequences of this geometric control in a range of materials spanning many orders of magnitude in length scale, from amorphous macroscopic networks and elastic continua to nanoscale lattices.

This book helps students, researchers and quantitative finance practitioners to understand both basic and advanced topics in the valuation and modeling of financial and commodity derivatives, their institutional framework and risk management. It provides an overview of the new regulatory requirements such as Basel III, the Fundamental Review of the Trading Book (FRTB), Interest Rate Risk of the Banking Book (IRRBB), or the Internal Capital Assessment Process (ICAAP). The reader will also find a detailed treatment of counterparty credit risk, stochastic volatility estimation methods such as MCMC and Particle Filters, and the concepts of model-free volatility, VIX index definition and the related volatility trading. The book can also be used as a teaching material for university derivatives and financial engineering courses.

This book is a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: ``Integrable Systems'' and ``Quantum Theories and Algebraic Geometry'', reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

This book focuses on the study of the interfacial water using molecular dynamics simulation and experimental sum frequency generation spectroscopy. It proposes a new definition of the free O-H groups at water-air interface and presents research on the structure and dynamics of these groups. Furthermore, it discusses the exponential decay nature of the orientation distribution of the free O-H groups of interfacial water and ascribes the origin of the down pointing free O-H groups to the presence of capillary waves on the surface. It also describes how, based on this new definition, a maximum surface H-bond density of around 200 K at ice surface was found, as the maximum results from two competing effects. Lastly, the book discusses the absorption of water molecules at the water-TiO2 interface. Providing insights into the combination of molecular dynamics simulation and experimental sum frequency generation spectroscopy, it is a valuable resource for researchers in the field.

This thesis describes the application of a Monte Carlo radiative transfer code to accretion disc winds in two types of systems spanning 9 orders of magnitude in mass and size. In both cases, the results provide important new insights. On small scales, the presence of disc winds in accreting white dwarf binary systems has long been inferred from the presence of ultraviolet absorption lines. Here, the thesis shows that the same winds can also produce optical emission lines and a recombination continuum. On large scales, the thesis constructs a simple model of disc winds in quasars that is capable of explaining both the observed absorption and emission signatures - a crucial advance that supports a disc-wind based unification scenario for quasars. Lastly, the thesis also includes a theoretical investigation into the equivalent width distribution of the emission lines in quasars, which reveals a major challenge to all unification scenarios.

The book provides a state-of-art overview of computational methods for nonlinear aeroelasticity and load analysis, focusing on key techniques and fundamental principles for CFD/CSD coupling in temporal domain. CFD/CSD coupling software design and applications of CFD/CSD coupling techniques are discussed in detail as well. It is an essential reference for researchers and students in mechanics and applied mathematics.

This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field.

This monograph studies optimization problems for rigid punches in elastic media and for high-speed penetration of rigid strikers into deformed elastoplastic, concrete, and composite media using variational calculations, tools from functional analysis, and stochastic and min-max (guaranteed) optimization approaches with incomplete data. The book presents analytical and numerical results developed by the authors during the last ten years.

This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.

This book was written to serve as a graduate-level textbook for special topics classes in mathematics, statistics, and economics, to introduce these topics to other researchers, and for use in short courses. It is an introduction to the theory of majorization and related notions, and contains detailed material on economic applications of majorization and the Lorenz order, investigating the theoretical aspects of these two interrelated orderings. Revising and expanding on an earlier monograph, Majorization and the Lorenz Order: A Brief Introduction, the authors provide a straightforward development and explanation of majorization concepts, addressing historical development of the topics, and providing up-to-date coverage of families of Lorenz curves. The exposition of multivariate Lorenz orderings sets it apart from existing treatments of these topics. Mathematicians, theoretical statisticians, economists, and other social scientists who already recognize the utility of the Lorenz order in income inequality contexts and arenas will find the book useful for its sound development of relevant concepts rigorously linked to both the majorization literature and the even more extensive body of research on economic applications. Barry C. Arnold, PhD, is Distinguished Professor in the Statistics Department at the University of California, Riverside. He is a Fellow of the American Statistical Society, the American Association for the Advancement of Science, and the Institute of Mathematical Statistics, and is an elected member of the International Statistical Institute. He is the author of more than two hundred publications and eight books. Jose Maria Sarabia, PhD, is Professor of Statistics and Quantitative Methods in Business and Economics in the Department of Economics at the University of Cantabria, Spain. He is author of more than one hundred and fifty publications and ten books and is an associate editor of several journals including TEST, Communications in Statistics, and Journal of Statistical Distributions and Applications.

This monograph describes advances in the theory of extremal problems in classes of functions defined by a majorizing modulus of continuity w. In particular, an extensive account is given of structural, limiting, and extremal properties of perfect w-splines generalizing standard polynomial perfect splines in the theory of Sobolev classes. In this context special attention is paid to the qualitative description of Chebyshev w-splines and w-polynomials associated with the Kolmogorov problem of n-widths and sharp additive inequalities between the norms of intermediate derivatives in functional classes with a bounding modulus of continuity. Since, as a rule, the techniques of the theory of Sobolev classes are inapplicable in such classes, novel geometrical methods are developed based on entirely new ideas. The book can be used profitably by pure or applied scientists looking for mathematical approaches to the solution of practical problems for which standard methods do not work. The scope of problems treated in the monograph, ranging from the maximization of integral functionals, characterization of the structure of equimeasurable functions, construction of Chebyshev splines through applications of fixed point theorems to the solution of integral equations related to the classical Euler equation, appeals to mathematicians specializing in approximation theory, functional and convex analysis, optimization, topology, and integral equations

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This thesis describes pioneering research on the extension of plasmonics schemes to the regime of high-intensity lasers. By presenting a rich and balanced mix of experimentation, theory and simulation, it provides a comprehensive overview of the emerging field of high field plasmonics, including open issues and perspectives for future research. Combining specially designed targets and innovative materials with ultrashort, high-contrast laser pulses, the author experimentally demonstrates the effects of plasmon excitation on electron and ion emission. Lastly, the work investigates possible further developments with the help of numerical simulations, revealing the potential of plasmonics effects in the relativistic regime for advances in laser-driven sources of radiation, and for the manipulation of extreme light at the sub-micron scale.

This book gathers outstanding papers on numerical modeling in Mechanical Engineering (Volume 2) as part of the proceedings of the 1st International Conference on Numerical Modeling in Engineering (NME 2018), which was held in Ghent, Belgium. The overall objective of the conference was to bring together international scientists and engineers in academia and industry from fields related to advanced numerical techniques, such as the finite element method (FEM), boundary element method (BEM), isogeometric analysis (IGA), etc., and their applications to a wide range of engineering disciplines. This book addresses various industrial engineering applications of numerical simulations to Mechanical and Materials Engineering, including: Aerospace applications, Acoustic analysis, Biomechanical applications, Contact problems and wear, Heat transfer analysis, Vibration and dynamics, Transient analysis, Nonlinear analysis, Composite materials, Polymers, Metal alloys, Fracture mechanics, Fatigue of materials, Creep behavior, Phase transformation, and Crystal plasticity.

This book focuses on the finite-time control of attitude stabilization, attitude tracking for individual spacecraft, and finite-time control of attitude synchronization. It discusses formation reconfiguration for multiple spacecraft in complex networks, and provides a new fast nonsingular terminal sliding mode surface (FNTSMS). Further, it presents newly designed controllers and several control laws to enhance the performance of spacecraft systems and meet related demands, such as strong disturbance rejection and high-precision control. As such, the book establishes a fundamental framework for these topics, while also highlighting the importance of integrated analysis. It is a useful resource for all researchers and students who are interested in this field, as well as engineers whose work involves designing flight vehicles.

This book addresses a broad range of problems commonly encountered in the fields of financial analysis, logistics and supply chain management, such as the use of big data analytics in the banking sector. Divided into twenty chapters, some of the contemporary topics discussed in the book are co-operative/non-cooperative supply chain models for imperfect quality items with trade-credit financing; a non-dominated sorting water cycle algorithm for the cardinality constrained portfolio problem; and determining initial, basic and feasible solutions for transportation problems by means of the "supply demand reparation method" and "continuous allocation method." In addition, the book delves into a comparison study on exponential smoothing and the Arima model for fuel prices; optimal policy for Weibull distributed deteriorating items varying with ramp type demand rate and shortages; an inventory model with shortages and deterioration for three different demand rates; outlier labeling methods for medical data; a garbage disposal plant as a validated model of a fault-tolerant system; and the design of a "least cost ration formulation application for cattle"; a preservation technology model for deteriorating items with advertisement dependent demand and trade credit; a time series model for stock price forecasting in India; and asset pricing using capital market curves. The book offers a valuable asset for all researchers and industry practitioners working in these areas, giving them a feel for the latest developments and encouraging them to pursue further research in this direction.

This book is a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: ``Integrable Systems'' and ``Quantum Theories and Algebraic Geometry'', reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

A sweeping exploration of the development and far-reaching applications of harmonic analysis such as signal processing, digital music, Fourier optics, radio astronomy, crystallography, medical imaging, spectroscopy, and more. Featuring a wealth of illustrations, examples, and material not found in other harmonic analysis books, this unique monograph skillfully blends together historical narrative with scientific exposition to create a comprehensive yet accessible work. While only an understanding of calculus is required to appreciate it, there are more technical sections that will charm even specialists in harmonic analysis. From undergraduates to professional scientists, engineers, and mathematicians, there is something for everyone here. The second edition of The Evolution of Applied Harmonic Analysis contains a new chapter on atmospheric physics and climate change, making it more relevant for today's audience. Praise for the first edition: "...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied." - R.N. Bracewell, Stanford University "The book under review is a unique and splendid telling of the triumphs of the fast Fourier transform. I can recommend it unconditionally... Elena Prestini... has taken one major mathematical idea, that of Fourier analysis, and chased down and described a half dozen varied areas in which Fourier analysis and the FFT are now in place. Her book is much to be applauded." - Society for Industrial and Applied Mathematics "This is not simply a book about mathematics, or even the history of mathematics; it is a story about how the discipline has been applied (to borrow Fourier's expression) to 'the public good and the explanation of natural phenomena.' ... This book constitutes a significant addition to the library of popular mathematical works, and a valuable resource for students of mathematics." - Mathematical Association of America Reviews

The increasing complexity of economic problems, coupled with advances in numerical methods and computer architectures, have stimulated the growth and interest in computational economics. Accompanying this activity is the need for the unification, documentation and presentation of fundamental methodologies for use by researchers and practitioners. "Network Economics: A Variational Inequality Approach" makes a contribution in this direction by providing a treatment of the theory of finite-dimensional variational inequalities, algorithms and applications. The focus of the volume is on network economics. Physical networks are pervasive in today's society in the form of transportation network, energy networks, financial networks, whereas mathematical networks provide a mechanism for studying a plethora of economic equilibirum problems through a common graphic structure. "Network Economics" establishes the connections among economic equilibrium problems through their network structure and demonstrates how the structure can then be used to address policy interventions, as well as to construct efficient numerical schemes for the computation of equilibria. The network framework provides not only a mechanism for the graphic representation of economic problems and a means for visualizing their similarities and differences, but in addition, a novel theoretical approach. Problems treated include congested transportation systems, oligopolistic market equilibrium problems, problems, of human migration and general financial equilibrium problems.

This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.