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Model Theory: Third Edition (Dover Books on Mathematics #58)
by H. Jerome Keisler C. C. ChangModel theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. This is the first and most successful textbook in logical model theory. Extensively updated and corrected in 1990 to accommodate developments in model theoretic methods -- including classification theory and nonstandard analysis -- the third edition added entirely new sections, exercises, and references. Each chapter introduces an individual method and discusses specific applications. Basic methods of constructing models include constants, elementary chains, Skolem functions, indiscernibles, ultraproducts, and special models. The final chapters present more advanced topics that feature a combination of several methods. This classic treatment covers most aspects of first-order model theory and many of its applications to algebra and set theory.
Model Theory and the Philosophy of Mathematical Practice: Formalization without Foundationalism
by John T. BaldwinMajor shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics. Explains the philosophical significance of the transformation in model theory and its impact on traditional mathematics; The technical logic is grounded in historical and philosophical contexts, making the subject accessible to philosophers as well as mathematicians; Includes source materials from model theorists discussing their methods and motivation.
Model Theory in Algebra, Analysis and Arithmetic
by Lou Dries Jochen Koenigsmann H. Dugald Macpherson Anand Pillay Carlo Toffalori Alex J. WilkiePresenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Model Theory of Fields: Lecture Notes in Logic 5, Second Edition
by David Marker Margit Messmer Anand PillayThe model theory of fields is a fascinating subject stretching from Tarski's work on the decidability of the theories of the real and complex fields to Hrushovksi's recent proof of the Mordell-Lang conjecture for function fields. This volume provides an insightful introduction to this active area, concentrating on connections to stability theory.
Model Theory of Stochastic Processes: Lecture Notes in Logic 14
by Sergio Fajardo H. Jerome KeislerThis book presents new research in probability theory using ideas from mathematical logic. It is a general study of stochastic processes on adapted probability spaces, employing the concept of similarity of stochastic processes based on the notion of adapted distribution. The authors use ideas from model theory and methods from nonstandard analysis
The Model Thinker: What You Need to Know to Make Data Work for You
by Scott E. PageHow anyone can become a data ninja From the stock market to genomics laboratories, census figures to marketing email blasts, we are awash with data. But as anyone who has ever opened up a spreadsheet packed with seemingly infinite lines of data knows, numbers aren't enough: we need to know how to make those numbers talk. In The Model Thinker, social scientist Scott E. Page shows us the mathematical, statistical, and computational models--from linear regression to random walks and far beyond--that can turn anyone into a genius. At the core of the book is Page's "many-model paradigm," which shows the reader how to apply multiple models to organize the data, leading to wiser choices, more accurate predictions, and more robust designs. The Model Thinker provides a toolkit for business people, students, scientists, pollsters, and bloggers to make them better, clearer thinkers, able to leverage data and information to their advantage.
Model Validation and Uncertainty Quantification, Vol. 3: Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024 (Conference Proceedings of the Society for Experimental Mechanics Series)
by Roland Platz Garrison Flynn Kyle Neal Scott OuelletteModel Validation and Uncertainty Quantification, Volume 3: Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics, 2024, the third volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Uncertainty Quantification in Dynamics Fusion of Test and Analysis Model Form Uncertainty: Round Robin Challenge UQVI (Uncertainty Quantification in Vibration Isolation) Recursive Bayesian System Identification Virtual Sensing & Realtime Monitoring Surrogate Modeling and Reduced Order Models
Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018 (Conference Proceedings of the Society for Experimental Mechanics Series)
by Robert BarthorpeModel Validation and Uncertainty Quantification, Volume 3: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018, the third volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on:Uncertainty Quantification in Material ModelsUncertainty Propagation in Structural DynamicsPractical Applications of MVUQAdvances in Model Validation & Uncertainty Quantification: Model UpdatingModel Validation & Uncertainty Quantification: Industrial ApplicationsControlling UncertaintyUncertainty in Early Stage DesignModeling of Musical InstrumentsOverview of Model Validation and Uncertainty
Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021 (Conference Proceedings of the Society for Experimental Mechanics Series)
by Zhu MaoModel Validation and Uncertainty Quantification, Volume 3: Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021, the third volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on:Inverse Problems and Uncertainty QuantificationControlling UncertaintyValidation of Models for Operating EnvironmentsModel Validation & Uncertainty Quantification: Decision MakingUncertainty Quantification in Structural DynamicsUncertainty in Early Stage DesignComputational and Uncertainty Quantification Tools
Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics 2023 (Conference Proceedings of the Society for Experimental Mechanics Series)
by Roland Platz Garrison Flynn Kyle Neal Scott OuelletteModel Validation and Uncertainty Quantification, Volume 3: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics, 2023, the third volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on:Introduction of Uncertainty QuantificationUncertainty Quantification in DynamicsModel Form Uncertainty and Selection incl. Round Robin ChallengeSensor and Information FusionVirtual Sensing, Certification, and Real-Time MonitoringSurrogate Modeling
Modeling, Analysis, Control and Removal of Oil and Hydrocarbon Spills (Earth and Environmental Sciences Library)
by Tatiana ChaplinaA large number of scientific works are devoted to the study and modeling of accidental oil spills. However, there is no single approach to the description of processes and a generally accepted system of models. An additional fundamental difficulty is the impossibility of conducting full-fledged full-scale experimental studies, which makes it difficult to verify the adequacy and accuracy of oil spill models. Our book is devoted to the problems of experimental investigation and theoretical description of spills, as well as the practical removal of various petroleum products from the water surface and ice. It provides an overview of the most well-known theoretical models of the process of spreading oil stains on the water surface. Also, in the relevant sections, an original spreading model based on an energy approach is proposed and analyzed. The results of new experimental studies of the dynamics of the process for various hydrocarbons on water, including variations in its temperatureand salinity, are presented. In the following chapters, a theoretical description of oil spreading on the upper and lower surfaces of floating ice is proposed, modeling phenomena in the Arctic and subarctic zones of the world ocean. New experimental data on the spreading of petroleum products on the ice surface are presented. The final part provides a brief overview of the existing most used and promising methods for removing of hydrocarbons from the water surface. New original constructive solutions to this problem are proposed, the technical characteristics of which have received theoretical justification and experimental confirmation.
Modeling and Analysis of Compositional Data (Statistics in Practice)
by Vera Pawlowsky-Glahn Juan José Egozcue Raimon Tolosana-DelgadoModeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method. Based upon short courses delivered by the authors, it provides a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to improve understanding, as well as data and a solutions manual which is available on an accompanying website. Complementing Pawlowsky-Glahn’s earlier collective text that provides an overview of the state-of-the-art in this field, Modeling and Analysis of Compositional Data fills a gap in the literature for a much-needed manual for teaching, self learning or consulting.
Modeling and Analysis of Dynamic Systems
by Ramin S. Esfandiari Bei LuModeling and Analysis of Dynamic Systems, Third Edition introduces MATLAB®, Simulink®, and Simscape™ and then utilizes them to perform symbolic, graphical, numerical, and simulation tasks. Written for senior level courses/modules, the textbook meticulously covers techniques for modeling a variety of engineering systems, methods of response analysis, and introductions to mechanical vibration, and to basic control systems. These features combine to provide students with a thorough knowledge of the mathematical modeling and analysis of dynamic systems. The Third Edition now includes Case Studies, expanded coverage of system identification, and updates to the computational tools included.
Modeling and Analysis of Linear Hyperbolic Systems of Balance Laws
by Krzysztof BarteckiThismonograph focuses on the mathematical modeling of distributed parameter systemsin which mass/energy transport or wave propagation phenomena occur and whichare described by partial differential equations of hyperbolic type. The case oflinear (or linearized) 2 x 2 hyperbolic systems of balance laws isconsidered, i. e. , systems described by two coupled linear partial differentialequations with two variables representing physical quantities, depending onboth time and one-dimensional spatial variable. Basedon practical examples of a double-pipe heat exchanger and a transportationpipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the samespatial point, and anti-collocated, inwhich the input signals are applied to the two different end points of thesystem. Theresults of this book emerge from the practical experience of the author gainedduring his studies conducted in the experimental installation of a heatexchange center as well as from his research experience in the field of mathematicaland computer modeling of dynamic systems. The book presents valuable resultsconcerning their state-space, transfer function and time-domain representations,which can be useful both for the open-loop analysis as well as for theclosed-loop design. Thebook is primarily intended to help professionals as well as undergraduate andpostgraduate students involved in modeling and automatic control of dynamicsystems.
Modeling and Analysis of Stochastic Systems (Chapman & Hall/CRC Texts in Statistical Science)
by Vidyadhar G. KulkarniBuilding on the author’s more than 35 years of teaching experience, Modeling and Analysis of Stochastic Systems, Third Edition, covers the most important classes of stochastic processes used in the modeling of diverse systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. The third edition has been updated with several new applications, including the Google search algorithm in discrete time Markov chains, several examples from health care and finance in continuous time Markov chains, and square root staffing rule in Queuing models. More than 50 new exercises have been added to enhance its use as a course text or for self-study. The sequence of chapters and exercises has been maintained between editions, to enable those now teaching from the second edition to use the third edition. Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, readers will be well-equipped to build and analyze useful stochastic models for real-life situations.
Modeling and Analytical Methods in Tribology
by Ilya I. Kudish Michael Judah CovitchImproving our understanding of friction, lubrication, and fatigue, Modeling and Analytical Methods in Tribology presents a fresh approach to tribology that links advances in applied mathematics with fundamental problems in tribology related to contact elasticity, fracture mechanics, and fluid film lubrication. The authors incorporate the classical
Modeling and Control for Micro/Nano Devices and Systems (Automation and Control Engineering #54)
by Ning Xi Mingjun Zhang AuthorMicro/nano-scale engineering—especially the design and implementation of ultra-fast and ultra-scale energy devices, sensors, and cellular and molecular systems—remains a daunting challenge. Modeling and control has played an essential role in many technological breakthroughs throughout the course of history. Therefore, the need for a practical guide to modeling and control for micro/nano-scale devices and systems has emerged. The first edited volume to address this rapidly growing field, Modeling and Control for Micro/Nano Devices and Systems gives control engineers, lab managers, high-tech researchers, and graduate students easy access to the expert contributors’ cutting-edge knowledge of micro/nanotechnology, energy, and bio-systems. The editors offer an integrated view from theory to practice, covering diverse topics ranging from micro/nano-scale sensors to energy devices and control of biology systems in cellular and molecular levels. The book also features numerous case studies for modeling of micro/nano devices and systems, and explains how the models can be used for control and optimization purposes. Readers benefit from learning the latest modeling techniques for micro/nano-scale devices and systems, and then applying those techniques to their own research and development efforts.
Modeling and Control in Vibrational and Structural Dynamics: A Differential Geometric Approach (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science)
by Peng-Fei YaoModeling and Control in Vibrational and Structural Dynamics: A Differential Geometric Approach describes the control behavior of mechanical objects, such as wave equations, plates, and shells. It shows how the differential geometric approach is used when the coefficients of partial differential equations (PDEs) are variable in space (waves/plates),
Modeling and Differential Equations in Biology (Lecture Notes In Pure And Applied Mathematics Ser. #58)
by T. A. BurtonFirst published in 1980. CRC Press is an imprint of Taylor & Francis.
Modeling and Interpreting Interactive Hypotheses in Regression Analysis
by Cindy D. Kam Robert J. Franzese Jr.Social scientists study complex phenomena about which they often propose intricate hypotheses tested with linear-interactive or multiplicative terms. While interaction terms are hardly new to social science research, researchers have yet to develop a common methodology for using and interpreting them. Modeling and Interpreting Interactive Hypotheses in Regression Analysisprovides step-by-step guidance on how to connect substantive theories to statistical models and how to interpret and present the results. "Kam and Franzese is a must-have for all empirical social scientists interested in teasing out the complexities of their data. " ---Janet M. Box-Steffensmeier, Ohio State University "Kam and Franzese have written what will become the definitive source on dealing with interaction terms and testing interactive hypotheses. It will serve as the standard reference for political scientists and will be one of those books that everyone will turn to when helping our students or doing our work. But more than that, this book is the best text I have seen for getting students to really think about the importance of careful specification and testing of their hypotheses. " ---David A. M. Peterson, Texas A&M University "Kam and Franzese have given scholars and teachers of regression models something they've needed for years: a clear, concise guide to understanding multiplicative interactions. Motivated by real substantive examples and packed with valuable examples and graphs, their book belongs on the shelf of every working social scientist. " ---Christopher Zorn, University of South Carolina "Kam and Franzese make it easy to model what good researchers have known for a long time: many important and interesting causal effects depend on the presence of other conditions. Their book shows how to explore interactive hypotheses in your own research and how to present your results. The book is straightforward yet technically sophisticated. There are no more excuses for misunderstanding, misrepresenting, or simply missing out on interaction effects!" ---Andrew Gould, University of Notre Dame Cindy D. Kam is Assistant Professor, Department of Political Science, University of California, Davis. Robert J. Franzese Jr. is Associate Professor, Department of Political Science, University of Michigan, and Research Associate Professor, Center for Political Studies, Institute for Social Research, University of Michigan. For datasets, syntax, and worksheets to help readers work through the examples covered in the book, visit: www. press. umich. edu/KamFranzese/Interactions. html
Modeling and Inverse Problems in the Presence of Uncertainty (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by H. T. Banks Shuhua Hu W. Clayton ThompsonModeling and Inverse Problems in the Presence of Uncertainty collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation i
Modeling and Optimization: Theory and Applications
by Boris Defourny Tamás TerlakyThis volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 13-15, 2014. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of deterministic and stochastic optimization techniques in energy, finance, logistics, analytics, healthcare, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.
Modeling and Optimization: Theory and Applications
by Martin Takáč Tamás TerlakyThis volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 17-19, 2016. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of deterministic and stochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.
Modeling and Optimization: Theory and Applications
by Luis F. Zuluaga Tamás TerlakyThis volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on July 30-August 1, 2012. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of optimization techniques in finance, logistics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.
Modeling and Optimization in Space Engineering: State of the Art and New Challenges (Springer Optimization and Its Applications #144)
by Giorgio Fasano János D. PintérThis book presents advanced case studies that address a range of important issues arising in space engineering. An overview of challenging operational scenarios is presented, with an in-depth exposition of related mathematical modeling, algorithmic and numerical solution aspects. The model development and optimization approaches discussed in the book can be extended also towards other application areas. The topics discussed illustrate current research trends and challenges in space engineering as summarized by the following list: • Next Generation Gravity Missions • Continuous-Thrust Trajectories by Evolutionary Neurocontrol • Nonparametric Importance Sampling for Launcher Stage Fallout • Dynamic System Control Dispatch • Optimal Launch Date of Interplanetary Missions • Optimal Topological Design • Evidence-Based Robust Optimization • Interplanetary Trajectory Design by Machine Learning • Real-Time Optimal Control • Optimal Finite Thrust Orbital Transfers • Planning and Scheduling of Multiple Satellite Missions • Trajectory Performance Analysis • Ascent Trajectory and Guidance Optimization • Small Satellite Attitude Determination and Control • Optimized Packings in Space Engineering • Time-Optimal Transfers of All-Electric GEO Satellites Researchers working on space engineering applications will find this work a valuable, practical source of information. Academics, graduate and post-graduate students working in aerospace, engineering, applied mathematics, operations research, and optimal control will find useful information regarding model development and solution techniques, in conjunction with real-world applications.