This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.

This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respect to macroscopic fluxes or thermodynamic forces. Both irreversible Boltzmann and generalized Boltzmann equations are used for deriving theories of irreversible transport equations and generalized hydrodynamic equations, which rigorously conform to the tenet. All observables described by the so-formulated theories therefore also strictly obey the tenet.

This book presents extensive information on the mechanisms of epitaxial growth in III-nitride compounds, drawing on a state-of-the-art computational approach that combines ab initio calculations, empirical interatomic potentials, and Monte Carlo simulations to do so. It discusses important theoretical aspects of surface structures and elemental growth processes during the epitaxial growth of III-nitride compounds. In addition, it discusses advanced fundamental structural and electronic properties, surface structures, fundamental growth processes and novel behavior of thin films in III-nitride semiconductors. As such, it will appeal to all researchers, engineers and graduate students seeking detailed information on crystal growth and its application to III-nitride compounds.

This volume is the result of two international workshops; "Infinite Analysis 11 Frontier of Integrability" held at University of Tokyo, Japan in July 25th to 29th, 2011, and "Symmetries, Integrable Systems and Representations" held at Universite Claude Bernard Lyon 1, France in December 13th to 16th, 2011.

Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions.

Through these topics, the readerwill find some recent developments in the field of mathematical physics and their interactions with several other domains.
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This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

Mathematics is undoubtedly the key to state-of-the-art high technology. It is aninternationaltechnicallanguageandprovestobeaneternallyyoungscience to those who have learned its ways. Long an indispensable part of research thanks to modeling and simulation, mathematics is enjoying particular vit- ity now more than ever. Nevertheless, this stormy development is resulting in increasingly high requirements for students in technical disciplines, while general interest in mathematics continues to wane at the same time. This book and its appendices on the Internet seek to deal with this issue, helping students master the di?cult transition from the receptive to the productive phase of their education. The author has repeatedly held a three-semester introductory course - titled Higher Mathematics at the University of Stuttgart and used a series of "handouts" to show further aspects, make the course contents more motiv- ing, and connect with the mechanics lectures taking place at the same time. One part of the book has more or less evolved from this on its own. True to the original objective, this part treats a variety of separate topics of varying degrees of di?culty; nevertheless, all these topics are oriented to mechanics. Anotherpartofthisbookseekstoo?eraselectionofunderstandablereal- ticmodelsthatcanbeimplementeddirectlyfromthemultitudeofmathema- calresources.TheauthordoesnotattempttohidehispreferenceofNumerical Mathematics and thus places importance on careful theoretical preparation.

This thesis investigates ultracold molecules as a resource for novel quantum many-body physics, in particular by utilizing their rich internal structure and strong, long-range dipole-dipole interactions. In addition, numerical methods based on matrix product states are analyzed in detail, and general algorithms for investigating the static and dynamic properties of essentially arbitrary one-dimensional quantum many-body systems are put forth. Finally, this thesis covers open-source implementations of matrix product state algorithms, as well as educational material designed to aid in the use of understanding such methods.

This book presents the state of the art in multilevel analysis, with an emphasis on more advanced topics. These topics are discussed conceptually, analyzed mathematically, and illustrated by empirical examples. Multilevel analysis is the statistical analysis of hierarchically and non-hierarchically nested data. The simplest example is clustered data, such as a sample of students clustered within schools. Multilevel data are especially prevalent in the social and behavioral sciences and in the biomedical sciences. The chapter authors are all leading experts in the field. Given the omnipresence of multilevel data in the social, behavioral, and biomedical sciences, this book is essential for empirical researchers in these fields.

This book introduces new concepts and mechanisms regarding the usage of both social media interactions and artifacts for peer education in digital educational games. Digital games in general, and digital educational games in particular, represent an area with a high potential for interdisciplinary innovation, not only from an information technology standpoint, but also from social science, psychological and didactic perspectives. This book presents an interdisciplinary approach to educational games, which is centered on information technology and aims at: (1) improving digital management by focusing on the exchange of learning outcomes and solution assessment in a peer-to-peer network of learners; (2) achieving digital implementation by using forms of interaction to change the course of educational games; and (3) providing digital support by fostering group-formation processes in educational situations to increase both the effects of educational games and knowledge exchange at the individual level. In addition to a systematic analysis of the relationship between software architecture, educational games and social media applications, the book also presents the implemented IT systems' architectures and algorithmic solutions as well as the resulting applicable evaluation findings from the field of interactive multimedia learning.

Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems. It is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay.

Replete with examples, Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference guide for graduate students, researchers, and professionals in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.

This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs) . As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.

The book you hold in your hands is the outcome of the "2014 Interdisciplinary Symposium on Complex Systems" held in the historical city of Florence. The book consists of 37 chapters from 4 areas of Physical Modeling of Complex Systems, Evolutionary Computations, Complex Biological Systems and Complex Networks. All 4 parts contain contributions that give interesting point of view on complexity in different areas in science and technology. The book starts with a comprehensive overview and classification of complexity problems entitled Physics in the world of ideas: Complexity as Energy" , followed by chapters about complexity measures and physical principles, its observation, modeling and its applications, to solving various problems including real-life applications. Further chapters contain recent research about evolution, randomness and complexity, as well as complexity in biological systems and complex networks. All selected papers represent innovative ideas, philosophical overviews and state-of-the-art discussions on aspects of complexity. The book will be useful as an instructional material for senior undergraduate and entry-level graduate students in computer science, physics, applied mathematics and engineering-type work in the area of complexity. The book will also be valuable as a resource of knowledge for practitioners who want to apply complexity to solve real-life problems in their own challenging applications.

Recent years have seen a number of introductory texts which focus on the applications of modern stochastic calculus to the theory of finance, and on the pricing models for derivative securities in particular. Some of these books develop the mathematics very quickly, making substantial demands on the readerOs background in advanced probability theory. Others emphasize the financial applications and do not attempt a rigorous coverage of the continuous-time calculus. This book provides a rigorous introduction for those who do not have a good background in stochastic calculus. The emphasis is on keeping the discussion self-contained rather than giving the most general results possible.

Vibro-impact dynamics has occupied a wide spectrum of studies by dyn- icists, physicists, and mathematicians. These studies may be classi?ed into three main categories: modeling, mapping and applications. The main te- niques used in modeling of vibro-impact systems include phenomenological modelings, Hertzian models, and non-smooth coordinate transformations- velopedbyZhuravlevandIvanov. Oneofthemostcriticalsituationsimpeded invibro-impactsystemsisthegrazingbifurcation. Grazingbifurcationisu- ally studied through discontinuity mapping techniques, which are very useful to uncover the rich dynamics in the process of impact interaction. Note the availablemappings arevalidonly intheabsenceofnon-impactnonlinearities. Complex dynamic phenomena of vibro-impact systems include subharmonic oscillations, chaotic motion, and coexistence of di?erent attractors for the sameexcitationand systemparametersbut under di?erent initial conditions. Selectedapplicationsofvibro-impactdynamics. Theseincludelumpedand continuous systems. Lumped systems cover a bouncing ball on an oscillating barrier, mass-spring-dashpot systems, normal and inverted pendulums, the spherical pendulum, the ship roll motion against icebergs, joints with fr- play, rotor-stator rubbing in rotating machinery, vocal folds, microactuators, strings, beams, pipes conveying ?uids with end-restraints, nuclear reactors and heat exchangers, and plates. These applications are discussed within the framework of the deterministic theory. Under random excitation the tre- ment requires special tools. The techniques of equivalent linearization and stochastic averaging have been applied to limited number of problems. One of the most bene?cial outcomesof vibro-impact dynamics is the development of impact dampers, which have witnessed signi?cant activities over the last four decades and have been used in several applications. On the other hand, vibro-impacthas detrimental e?ects on the operationsof mechanicalsystems and damage of pipes and rods in nuclear reactors.

This thesis describes the thorough analysis of the rare B meson decay into K* on data taken by the Belle Collaboration at the B-meson-factory KEKB over 10 years. This reaction is very interesting, because it in principle allows the observation of CP-violation effects. In the Standard Model however, no CP violation in this reaction is expected. An observation of CP asymmetries thus immediately implies new physics. This thesis presents an amplitude analysis of this decay and the search for CP violation in detail and discusses methods to solve related problems: The quantification of multivariate dependence and the improvement of numeric evaluation speed of normalization integrals in amplitude analysis. In addition it provides an overview of the theory, experimental setup, (blind) statistical data analysis and estimation of systematic uncertainties.

For courses in calculus-based physics. Practice makes perfect. The 15th Edition of University Physics with Modern Physics draws on a wealth of data insights from hundreds of faculty and thousands of student users to address one of the biggest challenges for students in introductory physics courses: seeing patterns and making connections between problem types. Students learn to recognise when to use similar steps in solving the same problem type and develop an understanding for problem solving approaches, rather than simply plugging in an equation. This edition addresses students' tendency to focus on the objects, situations, numbers, and questions posed in a problem, rather than recognising the underlying principle or the problem's type. New Key Concept statements at the end of worked examples address this challenge by identifying the main idea used in the solution to help students recognise the underlying concepts and strategy for the given problem. New Key Example Variation Problems appear within new Guided Practice sections and group problems by type to give students practice recognising when problems can be solved in a similar way, regardless of wording or numbers. These scaffolded problem sets help students see patterns, make connections between problems, and build confidence for tackling different problem types when exam time comes.

Pattern Formation in Morphogenesis is a rich source of interesting and challenging mathematical problems. The volume aims at showing how a combination of new discoveries in developmental biology and associated modelling and computational techniques has stimulated or may stimulate relevant advances in the field. Finally it aims at facilitating the process of unfolding a mutual recognition between Biologists and Mathematicians of their complementary skills, to the point where the resulting synergy generates new and novel discoveries. It offers an interdisciplinary interaction space between biologists from embryology, genetics and molecular biology who present their own work in the perspective of the advancement of their specific fields, and mathematicians who propose solutions based on the knowledge grasped from biologists.

This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising in particular, in finance, statistics, computer graphics and the solution of PDEs.

Approximation methods are vital in many challenging applications of computational science and engineering.

This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing.

It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems.

An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales.

Contributions of industrial mathematicians, including representatives from Microsoft and Schlumberger, foster the transfer of the latest approximation methods to real-world applications.

Mathematical demography is the centerpiece of quantitative social science. The founding works of this field from Roman times to the late Twentieth Century are collected here, in a new edition of a classic work by David R. Smith and Nathan Keyfitz. Commentaries by Smith and Keyfitz have been brought up to date and extended by Kenneth Wachter and Herve Le Bras, giving a synoptic picture of the leading achievements in formal population studies. Like the original collection, this new edition constitutes an indispensable source for students and scientists alike, and illustrates the deep roots and continuing vitality of mathematical demography.

Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Levy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes.

The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice."

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering and computer science.

Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows.

"Mathematical and Numerical Foundations of Turbulence Models and Applications" is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics, engineers, physical oceanographers, meteorologists and climatologists.

This volume provides a detailed discussion of the mathematical aspects and the physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy.

Such a formalism (Deformed Special Relativity, DSR) allows one

• to account for breakdown of local Lorentz invariance in the usual, special-relativistic meaning (however, Lorentz invariance is recovered in a generalized sense)
• to provide an effective geometrical description of the four fundamental interactions (electromagnetic, weak, strong and gravitational)

Moreover, the four-dimensional energy-dependent space-time is just a manifestation of a larger, five-dimensional space in which energy plays the role of a fifth (non-compactified) dimension. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism.

The mathematical properties of such a generalized KK scheme are illustrated. They include the solutions of the five-dimensional Einstein equations in vacuum in most cases of physical relevance, the infinitesimal symmetries of the theory for the phenomenological metrics of the four interactions, and the study of the five-dimensional geodesics.

The mathematical results concerning the geometry of the deformed five-dimensional spacetime (like its Killing symmetries) can be applied also to other multidimensional theories with infinite extra dimensions. Some experiments providing preliminary evidence for the hypothesized deformation of space-time for all thefour fundamental interactions are discussed.

Growing transportation costs and tight delivery schedules mean that good located decisions are more crucial than ever in the success or failure of industrial and puplic projects. The development of realistic location models is an essential phase in every locational decision process. Especially when dealing with geometric representations of continuous (planar) location model problems, the goegraphical reality must be incorporated. This text develops the mathematical implications of barriers to the geometrical and analytical characteristics of continuous location problems. Besides their relevance in the application of location theoretic results, location problems with barriers are also very interesting from a mathematical point of view. The nonconvexity of distance measures in the presence of barriers leads to nonconvex optimization problems. Most of the classical methods in continuous location theory rely heaily on the convexity of the objective function and will thus fail in this context. On the other hand, general methods in global optimization capable of treating nonconvex problems ignore the geometric charateristics of the location problems considered. Theoretic as well as algorithmic approaches are utilized to overcome the described difficulties for the solution of location problems with barriers. Depending on the barrier shapes, the underlying distance measure, and type of objective function, different concepts are conceived to handle the nonconvexity of the problem. This book will appeal to those working in operations research and management science and mathematicians interested in optimization theory and its applications.