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This book recasts the classical Gaussian error calculus from scratch, the inducements concerning both random and unknown systematic errors. The idea of this book is to create a formalism being fit to localize the true values of physical quantities considered – true with respect to the set of predefined physical units. Remarkably enough, the prevailingly practiced forms of error calculus do not feature this property which however proves in every respect, to be physically indispensable. The amended formalism, termed Generalized Gaussian Error Calculus by the author, treats unknown systematic errors as biases and brings random errors to bear via enhanced confidence intervals as laid down by students. The significantly extended second edition thoroughly restructures and systematizes the text as a whole and illustrates the formalism by numerous numerical examples. They demonstrate the basic principles of how to understand uncertainties to localize the true values of measured values - a perspective decisive in view of the contested physical explorations.
Measurement --- Error analysis (Mathematics) --- History. --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Numerical analysis --- Statistics --- Engineering mathematics. --- Mathematical physics. --- Measurement Science and Instrumentation. --- Mathematical and Computational Engineering. --- Mathematical Methods in Physics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Mathematics --- Physical measurements. --- Measurement . --- Applied mathematics. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Measuring --- Mensuration --- Technology --- Metrology --- Physical measurements --- Measurements, Physical --- Mathematical physics
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This book presents efficient metaheuristic algorithms for optimal design of structures. Many of these algorithms are developed by the author and his colleagues, consisting of Democratic Particle Swarm Optimization, Charged System Search, Magnetic Charged System Search, Field of Forces Optimization, Dolphin Echolocation Optimization, Colliding Bodies Optimization, Ray Optimization. These are presented together with algorithms which were developed by other authors and have been successfully applied to various optimization problems. These consist of Particle Swarm Optimization, Big Bang-Big Crunch Algorithm, Cuckoo Search Optimization, Imperialist Competitive Algorithm, and Chaos Embedded Metaheuristic Algorithms. Finally a multi-objective optimization method is presented to solve large-scale structural problems based on the Charged System Search algorithm. The concepts and algorithms presented in this book are not only applicable to optimization of skeletal structures and finite element models, but can equally be utilized for optimal design of other systems such as hydraulic and electrical networks. .
Structural design --- Data processing. --- Engineering mathematics. --- Mathematical optimization. --- Mechanical engineering. --- Mathematical and Computational Engineering. --- Optimization. --- Mechanical Engineering. --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Engineering analysis --- Mathematics --- Applied mathematics.
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This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.
Numerical analysis --- Data processing. --- Computer science --- Mathematics. --- Computer science. --- Algorithms. --- Computational Mathematics and Numerical Analysis. --- Applications of Mathematics. --- Computational Science and Engineering. --- Algorism --- Algebra --- Arithmetic --- Informatics --- Science --- Math --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Foundations --- Mathematics --- Computer mathematics. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis
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Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods and Optimization – A Consumer Guide presents methods for dealing with them. Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to · discover how to escape the dictatorship of those particular cases that are simple enough to receive a closed-form solution, and thus gain the ability to solve complex, real-life problems; · understand the principles behind recognized algorithms used in state-of-the-art numerical software; <· learn the advantages and limitations of these algorithms, to facilitate the choice of which pre-existing bricks to assemble for solving a given problem; and · acquire methods that allow a critical assessment of numerical results. Numerical Methods and Optimization – A Consumer Guide will be of interest to engineers and researchers who solve problems numerically with computers or supervise people doing so, and to students of both engineering and applied math ematics. .
Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Engineering mathematics. --- Computer science. --- Numerical analysis. --- Mathematical and Computational Engineering. --- Math Applications in Computer Science. --- Calculus of Variations and Optimal Control; Optimization. --- Numerical Analysis. --- Informatics --- Science --- Engineering --- Engineering analysis --- Mathematics --- Applied mathematics. --- Computer science—Mathematics. --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of
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Outside the professional circles of topography and applied mathematics, the life and work of André-Louis Cholesky (1875–1918) are still relatively unknown to the scientific community. This new book appreciably widens the exposure of his remarkable personal achievements in topography and mathematics to a much larger international audience. Cholesky is also interesting to historians because he is a perfect representative of the "scientists engineers" that, since the early 19th century, had issued from the French scientific high schools. Because they had received a high level of mathematical education, they were able to innovate in their practice of engineering. In the case of Cholesky, this resulted in original contributions in artillery, topography, numerical analysis and graphical calculation. In addition, the book places his education and works within the history of several European countries through the 17th to 19th centuries. The book begins with Cholesky's biography, followed by his family’s history and an introduction to topography. It continues with a historical analysis of an unpublished paper (translated into English) in which Cholesky explained his method for linear systems. Cholesky's other works are then described, such as his participation in teaching at a superior "school by correspondence" founded by Léon Eyrolles. His important unpublished book in French on graphical calculation, which is reproduced in its entirety, is analyzed in detail and compared to similar contemporary publications. The biography of Ernest Benoit, who wrote the first paper on Cholesky's method, is provided. Various documents, highlighting the life and the personality of Cholesky, round out his story and end the book.
Mathematics --- Mathematicians --- Armies --- History. --- Officers --- Army --- Military power --- Armed Forces --- Math --- Science --- Mathematics. --- Computer science --- History of Mathematical Sciences. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Annals --- Auxiliary sciences of history
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This edited volume provides insights into and tools for the modeling, analysis, optimization, and control of large-scale networks in the life sciences and in engineering. Large-scale systems are often the result of networked interactions between a large number of subsystems, and their analysis and control are becoming increasingly important. The chapters of this book present the basic concepts and theoretical foundations of network theory and discuss its applications in different scientific areas such as biochemical reactions, chemical production processes, systems biology, electrical circuits, and mobile agents. The aim is to identify common concepts, to understand the underlying mathematical ideas, and to inspire discussions across the borders of the various disciplines. The book originates from the interdisciplinary summer school “Large Scale Networks in Engineering and Life Sciences” hosted by the International Max Planck Research School Magdeburg, September 26-30, 2011, and will therefore be of interest to mathematicians, engineers, physicists, biologists, chemists, and anyone involved in the network sciences. In particular, due to their introductory nature the chapters can serve individually or as a whole as the basis of graduate courses and seminars, future summer schools, or as reference material for practitioners in the network sciences. .
Large scale systems --- Differential equations --- Mathematical models. --- 517.91 Differential equations --- Systems, Large scale --- Engineering systems --- System analysis --- Mathematics. --- Differential Equations. --- Computer science. --- Applications of Mathematics. --- Ordinary Differential Equations. --- Computational Science and Engineering. --- Informatics --- Science --- Math --- Applied mathematics. --- Engineering mathematics. --- Differential equations. --- Computer mathematics. --- Computer mathematics --- Electronic data processing --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- Data processing.
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Variational Inequalities and Frictional Contact Problems contains a carefully selected collection of results on elliptic and evolutionary quasi-variational inequalities including existence, uniqueness, regularity, dual formulations, numerical approximations and error estimates ones. By using a wide range of methods and arguments, the results are presented in a constructive way, with clarity and well justified proofs. This approach makes the subjects accessible to mathematicians and applied mathematicians. Moreover, this part of the book can be used as an excellent background for the investigation of more general classes of variational inequalities. The abstract variational inequalities considered in this book cover the variational formulations of many static and quasi-static contact problems. Based on these abstract results, in the last part of the book, certain static and quasi-static frictional contact problems in elasticity are studied in an almost exhaustive way. The readers will find a systematic and unified exposition on classical, variational and dual formulations, existence, uniqueness and regularity results, finite element approximations and related optimal control problems. This part of the book is an update of the Signorini problem with nonlocal Coulomb friction, a problem little studied and with few results in the literature. Also, in the quasi-static case, a control problem governed by a bilateral contact problem is studied. Despite the theoretical nature of the presented results, the book provides a background for the numerical analysis of contact problems. The materials presented are accessible to both graduate/under graduate students and to researchers in applied mathematics, mechanics, and engineering. The obtained results have numerous applications in mechanics, engineering and geophysics. The book contains a good amount of original results which, in this unified form, cannot be found anywhere else.
Variational inequalities (Mathematics) --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities --- Cell aggregation --- Global differential geometry. --- Engineering mathematics. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Differential Geometry. --- Mathematical and Computational Engineering. --- Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Geometry, Differential --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Mathematics --- Manifolds (Mathematics). --- Complex manifolds. --- Differential geometry. --- Applied mathematics. --- Differential geometry --- Analytic spaces --- Manifolds (Mathematics) --- Topology
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La théorie des probabilités et des processus stochastiques est sans aucun doute l'un des plus importants outils mathématiques des sciences modernes. Le théorie des probabilité s'illustre dans de nombreux domaines issus de la biologie, de la physique, et des sciences de l'ingénieur : dynamique des populations, traitement du signal et de l'image, chimie moléculaire, économétrie, sciences actuarielles, mathématiques financières, ainsi qu'en analyse de risque. Le but de cet ouvrage est de parcourir les principaux modèles et méthodes stochastiques de cette théorie en pleine expansion. Ce voyage ne nécessite aucun bagage spécifique sur la théorie des processus stochastiques. Les outils d'analyses nécessaires à une bonne compréhension sont donnés au fur et à mesure de leur construction, révélant ainsi leur nécessité. La théorie des processus stochastiques est une extension naturelle de la théorie de systèmes dynamiques à des phénomènes aléatoires. Elle contient des formalisation d'évolutions de phénomènes aléatoires rencontrés en physique, en biologique, en économie, ou en sciences de l'ingénieur, mais aussi des algorithmes d'exploration stochastique d'espaces de solutions complexes pour résoudre des problèmes d'estimation, d'optimisation et d'apprentissage statistique. Des techniques de résolution avancées en statistique bayésienne, en traitement du signal, en analyse d’événements rares, en combinatoire énumérative, en optimisation combinatoire, ainsi qu'en physique et chimie quantique sont exposées dans cet ouvrage. Stochastic Models and Methods Probability theory and stochastic process theory are undoubtedly among the most important mathematic tools for the modern sciences. Probability theory has applications in several fields, such as biology, physics and the engineering sciences: population dynamics, signal and image processing, molecular chemistry, econometrics, actuarial science, financial mathematics, and risk analysis. This book provides an overview of stochastic models and methods for this very active field. Stochastic process theory is a natural extension of dynamic systems to random events. The book covers the modeling of random events in physics, biology, economics and the engineering sciences, while also introducing advanced problem-solving techniques in Bayesian statistics, signal processing and rare event analysis. No scientific background in stochastic process theory is needed.
Stochastic processes --- Algorithms --- Mathematical models. --- Algorism --- Algebra --- Arithmetic --- Foundations --- Distribution (Probability theory. --- Algorithms. --- Mathematics. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk
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This book is a collection of papers presented at the Forum “The Impact of Applications on Mathematics” in October 2013. It describes an appropriate framework in which to highlight how real-world problems, over the centuries and today, have influenced and are influencing the development of mathematics and, thereby, how mathematics is reshaped, in order to advance mathematics and its application. The contents of this book address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.
Mathematics --- Applied mathematics --- Math --- Science --- Mathematics. --- Engineering mathematics. --- Computer simulation. --- Applications of Mathematics. --- Mathematical and Computational Engineering. --- Simulation and Modeling. --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Engineering --- Engineering analysis --- Mathematical analysis --- Applied mathematics.
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This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computer science are of vital importance to a broad range of communities, including mathematicians and computing professionals across different educational levels and disciplines. .
Computer science --- Applications of Mathematics. --- Mathematics --- Mathematics. --- Computer science. --- Mathematical Applications in Computer Science. --- Computers and Society. --- Math Applications in Computer Science. --- Informatics --- Science --- Math --- Computer science—Mathematics. --- Computer mathematics. --- Applied mathematics. --- Engineering mathematics. --- Computers and civilization. --- Civilization and computers --- Civilization --- Engineering --- Engineering analysis --- Mathematical analysis --- Computer mathematics --- Electronic data processing