Numerical analysis Books

Book SynopsisBasic R Programming.- Random Variable Generation.- Monte Carlo Integration.- Controlling and Accelerating Convergence.- Monte Carlo Optimization.- Metropolis#x2013;Hastings Algorithms.- Gibbs Samplers.- Convergence Monitoring and Adaptation for MCMC Algorithms.Trade ReviewFrom the reviews:“Robert and Casella’s new book uses the programming language R, a favorite amongst (Bayesian) statisticians to introduce in eight chapters both basic and advanced Monte Carlo techniques … . The book could be used as the basic textbook for a semester long course on computational statistics with emphasis on Monte Carlo tools … . useful for (and should be next to the computer of) a large body of hands on graduate students, researchers, instructors and practitioners … .” (Hedibert Freitas Lopes, Journal of the American Statistical Association, Vol. 106 (493), March, 2011)“Chapters focuses on MCMC methods the Metropolis–Hastings algorithm, Gibbs sampling, and monitoring and adaptation for MCMC algorithms. … There are exercises within and at the end of all chapters … . Overall, the level of the book makes it suitable for graduate students and researchers. Others who wish to implement Monte Carlo methods, particularly MCMC methods for Bayesian analysis will also find it useful.” (David Scott, International Statistical Review, Vol. 78 (3), 2010)“The primary audience is graduate students in statistics, biostatistics, engineering, etc. who need to know how to utilize Monte Carlo simulation methods to analyze their experiments and/or datasets. … this text does an effective job of including a selection of Monte Carlo methods and their application to a broad array of simulation problems. … Anyone who is an avid R user and has need to integrate and/or optimize complex functions will find this text to be a necessary addition to his or her personal library.” (Dean V. Neubauer, Technometrics, Vol. 53 (2), May, 2011)Table of ContentsBasic R Programming.- Random Variable Generation.- Monte Carlo Integration.- Controlling and Accelerating Convergence.- Monte Carlo Optimization.- Metropolis#x2013;Hastings Algorithms.- Gibbs Samplers.- Convergence Monitoring and Adaptation for MCMC Algorithms.

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Book SynopsisPreliminary concepts.- Nonlinear Finite Element Analysis Procedure.- Finite Element Analysis for Nonlinear Elastic Systems.- Finite Element Analysis for Elastoplastic Problems.- Finite Element Analysis for Contact Problems. Table of ContentsPreliminary concepts.- Nonlinear Finite Element Analysis Procedure.- Finite Element Analysis for Nonlinear Elastic Systems.- Finite Element Analysis for Elastoplastic Problems.- Finite Element Analysis for Contact Problems.

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Book SynopsisImplicit Functions and Solution MappingsTrade Review“The book represents the state of the art of the modern theory of inverse and implicit functions and provides an important source for studies of numerical methods and applications in this area. It can be warmly recommended to all specialists and advanced students working in optimization, analysis, numerical mathematics, and other mathematical fields, as well as to all those who apply variational analysis in engineering, physics, operations research, economics, finance, and more.” (Diethard Klatte, SIAM Review, Vol. 57 (2), June, 2015)“The book commences with a helpful context-setting preface followed by six chapters. Each chapter starts with a useful preamble and concludes with a careful and instructive commentary, while a good set of references, a notation guide and a somewhat brief index complete this study. … I unreservedly recommended this book to all practitioners and graduate students interested in modern optimization theory or control theory or to those just engaged by beautiful analysis cleanly described.” (Jonathan Michael Browein, IEEE Control Systems Magazine, February, 2012).“This book is devoted to the theory of inverse and implicit functions and some of its modifications for solution mappings in variational problems. … The book is targeted to a broad audience of researchers, teachers and graduate students. It can be used as well as a textbook as a reference book on the topic. Undoubtedly, it will be used by mathematicians dealing with functional and numerical analysis, optimization, adjacent branches and also by specialists in mechanics, physics, engineering, economics and so on.” (Peter Zabreiko, Zentralblatt MATH, Vol. 1178, 2010).“The present monograph will be a most welcome and valuable addition. … This book will save much time and effort, both for those doing research in variational analysis and for students learning the field. This important contribution fills a gap in the existing literature.” (Stephen M. Robinson, Mathematical Reviews, Issue 2010).Table of ContentsIntroduction and equation-solving background.- Solution mappings for variational problems.- Set-valued analysis of solution mappings.- Regularity properties through generalized derivatives.- Metric regularity in infinite dimensions.- Applications in numerical variational analysis.

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Book SynopsisRandom Number Generators, Principles and Practices has been written for programmers, hardware engineers, and sophisticated hobbyists interested in understanding random numbers generators and gaining the tools necessary to work with random number generators with confidence and knowledge. Using an approach that employs clear diagrams and running code examples rather than excessive mathematics, random number related topics such as entropy estimation, entropy extraction, entropy sources, PRNGs, randomness testing, distribution generation, and many others are exposed and demystified. If you have ever Wondered how to test if data is really random Needed to measure the randomness of data in real time as it is generated Wondered how to get randomness into your programs Wondered whether or not a random number generator is trustworthy Wanted to be able to choose between random number generator solutions Needed to turn uniform random data into a different distribution NeededTable of Contents1 Introduction 1.1 Tools 1.2 Terminology 1.3 The Many Types of Random Numbers 1.3.1 Uniform Random Numbers 2 Random Number Generators 2.1 Classes of Random Number Generators 2.2 Names for RNGs 3 Making Random Numbers 3.1 A Quick Overview of the RNG Types 3.2 The Structure of Full RNG Implementations 3.3 Pool Extractor Structures 3.4 Multiple Input Extractors 4 Physically Uncloneable Functions 21 4.1 The other kind âAS Static vs. Dynamic Random Number Generators . 5 Testing Random Numbers 5.1 Known Answer Tests 5.2 Distinguishing From Random 5.3 PRNG Test Suites 5.4 Entropy Measurements 5.5 Min Entropy Estimation 5.6 Model Equivalence Testing 5.7 Statistical Prerequisite Testing 5.8 The problem Distinguishing Entropy and Pseudo-randomness 5.9 PRNG Tests: DieHarder, NIST SP800-22,TestU01, China ICS 35.040 5.10 Entropy Measurements 5.11 Min Entropy Measurements 5.12 Modeling to Test a Source 5.13 Statistical Prerequisites 5.14 Testing for bias . 5.15 results that are âAŸtoo goodâAZ (E.G. Chi-square == 0.5) 5.16 Distinguishing Correlation from Bias 5.17 Testing for Stationary properties 5.18 FFT analysis 5.19 Online Testing 5.20 Working From the Source RNG 5.21 Tools 5.22 Summary 6 Entropy Extraction or Distillation 6.1 A simple extractor, the XOR gate 6.2 A simple way of improving the distribution of random numbers that have known missing values using XOR 7 Quantifying Entropy 7.1 Rényi Entropy 7.2 Distance From Uniform Topics to put somewhere in the book- in existing chapters and new chapters 8.1 XOR as a 2 bit extractor 8.2 Properties of real random numbers 8.3 Binomial distributions 8.4 Normal distributions 8.4.1 Dice, more dice 8.4.2 Central limit theorem 8.5 Seeing patterns 8.6 Regression to the mean 8.7 Lack of correlation, bias, algorithmic connections, predictability 8.8 What’s a True random number? 8.9 Random numbers in cryptography 8.10 Things they help with liveness, unpredictability, resistance to attacks 8.11 Examples of use 8.11.1 Salting Passwords . 8.11.2 802.11i exchange 8.11.3 PKMv2 exchange 8.11.4 Making Keys 8.12 Examples of RNG crypto failures 8.12.1 Sony PS3 attack 8.12.2 MiFare Classic 8.12.3 Online Poker 8.12.4 Debian OpenSSL Fiasco 8.12.5 Linux Boot Time Entropy 8.13 Humans and random numbers 8.14 Result of asking people for a random number 8.14.1 Normal People 8.14.2 Crypto People 8.15 Mental Random Number Tricks 8.15.1 How to think of a really random number 8.16 PRNGs 8.17 extractors 8.17.1 CBC MAC 8.17.2 BIW 8.17.3 Von Neumann 8.18 Extractor Theory 8.19 Random Number Standards 8.19.1 SP800-90A B C . 8.19.2 Ansi X9.82 8.20 PRNG Algorithms 8.20.1 SP800-90A CTR DRBG 8.20.2 SP800-90A SHA DRBG 8.20.3 XOR Construction 8.20.4 Oversampling Construction 8.21 Yarrow 8.22 Whirlpool 8.23 Linux Kernel random service 8.24 Appendices 8.25 Resources 8.25.1 SW Sources 8.25.2 Online random number sources 8.26 Example Algorithm Vectors 8.26.1 SP800-90A CTR DRBG 128 & 256 8.26.2 SP800-90A Hash DRBG SHA-1 & SHA 256 8.26.3 AES-CBC-MAC Conditioner 128 8.26.4 AES-CBC-MAC Conditioner 8.27 SP800-90 LZ Tests Issues

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Book SynopsisBiometrics, the science of using physical traits to identify individuals, is playing an increasing role in our security-conscious society and across the globe. Biometric authentication, or bioauthentication, systems are being used to secure everything from amusement parks to bank accounts to military installations. Yet developments in this field have not been matched by an equivalent improvement in the statistical methods for evaluating these systems. Compensating for this need, this unique text/reference provides a basic statistical methodology for practitioners and testers of bioauthentication devices, supplying a set of rigorous statistical methods for evaluating biometric authentication systems. This framework of methods can be extended and generalized for a wide range of applications and tests. This is the first single resource on statistical methods for estimation and comparison of the performance of biometric authentication systems. The book focuses on six common performance metrics: for each metric, statistical methods are derived for a single system that incorporates confidence intervals, hypothesis tests, sample size calculations, power calculations and prediction intervals. These methods are also extended to allow for the statistical comparison and evaluation of multiple systems for both independent and paired data. Topics and features: * Provides a statistical methodology for the most common biometric performance metrics: failure to enroll (FTE), failure to acquire (FTA), false non-match rate (FNMR), false match rate (FMR), and receiver operating characteristic (ROC) curves * Presents methods for the comparison of two or more biometric performance metrics * Introduces a new bootstrap methodology for FMR and ROC curve estimation * Supplies more than 120 examples, using publicly available biometric data where possible * Discusses the addition of prediction intervals to the bioauthentication statistical toolset * Describes sample-size and power calculations for FTE, FTA, FNMR and FMR Researchers, managers and decisions makers needing to compare biometric systems across a variety of metrics will find within this reference an invaluable set of statistical tools. Written for an upper-level undergraduate or master’s level audience with a quantitative background, readers are also expected to have an understanding of the topics in a typical undergraduate statistics course. Dr. Michael E. Schuckers is Associate Professor of Statistics at St. Lawrence University, Canton, NY, and a member of the Center for Identification Technology Research.Table of ContentsPart I: Introduction Introduction Statistical Background Part II: Primary Matching and Classification Measures False Non-Match Rate False Match Rate Receiver Operating Characteristic Curve and Equal Error Rate Part III: Biometric Specific Measures Failure to Enrol Failure to Acquire Part IV: Additional Topics and Appendices Additional Topics and Discussion Tables

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Book SynopsisThis volume gathers the latest advances and innovations in the field of flow-induced vibration and noise, as presented by leading international researchers at the 3rd International Symposium on Flow Induced Noise and Vibration Issues and Aspects (FLINOVIA), which was held in Lyon, France, in September 2019. It explores topics such as turbulent boundary layer-induced vibration and noise, tonal noise, noise due to ingested turbulence, fluid-structure interaction problems, and noise control techniques. The authors’ backgrounds represent a mix of academia, government, and industry, and several papers include applications to important problems for underwater vehicles, aerospace structures and commercial transportation. The book offers a valuable reference guide for all those interested in measurement, modelling, simulation and reproduction of the flow excitation and flow induced structural response.Table of ContentsSource Modeling.- Experimental Techniques.- Analytical Developments.- Numerical Methods.

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Book SynopsisThis book presents a system that combines the expertise of four algorithms, namely Gradient Tree Boosting, Logistic Regression, Random Forest and Support Vector Classifier to trade with several cryptocurrencies. A new method for resampling financial data is presented as alternative to the classical time sampled data commonly used in financial market trading. The new resampling method uses a closing value threshold to resample the data creating a signal better suited for financial trading, thus achieving higher returns without increased risk. The performance of the algorithm with the new resampling method and the classical time sampled data are compared and the advantages of using the system developed in this work are highlighted.Trade Review“The book contains little theory and presents mostly detailed numerical experiments, it reads very engagingly and inspires with many ideas. It is certainly not a reference book but rather a short monograph on a very clearly defined topic. It will be interesting to see whether the trading strategies presented can be transferred from the crypto markets to the presumably more efficient standard stock markets … as published strategies tend to make markets more efficient.” (Volker H. Schulz, SIAM Review, Vol. 64 (3), September, 2022)Table of ContentsChapter 1 - Introduction Chapter 2 - Related work Chapter 3 - Implementation Chapter 4 - Results Chapter 5 - Conclusions and future work

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Book SynopsisThis text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.Trade Review“This book has a large amount of new exercise problems that are uniformly distributed across the text. … this book is a very nice text which will serve well for the undergraduate as well as graduate students and will also become a ready reference for scholars.” (Murli M. Gupta, Mathematical Reviews, April, 2023)“Many of the SIAM Review readership will be interested in NMEPPDE from the standpoint of self-study or classroom education. … NMEPPDE offers the applied mathematics reader nearly a single point of entry to our broad and challenging area. … a bit of open space on the bookshelf could profitably be well filled with a copy of NMEPPDE.” (Robert C. Kirby, SIAM Review, Vol. 65 (1), March, 2023)Table of ContentsFor Example: Modelling Processes in Porous Media with Differential Equations.- For the Beginning: The Finite Difference Method for the Poisson Equation.- The Finite Element Method for the Poisson Equation.- The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order.- Grid Generation and A Posteriori Error Estimation.- Iterative Methods for Systems of Linear Equations.- Beyond Coercivity, Consistency and Conformity.- Mixed and Nonconforming Discretization Methods.- The Finite Volume Method.- Discretization Methods for Parabolic Initial Boundary Value Problems.- Discretization Methods for Convection-Dominated Problems.- An Outlook to Nonlinear Partial Differential Equations.- Appendices.

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Book Synopsis1 Introduction.- 2 Hilbert space splittings: Abstract theory.- References.- 3 Hilbert space splittings: Examples and extensions.- References.- 4 Schwarz iterative methods: Finite Omega.- References.- 5 Special topics and extensions.- References.- 6 Schwarz approximation methods: Infinite Omega.- References.- 7 Applications to PDE solvers.- References.- A Hilbert space basics.- A.1 Spaces: Basic notation, definitions and properties.- A.2 Operators between Hilbert spaces.- A.3 Linear equations and variational problems.- A.4 Constructions on Hilbert spaces.- A.5 Sobolev spaces on domains.- A.6 Reproducing kernel Hilbert spaces (RKHS).- References.- Index.

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Book Synopsis.- Bounding the price-of-fair-sharing using knapsack-cover constraints to guide near-optimal cost-recovery algorithms..- Improved online scheduling with restarts on a single machine..- Searching in Euclidean Spaces with Predictions..- Lower Bounds for Approximate (& Exact) k-Disjoint-Shortest-Paths...- Approximating delta-Covering..- Fast Approximation Algorithms for Euclidean Minimum Weight Perfect Matching..- Approximation Algorithms for k-Scenario Matching..- Tight Approximation Bounds on a Simple Algorithm for Minimum Average Search Time in Trees..- Online Deterministic Minimum Cost Bipartite Matching with Delays on a Line..- Maximizing Throughput for Parallel Jobs with Speed-up Curves..- Improved approximation algorithms for covering pliable set families and flexible graph connectivity..- Small additive error for unsplittable multicommodity flow in outerplanar graphs..- Complexity of Fixed Order Routing..- Approximate Min-Sum Subset Convolution..- Online String Attractors.

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Book SynopsisPart 1 - Extreme Scientific Computing Software Management.- Chapter 1 Linux Command Line.- Chapter 2: Version Control and Repositories.- Chapter 3: Building Software.- Part 2 - Programming Patterns and Modern C++.- Chapter 4: The C++ Ecosystem.- Chapter 5: Primitive C++.- Chapter 6: Advanced C++.- Chapter 7: Modern C++ and guidelines.- Chapter 8: The Standard Template Library.

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Book SynopsisChapter 1. Introduction.- Part I. Theory and Finite Elements for Elliptic PDEs.- Chapter 2. Topics from the Theory of Elliptic PDEs.- Chapter 3. Topics from Finite Elements for Elliptic PDEs.- Part II. Distributed Control Problems.- Chapter 4. No Inequality Constraints.- Chapter 5. Control Constraints.- Chapter 6. Bang-Bang Controls.- Chapter 7. Semilinear State Equation.- Part III. Boundary Control Problems.- Chapter 8. Neumann Control.- Chapter 9. Dirichlet Control.- Part IV. Problems Involving Dirac Measures.- Chapter 10. Pointwise Control.- Chapter 11. Pointwise Tracking.- Chapter 12. Finitely Many Pointwise State Constraints.- Part V. Problems Involving General Measures.- Chapter 13. State Constraints.- Chapter 14. Sparse Controls.

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Book Synopsis.- GRASP-based memetic algorithm for Multi-period technician routingproblem with mandatory assigned tasks and selective tasks..- Investigation of Structures for Routing Rules Designed by GeneticProgramming for the Electric Vehicle Routing Problem,..- Optimizing Scheduling for Energy Sales in Public Stations: A RevenueManagement Perspective..- A study of an ant-based algorithm to model cyclist behavior inbicycle-friendly cities..- Paving the way towards evolutionary machine teaching: an applicationto 4-part harmony..- Scalable Local Optima Networks for Continuous Search Spaces..- Comparing Quantum Annealer and Metaheuristic Methods to Solve theSteiner Tree Problem..- Classi cation vs Regression Models in a Decision Tree-based InteractiveEvolutionary Multi-objective Optimization Algorithm..- Tackling Long-Range Dependencies in Dynamic Range CompressionModeling via Deep Learning..- Optimizing Reservoir Computing with Genetic Algorithm forHigh-Dimensional SARS-CoV-2 Hospitalization Forecasting: Impacts ofGenetic Algorithm Hyperparameters on Feature Selection andReservoir Computing Hyperparameter Tuning..- Can Mutations Replace Local Search? Studying the E ect of RepeatedGenetic Programming Operators in the Unrelated MachinesEnvironment..- Optimizing the Viability of interacting systems with EvolutionaryAlgorithms..- Single-objective constrained optimization for Gene RegulatoryNetworks Modeling..- Symbolic Regression of Con dence Intervals for Conformal Prediction..- A New Step Size Update Strategy for CMA-ES in Multi-objectiveOptimisation..- UMDA with random a ne maps.

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Book SynopsisMathematical models cannot be solved using the traditional analytical methods for dynamic equations on time scales. These models must be dealt with using computational methods. This textbook introduces numerical methods for initial value problems for dynamic equations on time scales. Hands-on examples utilizing MATLAB and practical problems illustrate a wide variety of solution techniques.

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Book SynopsisThe first part of this book is mainly intended as a textbook for students at the Sophomore-Junior level, majoring in mathematics, engineering, or the sciences in general. The book includes the basic topics in Ordinary Differential Equations, normally taught at the undergraduate level, such as linear and nonlinear equations and systems, Bessel functions, Laplace transform, stability, etc. It is written with ample flexibility to make it appropriate either as a course stressing application, or a course stressing rigor and analytical thinking. It also offers sufficient material for a one-semester graduate course, covering topics such as phase plane analysis, oscillation, Sturm-Liouville equations, Euler-Lagrange equations in Calculus of Variations, first and second order linear PDE in 2D. There are substantial lists of exercises at the ends of the chapters. In this edition complete solutions to all even number problems are given in the back of the book.The 2nd edition also includes some new problems and examples. An effort has been made to make the material more suitable and self-contained for undergraduate students with minimal knowledge of Calculus. For example, a detailed review of matrices and determinants has been added to the chapter on systems of equations. The second edition also contains corrections of some misprints and errors in the first edition.

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Book SynopsisThe organization of the material is presented as follows: This introductory chapter I represents a theoretical analysis of the computational algorithms for a numerical solution of the basic equations in continuum mechanics. In this chapter, the general requirements for computational grids, discretization, and iterative methods for black-box software are examined. Finally, a concept of a two-grid algorithm for (de-)coupled solving multidimensional non-linear (initial-)boundary value problems in continuum mechanics (multiphysics simulation) in complex domains is presented. Chapter II contains descriptions of the sequential Robust Multigrid Technique which is developed as a general-purpose solver in black-box codes. This chapter presents the main components of the Robust Multigrid Technique (RMT) used in the two-grid algorithm (Chapter I) to compute the auxiliary (structured) grid correction. This includes the generation of multigrid structures, computation of index mapping, and integral evaluation. Finite volume discretization on the multigrid structures will be explained by studying a 1D linear model problem. In addition, the algorithmic complexity of RMT and black-box optimization of the problem-dependent components of RMT are analysed. Chapter III provides a description of parallel RMT. This chapter introduces parallel RMT-based algorithms for solving the boundary value problems and initial-boundary value problems in unified manner. Section 1 presents a comparative analysis of the parallel RMT and the sequential V-cycle. Sections 2 and 3 present a geometric and an algebraic parallelism of RMT, i.e. parallelization of the smoothing iterations on the coarse and the levels. A parallel multigrid cycle will be considered in Section 4. A parallel RMT for the time-dependent problems is given in Section 5. Finally, the basic properties of parallel RMT will be summarized in Section 6. Theoretical aspects of the used algorithms for solving multidimensional problems are discussed in Chapters IV. This chapter contains the theoretical aspects of the algorithms used for the numerical solving of the resulting system of linear algebraic equations obtained from discrete multidimensional (initial-)boundary value problems.

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Book SynopsisThis book presents a comprehensive set of guidelines and applications of DIgSILENT PowerFactory, an advanced power system simulation software package, for different types of power systems studies. Written by specialists in the field, it combines expertise and years of experience in the use of DIgSILENT PowerFactory with a deep understanding of power systems analysis. These complementary approaches therefore provide a fresh perspective on how to model, simulate and analyse power systems. It presents methodological approaches for modelling of system components, including both classical and non-conventional devices used in generation, transmission and distribution systems, discussing relevant assumptions and implications on performance assessment. This background is complemented with several guidelines for advanced use of DSL and DPL languages as well as for interfacing with other software packages, which is of great value for creating and performing different types of steady-state and dynamic performance simulation analysis. All employed test case studies are provided as supporting material to the reader to ease recreation of all examples presented in the book as well as to facilitate their use in other cases related to planning and operation studies. Providing an invaluable resource for the formal instruction of power system undergraduate/postgraduate students, this book is also a useful reference for engineers working in power system operation and planning.Table of ContentsLoad Flow Calculation and its Application.- Modelling of Transmission Systems under Unsymmetrical Conditions and contingency analysis using DIgSILENT PowerFactory.- Probabilistic load flow module for PowerFactory.- Unbalanced Power Flow in Distribution Systems using TRX Matrix: Implementation using DIgSILENT Programming Language.- Primal-dual interior point algorithm applied to DC optimal power flow using DIgSILENT Programming Language.- Indices to Assess the Integration of Renewable Energy Resources on Standard Test Networks through DIgSILENT’s Programming Language.- Modelling of automatic generation control in power systems.- Gas Turbine Modelling for Power System Dynamic Simulation Studies.- Implementation of Simplified Models of DFG-Based Wind Turbines for RMS-Type Simulation in DIgSILENT Power Factory.- Parameterized modal analysis using DIgSILENT Programming Language.- Probabilistic Approach for Risk Evaluation of Power System Oscillatory Stability.- Mean-Variance Mapping Optimization Algorithm for Power System Applications in DIgSILENT Power Factory.- Application and Requirement of DIgSILENT PowerFactory to Matlab/Simulink Interface.- Advanced applications of DPL language: Simulation automation and management of results.- Interfacing PowerFactory: co-simulation, real-time simulation and controller hardware-in-the-loop applications.- PowerFactory as a software stand-in for Hardware-In-Loop Testing.- Programming of simplified models of Flexible Alternating Current Transmission System (FACTS) devices using DIgSILENT Simulation Language.- Active and Reactive Power Control of Wind Farm based on Integrated Platform of PowerFactory and Matlab.- Implementation of Simplified Models of Local Controller for Muti-terminal HVDC Systems in DIgSILENT Power Factory.- Estimation of Equivalent Model for Clusters of Induction Generators based on PMU Measurements.

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Book SynopsisThis book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics.A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.Trade Review“This is the second edition of an undergraduate introduction to ordinary differential equations suitable for mathematicians and engineers. … The style is clean and concise with many examples and exercises. Basic results are proven, more involved results are only stated. The new edition features some new exercises and better explanations at various points. So if you are looking for an application oriented introduction which is still concise and rigorous, this book might be just right for you.” (G. Teschl, Monatshefte für Mathematik, 2016)Table of Contents1 First order linear differential equations.- 2 Theory of first order differential equations.- 3 First order nonlinear differential equations.- 4 Existence and uniqueness for systems and higher order equations.- 5 Second order equations.- 6 Higher order linear equations.- 7 Systems of first order equations.- 8 Qualitative analysis of 2x2 systems and nonlinear second order equations.- 9 Sturm Liouville eigenvalue theory.- 10 Solutions by infinite series and Bessel functions.- 11 Laplace transform.- 12 Stability theory.- 13 Boundary value problems.- 14 Appendix A. Numerical methods.- 15 Answers to selected exercises.

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Book SynopsisThe authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.Table of ContentsIntroduction.- I. Applications: Methods I: Planar reduction; Method II: The energy-momentum map.- II. Theory: Birkhoff Normalization; Singularity Theory; Gröbner bases and Standard bases; Computing normalizing transformations.- Appendix A.1. Classification of term orders; Appendix A.2. Proof of Proposition 5.8.- References.- Index.

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Book SynopsisThese notes are an elaboration of the first part of a course on foliations which I have given at Strasbourg in 1976 and at Tunis in 1977. They are concerned mostly with dynamical sys­ tems in dimensions one and two, in particular with a view to their applications to foliated manifolds. An important chapter, however, is missing, which would have been dealing with structural stability. The publication of the French edition was re­ alized by-the efforts of the secretariat and the printing office of the Department of Mathematics of Strasbourg. I am deeply grateful to all those who contributed, in particular to Mme. Lambert for typing the manuscript, and to Messrs. Bodo and Christ for its reproduction. Strasbourg, January 1979. Table of Contents I. VECTOR FIELDS ON MANIFOLDS 1. Integration of vector fields. 1 2. General theory of orbits. 13 3. Irlvariant and minimaI sets. 18 4. Limit sets. 21 5. Direction fields. 27 A. Vector fields and isotopies. 34 II. THE LOCAL BEHAVIOUR OF VECTOR FIELDS 39 1. Stability and conjugation. 39 2. Linear differential equations. 44 3. Linear differential equations with constant coefficients. 47 4. Linear differential equations with periodic coefficients. 50 5. Variation field of a vector field. 52 6. Behaviour near a singular point. 57 7. Behaviour near a periodic orbit. 59 A. Conjugation of contractions in R. 67 III. PLANAR VECTOR FIELDS 75 1. Limit sets in the plane. 75 2. Periodic orbits. 82 3. Singular points. 90 4. The Poincare index.Table of ContentsI. Vector Fields on Manifolds.- 1. Integration of vector fields.- 2. General theory of orbits.- 3. Invariant and minimal sets.- 4. Limit sets.- 5. Direction fields.- A. Vector fields and isotopies.- II. The Local Behaviour of Vector Fields.- 1. Stability and conjugation.- 2. Linear differential equations.- 3. Linear differential equations with constant coefficients.- 4. Linear differential equations with periodic coefficients.- 5. Variation field of a vector field.- 6. Behaviour near a singular point.- 7. Behaviour near a periodic orbit.- A. Conjugation of contractions in R.- III. Planar Vector Fields.- 1. Limit sets in the plane.- 2. Periodic orbits.- 3. Singular points.- 4. The Poincaré index.- 5. Planar direction fields.- 6. Direction, fields on cylinders and Moebius strips.- A. Singular generic foliations of a disc.- IV. Direction Fields on the Torus and Homeomorphisms of the Circle.- 1. Direction fields on the torus.- 2. Direction fields on a Klein bottle.- 3. Homeomorphisms of the circle without periodic point.- 4. Rotation number of Poincaré.- 5. Conjugation of circle homeomorphisms to rotations.- A. Homeomorphism groups of an interval.- B. Homeomorphism groups of the circle.- V. Vector Fields on Surfaces.- 1. Classification of compact surfaces.- 2. Vector fields on surfaces.- 3. The index theorem.- A. Elements of differential geometry of surfaces.

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Book SynopsisHigh resolution upwind and centered methods are a mature generation of computational techniques. They are applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. For its third edition the book has been thoroughly revised to contain new material.Table of ContentsThe Equations of Fluid Dynamics.- Notions on Hyperbolic Partial Differential Equations.- Some Properties of the Euler Equations.- The Riemann Problem for the Euler Equations.- Notions on Numerical Methods.- The Method of Godunov for Non#x2014;linear Systems.- Random Choice and Related Methods.- Flux Vector Splitting Methods.- Approximate#x2014;State Riemann Solvers.- The HLL and HLLC Riemann Solvers.- The Riemann Solver of Roe.- The Riemann Solver of Osher.- High#x2013;Order and TVD Methods for Scalar Equations.- High#x2013;Order and TVD Schemes for Non#x2013;Linear Systems.- Splitting Schemes for PDEs with Source Terms.- Methods for Multi#x2013;Dimensional PDEs.- Multidimensional Test Problems.- FORCE Fluxes in Multiple Space Dimensions.- The Generalized Riemann Problem.- The ADER Approach.- Concluding Remarks.

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Book SynopsisWave propagation is an important topic in engineering sciences, especially, in the field of solid mechanics. A description of wave propagation phenomena is given by Graff [98]: The effect of a sharply applied, localized disturbance in a medium soon transmits or 'spreads' to other parts of the medium. These effects are familiar to everyone, e.g., transmission of sound in air, the spreading of ripples on a pond of water, or the transmission of radio waves. From all wave types in nature, here, attention is focused only on waves in solids. Thus, solely mechanical disturbances in contrast to electro-magnetic or acoustic disturbances are considered. of waves - the compression wave similar to the In solids, there are two types pressure wave in fluids and, additionally, the shear wave. Due to continual reflec­ tions at boundaries and propagation of waves in bounded solids after some time a steady state is reached. Depending on the influence of the inertia terms, this state is governed by a static or dynamic equilibrium in frequency domain. However, if the rate of onset of the load is high compared to the time needed to reach this steady state, wave propagation phenomena have to be considered.Table of Contents1. Introduction.- 2. Convolution quadrature method.- 2.1 Basic theory of the convolution quadrature method.- 2.2 Numerical tests.- 2.2.1 Series expansion of the test functions f1 and f2.- 2.2.2 Computing the integration weights ?n.- 2.2.3 Numerical convolution.- 3. Viscoelastically supported Euler-Bernoulli beam.- 3.1 Integral equation for a beam resting on viscoelastic foundation.- 3.1.1 Fundamental solutions.- 3.1.2 Integral equation.- 3.2 Numerical example.- 3.2.1 Fixed-simply supported beam.- 3.2.2 Fixed-free viscoelastic supported beam.- 4. Time domain boundary element formulation.- 4.1 Integral equation for elastodynamics.- 4.2 Boundary element formulation for elastodynamics.- 4.3 Validation of proposed method: Wave propagation in a rod.- 4.3.1 Influence of the spatial and time discretization.- 4.3.2 Comparison with the “classical” time domain BE formulation.- 5. Viscoelastodynamic boundary element formulation.- 5.1 Viscoelastic constitutive equation.- 5.2 Boundary integral equation.- 5.3 Boundary element formulation.- 5.4 Validation of the method and parameter study.- 5.4.1 Three-dimensional rod.- 5.4.2 Elastic foundation on viscoelastic half space.- 6. Poroelastodynamic boundary element formulation.- 6.1 Biot’s theory of poroelasticity.- 6.1.1 Elastic skeleton.- 6.1.2 Viscoelastic skeleton.- 6.2 Fundamental solutions.- 6.3 Poroelastic Boundary Integral Formulation.- 6.3.1 Boundary integral equation.- 6.3.2 Boundary element formulation.- 6.4 Numerical studies.- 6.4.1 Influence of time step size and mesh size.- 6.4.2 Poroelastic half space.- 7. Wave propagation.- 7.1 Wave propagation in poroelastic one-dimensional column.- 7.1.1 Analytical solution.- 7.1.2 Poroelastic results.- 7.1.3 Poroviscoelastic results.- 7.2 Waves in half space.- 7.2.1 Rayleigh surface wave.- 7.2.2 Slow compressional wave in poroelastic half space.- 8. Conclusions — Applications.- 8.1 Summary.- 8.2 Outlook on further applications.- A. Mathematic preliminaries.- A.1 Distributions or generalized functions.- A.2 Convolution integrals.- A.3 Laplace transform.- A.4 Linear multistep method.- B. BEM details.- B.1 Fundamental solutions.- B.1.1 Visco- and elastodynamic fundamental solutions.- B.1.2 Poroelastodynamic fundamental solutions.- B.2 “Classical” time domain BE formulation.- Notation Index.- References.

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Book SynopsisThis work provides an introduction to four central problems in analytic number theory. These are (1) the problems of estimating the number of integer points in planar domains, (2) the problem of the distribution of prime numbers in the sequence of all natural numbers and in arithmetic progressions, (3) Goldbach's problems on sums of primes, and (4) Waring's problem on sums of k-th powers. The following fundamental methods of analytic number theory are used to solve these problems: complex integration, I.M. Vinogradov's method of trigonometric sums, and the circle method of G.H. Hardy, J.E. Littlewood, and S. Ramanujan. There are numerous exercises at the end of each chapter. These exercises either refine the theorems proved in the text, or lead to new ideas in number theory. The author also includes a section of hints for the solution of the exercises.

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Book SynopsisThe subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. James Clerk Maxwell, for example, put electricity and magnetism into a unified theory by establishing Maxwell's equations for electromagnetic theory, which gave solutions for prob­ lems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechanical processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier­ Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forecasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.Table of Contents1. Background Mathematics.- 1.1 Introduction.- 1.2 Vector and Matrix Norms.- 1.3 Gerschgorin’s Theorems.- 1.4 Iterative Solution of Linear Algebraic Equations.- 1.5 Further Results on Eigenvalues and Eigenvectors.- 1.6 Classification of Second Order Partial Differential Equations.- 2. Finite Differences and Parabolic Equations.- 2.1 Finite Difference Approximations to Derivatives.- 2.2 Parabolic Equations.- 2.3 Local Truncation Error.- 2.4 Consistency.- 2.5 Convergence.- 2.6 Stability.- 2.7 The Crank-Nicolson Implicit Method.- 2.8 Parabolic Equations in Cylindrical and Spherical Polar Coordinates.- 3. Hyperbolic Equations and Characteristics.- 3.1 First Order Quasi-linear Equations.- 3.2 Lax-Wendroff and Wendroff Methods.- 3.3 Second Order Quasi-linear Hyperbolic Equations.- 3.4 Reetangular Nets and Finite Difference Methods for Second Order Hyperbolic Equations.- 4. Elliptic Equations.- 4.1 Laplace’s Equation.- 4.2 Curved Boundaries.- 4.3 Solution of Sparse Systems of Linear Equations.- 5. Finite Element Method for Ordinary Differential Equations.- 5.1 Introduction.- 5.2 The Collocation Method.- 5.3 The Least Squares Method.- 5.4 The Galerkin Method.- 5.5 Symmetrie Variational Forrnulation.- 5.6 Finite Element Method.- 5.7 Some Worked Examples.- 6. Finite Elements for Partial Differential Equations.- 6.1 Introduction.- 6.2 Variational Methods.- 6.3 Some Specific Elements.- 6.4 Assembly of the Elements.- 6.5 Worked Example.- 6.6 A General Variational Principle.- 6.7 Assembly and Solution.- 6.8 Solution of the Worked Example.- 6.9 Further Interpolation Functions.- 6.10 Quadrature Methods and Storage Considerations.- 6.11 Boundary Element Method.- A. Solutions to Exercises.- References and Further Reading.

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Book SynopsisBackward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives. They are of growing importance for nonlinear pricing problems such as CVA computations that have been developed since the crisis. Although BSDEs are well known to academics, they are less familiar to practitioners in the financial industry. In order to fill this gap, this book revisits financial modeling and computational finance from a BSDE perspective, presenting a unified view of the pricing and hedging theory across all asset classes. It also contains a review of quantitative finance tools, including Fourier techniques, Monte Carlo methods, finite differences and model calibration schemes. With a view to use in graduate courses in computational finance and financial modeling, corrected problem sets and Matlab sheets have been provided. Stéphane Crépey’s book starts with a few chapters on classical stochastic processes material, and then... fasten your seatbelt... the author starts traveling backwards in time through backward stochastic differential equations (BSDEs). This does not mean that one has to read the book backwards, like a manga! Rather, the possibility to move backwards in time, even if from a variety of final scenarios following a probability law, opens a multitude of possibilities for all those pricing problems whose solution is not a straightforward expectation. For example, this allows for framing problems like pricing with credit and funding costs in a rigorous mathematical setup. This is, as far as I know, the first book written for several levels of audiences, with applications to financial modeling and using BSDEs as one of the main tools, and as the song says: "it's never as good as the first time".Damiano Brigo, Chair of Mathematical Finance, Imperial College LondonWhile the classical theory of arbitrage free pricing has matured, and is now well understood and used by the finance industry, the theory of BSDEs continues to enjoy a rapid growth and remains a domain restricted to academic researchers and a handful of practitioners. Crépey’s book presents this novel approach to a wider community of researchers involved in mathematical modeling in finance. It is clearly an essential reference for anyone interested in the latest developments in financial mathematics. Marek Musiela, Deputy Director of the Oxford-Man Institute of Quantitative FinanceTable of ContentsPart I: An Introductory Course in Stochastic Processes.- 1.Some classes of Discrete-Time Stochastic Processes.-2.Some Classes of Continuous-Time Stochastic Processes.- 3.Elements of Stochastic Analysis.- Part II: Pricing Equations.- 4.Martingale Modeling.- 5.Benchmark Models.- Part III: Numerical Solutions.- 6.Monte Carlo Methods.- 7.Tree Methods.- 8.Finite Differences.- 9.Callibration Methods.- Part IV: Applications.- 10.Simulation/ Regression Pricing Schemes in Diffusive Setups.- 11.Simulation/ Regression Pricing Schemes in Pure Jump Setups.- Part V: Jump-Diffusion Setup with Regime Switching (**).- 12.Backward Stochastic Differential Equations.- 13.Analytic Approach.- 14.Extensions.- Part VI: Appendix.- A.Technical Proofs (**).- B.Exercises.- C.Corrected Problem Sets.​

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Book SynopsisThis self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix.The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition.Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.Trade Review“Every line of the book reflects that the author is the leading expert for hierarchical matrices. … Hierarchical matrices: algorithms and analysis is without a doubt a beautiful, comprehensive introduction to hierarchical matrices that can serve as both a graduate level textbook and a valuable resource for future research.” (Thomas Mach, Mathematical Reviews, April, 2017)“The book ‘Hierarchical matrices: algorithms and analysis’ is a self-contained monograph which presents an efficient possibility to handle the numerical treatment of fully populated large scale matrices appearing in scientific computations, and therefore it is of interest to scientists in computational mathematics, physics, chemistry and engineering.” (Constantin Popa, zbMATH 1336.65041, 2016)Table of ContentsPreface.- Part I: Introductory and Preparatory Topics.- 1. Introduction.- 2. Rank-r Matrices.- 3. Introductory Example.- 4. Separable Expansions and Low-Rank Matrices.- 5. Matrix Partition.- Part II: H-Matrices and Their Arithmetic.- 6. Definition and Properties of Hierarchical Matrices.- 7. Formatted Matrix Operations for Hierarchical Matrices.- 8. H2-Matrices.- 9. Miscellaneous Supplements.- Part III: Applications.- 10. Applications to Discretised Integral Operators.- 11. Applications to Finite Element Matrices.- 12. Inversion with Partial Evaluation.- 13. Eigenvalue Problems.- 14. Matrix Functions.- 15. Matrix Equations.- 16. Tensor Spaces.- Part IV: Appendices.- A. Graphs and Trees.- B. Polynomials.- C. Linear Algebra and Functional Analysis.- D. Sinc Functions and Exponential Sums.- E. Asymptotically Smooth Functions.- References.- Index.

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Book SynopsisDesigned to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises.Most chapters open with a review followed by theoretical and programming exercises, with detailed solutions provided for all problems including programs. Many of the MATLAB exercises are presented as Russian dolls: each question improves and completes the previous program and results are provided to validate the intermediate programs.The book offers useful MATLAB commands, advice on tables, vectors, matrices and basic commands for plotting. It contains material on eigenvalues and eigenvectors and important norms of vectors and matrices including perturbation theory; iterative methods for solving nonlinear and linear equations; polynomial and piecewise polynomial interpolation; Bézier curves; approximations of functions and integrals and more. The last two chapters considers ordinary differential equations including two point boundary value problems, and deal with finite difference methods for some partial differential equations.The format is designed to assist students working alone, with concise Review paragraphs, Math Hint footnotes on the mathematical aspects of a problem and MATLAB Hint footnotes with tips on programming.Trade ReviewFrom the book reviews:“This is a very interesting and useful book for any advanced undergraduate and beginning graduate student on mathematics, statistics, computational physics, chemistry, and engineering, with a focus on numerical analysis and computational science. The main scope of this book is to provide students with the opportunity to apply numerical analysis and the well-known MATLAB to solve problems in their own specialties.” (T. E. Simos, Computing Reviews, January, 2015)“This is an interesting new kind of book in the area of numerical analysis. … It is widely accepted that solving exercises is essential to achieve a deeper understanding of a mathematical topic. Under this point of view the present book can be seen as an adequate vehicle to really get into the field of numerical analysis. … the book can also serve as a rich source of exercises for university courses.” (Rolf Dieter Grigorieff, zbMATH, Vol. 1304, 2015)Table of Contents1 An Introduction to MATLAB commands.- 2 Matrices and Linear Systems.- 3 Matrices, Eigenvalues and Eigenvectors.- 4 Matrices, Norms and Conditioning.- 5 Iterative Methods.- 6 Polynomial Interpolation.- 7 Bézier Curves and Bernstein Polynomials.- 8 Piecewise Polynomials, Interpolation and Applications.- 9 Approximation of Integrals.- 10 Linear Least Squares Methods.- 11 Continuous and Discrete Approximations.- 12 Ordinary Differential Equations, One Step Methods.- 13 Finite Differences for differential and partial differential equations.- References.- Index of Names.- Subject Index.- MATLAB Index.

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