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.

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.

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.

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.

This book contains contributions from the Spanish Relativity Meeting, ERE 2012, held in" "Guimaraes, Portugal, September 2012. It features more than 70 papers on a range of topics in general relativity and gravitation, from mathematical cosmology, numerical relativity and black holes to string theory and quantum gravity.

Under the title "Progress in Mathematical Relativity, Gravitation and Cosmology," ERE 2012 was attended by an exceptional international list of over a hundred participants from the five continents and over forty countries. ERE is organized every year by one of the Spanish or Portuguese groups working in this area and is supported by the Spanish Society of Gravitation and Relativity (SEGRE).

This book will be of interest to researchers in mathematics and physics.

"

Cognitive Intelligence with Neutrosophic Statistics in Bioinformatics investigates and presents the many applications that have arisen in the last ten years using neutrosophic statistics in bioinformatics, medicine, agriculture and cognitive science. This book will be very useful to the scientific community, appealing to audiences interested in fuzzy, vague concepts from which uncertain data are collected, including academic researchers, practicing engineers and graduate students. Neutrosophic statistics is a generalization of classical statistics. In classical statistics, the data is known, formed by crisp numbers. In comparison, data in neutrosophic statistics has some indeterminacy. This data may be ambiguous, vague, imprecise, incomplete, and even unknown. Neutrosophic statistics refers to a set of data, such that the data or a part of it are indeterminate in some degree, and to methods used to analyze the data.

The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of conferences held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. The ?rst ENUMATH conference was held in Paris (1995), and the series continued by the one in Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), and Santiago de Compostela (2005). This volume contains a selection of invited plenary lectures, papers presented in minisymposia, and contributed papers of ENUMATH 2007, held in Graz, Austria, September 10-14, 2007. We are happy that so many people have shown their interest in this conference. In addition to the ten invited presentations and the public lecture, we had more than 240 talks in nine minisymposia and ?fty four sessions of contributed talks, and about 316 participants from all over the world, specially from Europe. A total of 98 contributions appear in these proceedings. Topics include theoretical aspects of new numerical techniques and algorithms, as well as to applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scienti?c computing and their applications. We would like to thank all the participants for the attendance and for their va- ablecontributionsanddiscussionsduringtheconference.Specialthanksgothe m- isymposium organizers, who made a large contribution to the conference, the chair persons, and all speakers.

This thesis focuses on the construction and application of an electron radiation belt kinetic model including various adiabatic and non-adiabatic processes. The terrestrial radiation belt was discovered over 50 years ago and has received a resurgence of interest in recent years. The main drivers of radiation belt research are the fundamental science questions surrounding its complex and dramatic dynamics and particularly its potential hazards posed to space-borne systems. The establishment of physics-based radiation belt models will be able to identify the contributions of various mechanisms, forecast the future radiation belt evolution and then mitigate its adverse space weather effects. Dr. Su is now an Professor works in Department of Geophysics and Planetary Sciences, University of Science and Technology of China, Hefei, China.

Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group. In some problems and applications, an additional algebraic or topological structure is assumed in order to define equations and obtain significant results about them. Reflecting the author's past research experience, the majority of examples involve equations in finite dimensional Euclidean spaces. The book first introduces difference equations on groups, building a foundation for later chapters and illustrating the wide variety of possible formulations and interpretations of difference equations that occur in concrete contexts. The author then proposes a systematic method of decomposition for recursive difference equations that uses a semiconjugate relation between maps. Focusing on large classes of difference equations, he shows how to find the semiconjugate relations and accompanying factorizations of two difference equations with strictly lower orders. The final chapter goes beyond semiconjugacy by extending the fundamental ideas based on form symmetries to nonrecursive difference equations. With numerous examples and exercises, this book is an ideal introduction to an exciting new domain in the area of difference equations. It takes a fresh and all-inclusive look at difference equations and develops a systematic procedure for examining how these equations are constructed and solved.

The original edition of this book was celebrated for its coverage of the central concepts of practical optimization techniques. This updated edition expands and illuminates the connection between the purely analytical character of an optimization problem, expressed by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. Incorporating modern theoretical insights, this classic text is even more useful.

This book presents recent research on robustness in econometrics. Robust data processing techniques - i.e., techniques that yield results minimally affected by outliers - and their applications to real-life economic and financial situations are the main focus of this book. The book also discusses applications of more traditional statistical techniques to econometric problems. Econometrics is a branch of economics that uses mathematical (especially statistical) methods to analyze economic systems, to forecast economic and financial dynamics, and to develop strategies for achieving desirable economic performance. In day-by-day data, we often encounter outliers that do not reflect the long-term economic trends, e.g., unexpected and abrupt fluctuations. As such, it is important to develop robust data processing techniques that can accommodate these fluctuations.

"This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic "basic" terms involved in the formulation of the dynamic OE4 theory in three space dimensions, as well as selected contributions presented at the fourth meeting on Particle Systems and PDEs, which was held at the University of Minho's Centre of Mathematics in December 2015. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, offering them a forum to present their recent results and discuss their topics of expertise. The meeting was also intended to present to a vast and varied public, including young researchers, the area of interacting particle systems, its underlying motivation, and its relation to partial differential equations. The book will be of great interest to probabilists, analysts, and all mathematicians whose work focuses on topics in mathematical physics, stochastic processes and differential equations in general, as well as physicists working in statistical mechanics and kinetic theory."

Multi-agent systems have numerous civilian, homeland security, and military applications; however, for all these applications, communication bandwidth, sensing range, power constraints, and stealth requirements preclude centralized command and control. The alternative is distributed coordination, which is more promising in terms of scalability, robustness, and flexibility. Distributed Coordination of Multi-agent Networks introduces problems, models, and issues such as collective periodic motion coordination, collective tracking with a dynamic leader, and containment control with multiple leaders, and explores ideas for their solution. Solving these problems extends the existing application domains of multi-agent networks; for example, collective periodic motion coordination is appropriate for applications involving repetitive movements, collective tracking guarantees tracking of a dynamic leader by multiple followers in the presence of reduced interaction and partial measurements, and containment control enables maneuvering of multiple followers by multiple leaders. The authors models for distributed coordination arise from physical constraints and the complex environments in which multi-agent systems operate; they include Lagrangian models more realistic for mechanical-systems modeling than point models and fractional-order systems which better represent the consequences of environmental complexity. Other issues addressed in the text include the time delays inherent in networked systems, optimality concerns associated with the deisgn of energy-efficent algorithms, and the use of sampled-data settings in systems with intermittent neightbor-neighbor contact. Researchers, graduate students, and engineers interested in the field of multi-agent systems will find this monograph useful in introducing them to presently emerging research directions and problems in distributed coordination of multi-agent networks. The Communications and Control Engineering series reports major technological advances which have potential for great impact in the fields of communication and control. It reflects research in industrial and academic institutions around the world so that the readership can exploit new possibilities as they become available.

The most accessible introduction to the theory and practice of multivariate analysis

Multivariate Statistical Inference and Applications is a user-friendly introduction to basic multivariate analysis theory and practice for statistics majors as well as nonmajors with little or no background in theoretical statistics. Among the many special features of this extremely accessible first text on multivariate analysis are:

• Clear, step-by-step explanations of all key concepts and procedures along with original, easy-to-follow proofs
• Numerous problems, examples, and tables of distributions
• Many real-world data sets drawn from a wide range of disciplines
• Reviews of univariate procedures that give rise to multivariate techniques
• An extensive survey of the world literature on multivariate analysis
• An in-depth review of matrix theory
• A disk including all the data sets and SAS command files for all examples and numerical problems found in the book

These same features also make Multivariate Statistical Inference and Applications an excellent professional resource for scientists and clinicians who need to acquaint themselves with multivariate techniques. It can be used as a stand-alone introduction or in concert with its more methods-oriented sibling volume, the critically acclaimed Methods of Multivariate Analysis.

The book illustrates the theoretical results of fractional derivatives via applications in signals and systems, covering continuous and discrete derivatives, and the corresponding linear systems. Both time and frequency analysis are presented. Some advanced topics are included like derivatives of stochastic processes. It is an essential reference for researchers in mathematics, physics, and engineering.

This monograph has arisen from the multidisciplinary research extending over biology, robotics and hybrid systems theory. It is inspired by modeling reactive behavior of the immune system cell population, where each cell is considered an independent agent. The authors formulate the optimal control of maximizing the probability of robotic presence in a given region and discuss the application of the Minimum Principle for partial differential equations to this problem.

This book discusses group theory investigations of zincblende and wurtzite semiconductors under symmetry-breaking conditions. The text presents the group theory elements required to develop a multitude of symmetry-breaking problems, giving scientists a fast track to bypass the need for recalculating electronic states. The text is not only a valuable resource for speeding up calculations but also illustrates the construction of effective Hamiltonians for a chosen set of electronic states in crystalline semiconductors. Since Hamiltonians have to be invariant under the transformations of the point group, the crystal symmetry determines the multiplet structure of these states in the presence of spin-orbit, crystal-field, or exchange interactions. Symmetry-breaking leads to additional coupling of the states, resulting in shifts and/or splittings of the multiplets. Such interactions may be intrinsic, as in the case of the quasi-particle dispersion, or extrinsic, induced by magnetic, electric, or strain fields. Using a power expansion of the perturbations these interaction terms can be determined in their parameterized form in a unique way. The hierarchic structure of this invariant development allows to estimate the importance of particular symmetry-breaking effects in the Hamiltonian. A number of selected experimental curves are included to illustrate the symmetry-based discussions, which are especially important in optical spectroscopy. This text is written for graduate students and researchers who want to understand and simulate experimental findings reflecting the fine structure of electronic or excitonic states in crystalline semiconductors.

This book is for students following an introductory course in numerical methods, numerical techniques or numerical analysis. It introduces MATLAB as a computing environment for experimenting with numerical methods. It approaches the subject from a pragmatic viewpoint; theory is kept at a minimum commensurate with comprehensive coverage of the subject and it contains abundant worked examples which provide easy understanding through a clear and concise theoretical treatment. This edition places even greater emphasis on 'learning by doing' than the previous edition.

Fully documented MATLAB code for the numerical methods described in the book will be available as supplementary material to the book on http: //extras.springer.com

"