Expert practical and theoretical coverage of runs and scans

This volume presents both theoretical and applied aspects of runs and scans, and illustrates their important role in reliability analysis through various applications from science and engineering. Runs and Scans with Applications presents new and exciting content in a systematic and cohesive way in a single comprehensive volume, complete with relevant approximations and explanations of some limit theorems.

The authors provide detailed discussions of both classical and current problems, such as:

• Sooner and later waiting time
• Consecutive systems
• Start-up demonstration testing in life-testing experiments
• Learning and memory models
• "Match" in genetic codes

Runs and Scans with Applications offers broad coverage of the subject in the context of reliability and life-testing settings and serves as an authoritative reference for students and professionals alike.

This book provides a tutorial in the use of Altair Compose and Altair Activate, software packages that provide system modeling and simulation facilities. Advanced system modeling software provide multiple ways of creating models: models can be programmed in specialized languages, graphically constructed as block-diagrams and state machines, or expressed mathematically in equation-based languages. Compose and Activate are introduced in this text in two parts. The first part introduces the multi-language environment of Compose and its use for modeling, simulation and optimization. The second describes the graphical system modeling and optimization with Activate, an open-system environment providing signal-based modeling as well as physical system component-based modeling. Throughout both parts are applied examples from mechanical, biological, and electrical systems, as well as control and signal processing systems. This book will be an invaluable addition with many examples both for those just interested in OML and those doing industrial scale modeling, simulation, and design. All examples are worked using the free basic editions of Activate and Compose that are available.

This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stackel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.

This is the second of a two-volume series on sampling theory. The mathematical foundations were laid in the first volume, and this book surveys the many applications of sampling theory both within mathematics and in other areas of science. Many of the topics covered here are not found in other books, and all are given an up to date treatment bringing the reader's knowledge up to research level. This book consists of ten chapters, written by ten different teams of authors, and the contents range over a wide variety of topics including combinatorial analysis, number theory, neural networks, derivative sampling, wavelets, stochastic signals, random fields, and abstract harmonic analysis. There is a comprehensive, up to date bibliography.

This book demonstrates Microsoft EXCEL(R)-based Fourier transform of selected physics examples, as well as describing spectral density of the auto-regression process in relation to Fourier transform. Rather than offering rigorous mathematics, the book provides readers with an opportunity to gain an understanding of Fourier transform through the examples. They will acquire and analyze their own data following the step-by-step procedure outlined, and a hands-on acoustic spectral analysis is suggested as the ideal long-term student project.

Hardbound. J. Neyman, one of the pioneers in laying the foundations of modern statistical theory, stressed the importance of stochastic processes in a paper written in 1960 in the following terms: Currently in the period of dynamic indeterminism in science, there is hardly a serious piece of research, if treated realistically, does not involve operations on stochastic processes. Arising from the need to solve practical problems, several major advances have taken place in the theory of stochastic processes and their applications. Books by Doob (1953; J. Wiley and Sons), Feller (1957, 1966; J. Wiley and Sons) and Loeve (1960; D. van Nostrand and Col., Inc.) among others, have created growing awareness and interest in the use of stochastic processes in scientific and technological studies.The literature on stochastic processes is very extensive and is distributed in several books and journals. There is a need to review the different lines of

This book provides an interdisciplinary approach to complexity, combining ideas from areas like complex networks, cellular automata, multi-agent systems, self-organization and game theory. The first part of the book provides an extensive introduction to these areas, while the second explores a range of research scenarios. Lastly, the book presents CellNet, a software framework that offers a hands-on approach to the scenarios described throughout the book. In light of the introductory chapters, the research chapters, and the CellNet simulating framework, this book can be used to teach undergraduate and master's students in disciplines like artificial intelligence, computer science, applied mathematics, economics and engineering. Moreover, the book will be particularly interesting for Ph.D. and postdoctoral researchers seeking a general perspective on how to design and create their own models.

This book provides a coherent framework for understanding shrinkage estimation in statistics. The term refers to modifying a classical estimator by moving it closer to a target which could be known a priori or arise from a model. The goal is to construct estimators with improved statistical properties. The book focuses primarily on point and loss estimation of the mean vector of multivariate normal and spherically symmetric distributions. Chapter 1 reviews the statistical and decision theoretic terminology and results that will be used throughout the book. Chapter 2 is concerned with estimating the mean vector of a multivariate normal distribution under quadratic loss from a frequentist perspective. In Chapter 3 the authors take a Bayesian view of shrinkage estimation in the normal setting. Chapter 4 introduces the general classes of spherically and elliptically symmetric distributions. Point and loss estimation for these broad classes are studied in subsequent chapters. In particular, Chapter 5 extends many of the results from Chapters 2 and 3 to spherically and elliptically symmetric distributions. Chapter 6 considers the general linear model with spherically symmetric error distributions when a residual vector is available. Chapter 7 then considers the problem of estimating a location vector which is constrained to lie in a convex set. Much of the chapter is devoted to one of two types of constraint sets, balls and polyhedral cones. In Chapter 8 the authors focus on loss estimation and data-dependent evidence reports. Appendices cover a number of technical topics including weakly differentiable functions; examples where Stein's identity doesn't hold; Stein's lemma and Stokes' theorem for smooth boundaries; harmonic, superharmonic and subharmonic functions; and modified Bessel functions.

Domain theory is a subject that emerged as a response to natural concerns in the semantics of computation, and it involves the study of ordered sets that possess an unusual amount of mathematical structure. Disorder in Domain Theory explores the connection between domain theory and quantum information science and the concept that relates them: disorder.

'This book offers one of the few places where a collection of results from the literature can be found ... The book has an extensive bibliography ... It is very nice to have the compendium of results that is presented here.'zbMATHA mathematical billiard is a mechanical system consisting of a billiard ball on a table of any form (which can be planar or even a multidimensional domain) but without billiard pockets. The ball moves and its trajectory is defined by the ball's initial position and its initial speed vector. The ball's reflections from the boundary of the table are assumed to have the property that the reflection and incidence angles are the same. This book comprehensively presents known results on the behavior of a trajectory of a billiard ball on a planar table (having one of the following forms: circle, ellipse, triangle, rectangle, polygon and some general convex domains). It provides a systematic review of the theory of dynamical systems, with a concise presentation of billiards in elementary mathematics and simple billiards related to geometry and physics.The description of these trajectories leads to the solution of various questions in mathematics and mechanics: problems related to liquid transfusion, lighting of mirror rooms, crushing of stones in a kidney, collisions of gas particles, etc. The analysis of billiard trajectories can involve methods of geometry, dynamical systems, and ergodic theory, as well as methods of theoretical physics and mechanics, which has applications in the fields of biology, mathematics, medicine, and physics.

This book discusses risk management, product pricing, capital management and Return on Equity comprehensively and seamlessly. Strategic planning, including the required quantitative methods, is an essential part of bank management and control. A thorough introduction to the advanced methods of risk management for Credit Risk, Counterparty Credit Risk, Market Risk, Operational Risk and Risk Aggregation is provided. In addition, directly applicable concepts and data such as macroeconomic scenarios for strategic planning and stress testing as well as detailed scenarios for Operational Risk and advanced concepts for Credit Risk are presented in straightforward language. The book highlights the implications and chances of the Basel III and Basel IV implementations (2022 onwards), especially in terms of capital management and Return on Equity. A wealth of essential background information from practice, international observations and comparisons, along with numerous illustrative examples, make this book a useful resource for established and future professionals in bank management, risk management, capital management, controlling and accounting.

This book is a rare jewel, describing fundamental research in a highly dynamic field of subatomic physics. It presents an overview of cross section measurements of deeply virtual Compton scattering. Understanding the structure of the proton is one of the most important challenges that physics faces today. A typical tool for experimentally accessing the internal structure of the proton is lepton-nucleon scattering. In particular, deeply virtual Compton scattering at large photon virtuality and small four-momentum transfer to the proton provides a tool for deriving a three-dimensional tomographic image of the proton. Using clear language, this book presents the highly complex procedure used to derive the momentum-dissected transverse size of the proton from a pioneering measurement taken at CERN. It describes in detail the foundations of the measurement and the data analysis, and includes exhaustive studies of potential systematic uncertainties, which could bias the result.

Numerical and computational methods play a major role in modelling compressible flow and are important tools in solving fluid dynamical problems faced in many areas of science and technology. This book thoroughly surveys and analyzes up-to-date methods, while reviewing the basic theoretical mathematical analysis.

This book addresses the mechanism of enrichment of heavy elements in galaxies, a long standing problem in astronomy. It mainly focuses on explaining the origin of heavy elements by performing state-of-the-art, high-resolution hydrodynamic simulations of dwarf galaxies. In this book, the author successfully develops a model of galactic chemodynamical evolution by means of which the neutron star mergers can be used to explain the observed abundance pattern of the heavy elements synthesized by the rapid neutron capture process, such as europium, gold, and uranium in the Local Group dwarf galaxies. The book argues that heavy elements are significant indicators of the evolutionary history of the early galaxies, and presents theoretical findings that open new avenues to understanding the formation and evolution of galaxies based on the abundance of heavy elements in metal-poor stars.

This book includes a collection of articles that present recent developments in the fields of optimization and dynamic game theory, economic dynamics, dynamic theory of the firm, and population dynamics and non standard applications of optimal control theory. The authors of the articles are well respected authorities in their fields and are known for their high quality research in the fields of optimization and economic dynamics.

"Difference Equations, Second Edition," presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.

* Phase plane analysis for systems of two linear equations
* Use of equations of variation to approximate solutions
* Fundamental matrices and Floquet theory for periodic systems
* LaSalle invariance theorem
* Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory
* Appendix on the use of "Mathematica" for analyzing difference equaitons
* Exponential generating functions
* Many new examples and exercises

This thesis describes the structures of six-dimensional (6d) superconformal field theories and its torus compactifications. The first half summarizes various aspects of 6d field theories, while the latter half investigates torus compactifications of these theories, and relates them to four-dimensional superconformal field theories in the class, called class S. It is known that compactifications of 6d conformal field theories with maximal supersymmetries provide numerous insights into four-dimensional superconformal field theories. This thesis generalizes the story to the theories with smaller supersymmetry, constructing those six-dimensional theories as brane configurations in the M-theory, and highlighting the importance of fractionalization of M5-branes. This result establishes new dualities between the theories with eight supercharges.

This book presents the second volume of Piola's original Italian text together with the English-language translation and comments, showing convincingly that Gabrio Piola's work must still be regarded as a modern theory. Gabrio Piola's work has had an enormous impact on the development of applied mathematics and continuum mechanics. As such, a committee of scientific experts took it upon themselves to translate his complete works. In a second step, they commented on Piola's work and compared it to modern theories in mechanics in order to stress Piola's impact on modern science and prove and confirm that he achieved significant milestones in applied mathematics.