Optimization Books

Book SynopsisTable of ContentsPart 1. MATLAB 1. Introduction to MATLAB 2. Vectors and Matrices (Arrays) 3. Plotting in MATLAB 4. Three-Dimensional Plots 5. Functions 6. Control Flow 7. Miscellaneous Commands and Code Improvement Part 2. Mathematics and MATLAB 8. Transformations and Fern Fractals 9. Complex Numbers and Fractals 10. Series and Taylor Polynomials 11. Numerical Integration 12. The Gram–Schmidt Process Appendices A. Publishing and Live Scripts B. Final Projects C. Linear Algebra Projects D. Multivariable Calculus Projects

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Book SynopsisGraph connectivities and submodular functions are two widely applied and fast developing fields of combinatorial optimization. This book not only includes the most recent results, but also highlights several surprising connections between diverse topics within combinatorial optimization. It offers a unified treatment of developments in the concepts and algorithmic methods of the area, starting from basic results on graphs, matroids and polyhedral combinatorics, through the advanced topics of connectivity issues of graphs and networks, to the abstract theory and applications of submodular optimization. Difficult theorems and algorithms are made accessible to graduate students in mathematics, computer science, operations research, informatics and communication. The book is not only a rich source of elegant material for an advanced course in combinatorial optimization, but it also serves as a reference for established researchers by providing efficient tools for applied areas like infocomTrade ReviewThe title of the book is wisely chosen: it deals, among other subjects, with graph connectivity, and it provides connections between graph theoretical results and underlying combinatorial structures...The book is readable for students, researchers, possibly also practitioners. * Mathematical Reviews *Table of ContentsPART I - BASIC COMBINATORIAL OPTIMIZATION; PART II - HIGHER-ORDER CONNECTIONS; PART III - SEMIMODULAR OPTIMIZATION

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Book SynopsisNew edition of a graduate-level textbook on that focuses on online convex optimization, a machine learning framework that views optimization as a process.In many practical applications, the environment is so complex that it is not feasible to lay out a comprehensive theoretical model and use classical algorithmic theory and/or mathematical optimization. Introduction to Online Convex Optimization presents a robust machine learning approach that contains elements of mathematical optimization, game theory, and learning theory: an optimization method that learns from experience as more aspects of the problem are observed. This view of optimization as a process has led to some spectacular successes in modeling and systems that have become part of our daily lives. Based on the “Theoretical Machine Learning” course taught by the author at Princeton University, the second edition of this widely used graduate level text features:Thoroughly updat

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Book SynopsisReliability and maintenance modeling with optimization is the most fundamental and interdisciplinary research area that can be applied to every technical and management field. Reliability and Maintenance Modeling with Optimization: Advances and Applications aims at providing the most recent advances and achievements in reliability and maintenance.The book discusses replacement, repair, and inspection, offers estimation and statistical tests, covers accelerated life testing, explores warranty analysis manufacturing, and includes service reliability.The targeted readers are researchers interested in reliability and maintenance engineering. The book can serve as supplemental reading in professional seminars for engineers, designers, project managers, and graduate students.Table of Contents1. Nine Memorial Research Works. 2. Replacement First and Last Policies with Random Times for Redundant Systems. 3. Backup Policies with Random Data Updates. 4. An Optimal Age Replacement Policy for a Reparable System Consisting of Main and Auxiliary Subsystems. 5. Extended replacement policy in damage models. 6. Optimal Checking Policy for a Server System with Cyber Attack. 7. Reliability Analysis of Congestion Control Scheme with Code Error Correction Methods. 8. The Optimal Design of Consecutive-k Systems. 9. Optimal Social Infrastructure Maintenance Models. 10. Optimal Maintenance Problem with OSS-Oriented EVM for OSS Project. 11. Reliability Assessment Model Based on Wiener Process Considering Network Environment for Edge Computing. 12. Approximated Estimation of Software Target Failure Measures Conforming IEC 61508. 13. Phase-Type Expansion of Markov Regenerative Processes and Its Application to Reliability Problems. 14. A Hybrid Model Fitting Framework considering Accuracy and Performance. 15. Alternating α-Series Process. 16. Optimum Staggered Testing Strategy for Redundant Safety Instrumented Systems with Different Testing Intervals. 17. Modules Of Multi-State Systems - Introduction To Three Modules Theorem. 18. A postponed repair model for a mission-based system based on a three-stage failure process.

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Book Synopsis1 Introduction to Lie Groups.- 1.1. Manifolds.- 1.2. Lie Groups.- 1.3. Vector Fields.- 1.4. Lie Algebras.- 1.5. Differential Forms.- Notes.- Exercises.- 2 Symmetry Groups of Differential Equations.- 2.1. Symmetries of Algebraic Equations.- 2.2. Groups and Differential Equations.- 2.3. Prolongation.- 2.4. Calculation of Symmetry Groups.- 2.5. Integration of Ordinary Differential Equations.- 2.6. Nondegeneracy Conditions for Differential Equations.- Notes.- Exercises.- 3 Group-Invariant Solutions.- 3.1. Construction of Group-Invariant Solutions.- 3.2. Examples of Group-Invariant Solutions.- 3.3. Classification of Group-Invariant Solutions.- 3.4. Quotient Manifolds.- 3.5. Group-Invariant Prolongations and Reduction.- Notes.- Exercises.- 4 Symmetry Groups and Conservation Laws.- 4.1. The Calculus of Variations.- 4.2. Variational Symmetries.- 4.3. Conservation Laws.- 4.4. Noether's Theorem.- Notes.- Exercises.- 5 Generalized Symmetries.- 5.1. Generalized Symmetries of Differential Equations.- 5.2. Récursion Operators, Master Symmetries and Formal Symmetries.- 5.3. Generalized Symmetries and Conservation Laws.- 5.4. The Variational Complex.- Notes.- Exercises.- 6 Finite-Dimensional Hamiltonian Systems.- 6.1. Poisson Brackets.- 6.2. Symplectic Structures and Foliations.- 6.3. Symmetries, First Integrals and Reduction of Order.- Notes.- Exercises.- 7 Hamiltonian Methods for Evolution Equations.- 7.1. Poisson Brackets.- 7.2. Symmetries and Conservation Laws.- 7.3. Bi-Hamiltonian Systems.- Notes.- Exercises.- References.- Symbol Index.- Author Index.Table of Contents1 Introduction to Lie Groups.- 1.1. Manifolds.- Change of Coordinates.- Maps Between Manifolds.- The Maximal Rank Condition.- Submanifolds.- Regular Submanifolds.- Implicit Submanifolds.- Curves and Connectedness.- 1.2. Lie Groups.- Lie Subgroups.- Local Lie Groups.- Local Transformation Groups.- Orbits.- 1.3. Vector Fields.- Flows.- Action on Functions.- Differentials.- Lie Brackets.- Tangent Spaces and Vectors Fields on Submanifolds.- Frobenius’ Theorem.- 1.4. Lie Algebras.- One-Parameter Subgroups.- Subalgebras.- The Exponential Map.- Lie Algebras of Local Lie Groups.- Structure Constants.- Commutator Tables.- Infinitesimal Group Actions.- 1.5. Differential Forms.- Pull-Back and Change of Coordinates.- Interior Products.- The Differential.- The de Rham Complex.- Lie Derivatives.- Homotopy Operators.- Integration and Stokes’ Theorem.- Notes.- Exercises.- 2 Symmetry Groups of Differential Equations.- 2.1. Symmetries of Algebraic Equations.- Invariant Subsets.- Invariant Functions.- Infinitesimal Invariance.- Local Invariance.- Invariants and Functional Dependence.- Methods for Constructing Invariants.- 2.2. Groups and Differential Equations.- 2.3. Prolongation.- Systems of Differential Equations.- Prolongation of Group Actions.- Invariance of Differential Equations.- Prolongation of Vector Fields.- Infinitesimal Invariance.- The Prolongation Formula.- Total Derivatives.- The General Prolongation Formula.- Properties of Prolonged Vector Fields.- Characteristics of Symmetries.- 2.4. Calculation of Symmetry Groups.- 2.5. Integration of Ordinary Differential Equations.- First Order Equations.- Higher Order Equations.- Differential Invariants.- Multi-parameter Symmetry Groups.- Solvable Groups.- Systems of Ordinary Differential Equations.- 2.6. Nondegeneracy Conditions for Differential Equations.- Local Solvability.- In variance Criteria.- The Cauchy—Kovalevskaya Theorem.- Characteristics.- Normal Systems.- Prolongation of Differential Equations.- Notes.- Exercises.- 3 Group-Invariant Solutions.- 3.1. Construction of Group-Invariant Solutions.- 3.2. Examples of Group-Invariant Solutions.- 3.3. Classification of Group-Invariant Solutions.- The Adjoint Representation.- Classification of Subgroups and Subalgebras.- Classification of Group-Invariant Solutions.- 3.4. Quotient Manifolds.- Dimensional Analysis.- 3.5. Group-Invariant Prolongations and Reduction.- Extended Jet Bundles.- Differential Equations.- Group Actions.- The Invariant Jet Space.- Connection with the Quotient Manifold.- The Reduced Equation.- Local Coordinates.- Notes.- Exercises.- 4 Symmetry Groups and Conservation Laws.- 4.1. The Calculus of Variations.- The Variational Derivative.- Null Lagrangians and Divergences.- Invariance of the Euler Operator.- 4.2. Variational Symmetries.- Infinitesimal Criterion of Invariance.- Symmetries of the Euler—Lagrange Equations.- Reduction of Order.- 4.3. Conservation Laws.- Trivial Conservation Laws.- Characteristics of Conservation Laws.- 4.4. Noether’s Theorem.- Divergence Symmetries.- Notes.- Exercises.- 5 Generalized Symmetries.- 5.1. Generalized Symmetries of Differential Equations.- Differential Functions.- Generalized Vector Fields.- Evolutionary Vector Fields.- Equivalence and Trivial Symmetries.- Computation of Generalized Symmetries.- Group Transformations.- Symmetries and Prolongations.- The Lie Bracket.- Evolution Equations.- 5.2. Récursion Operators, Master Symmetries and Formal Symmetries.- Frechet Derivatives.- Lie Derivatives of Differential Operators.- Criteria for Recursion Operators.- The Korteweg—de Vries Equation.- Master Symmetries.- Pseudo-differential Operators.- Formal Symmetries.- 5.3. Generalized Symmetries and Conservation Laws.- Adjoints of Differential Operators.- Characteristics of Conservation Laws.- Variational Symmetries.- Group Transformations.- Noether’s Theorem.- Self-adjoint Linear Systems.- Action of Symmetries on Conservation Laws.- Abnormal Systems and Noether’s Second Theorem.- Formal Symmetries and Conservation Laws.- 5.4. The Variational Complex.- The D-Complex.- Vertical Forms.- Total Derivatives of Vertical Forms.- Functionals and Functional Forms.- The Variational Differential.- Higher Euler Operators.- The Total Homotopy Operator.- Notes.- Exercises.- 6 Finite-Dimensional Hamiltonian Systems.- 6.1. Poisson Brackets.- Hamiltonian Vector Fields.- The Structure Functions.- The Lie-Poisson Structure.- 6.2. Symplectic Structures and Foliations.- The Correspondence Between One-Forms and Vector Fields.- Rank of a Poisson Structure.- Symplectic Manifolds.- Maps Between Poisson Manifolds.- Poisson Submanifolds.- Darboux’ Theorem.- The Co-adjoint Representation.- 6.3. Symmetries, First Integrals and Reduction of Order.- First Integrals.- Hamiltonian Symmetry Groups.- Reduction of Order in Hamiltonian Systems.- Reduction Using Multi-parameter Groups.- Hamiltonian Transformation Groups.- The Momentum Map.- Notes.- Exercises.- 7 Hamiltonian Methods for Evolution Equations.- 7.1. Poisson Brackets.- The Jacobi Identity.- Functional Multi-vectors.- 7.2. Symmetries and Conservation Laws.- Distinguished Functionals.- Lie Brackets.- Conservation Laws.- 7.3. Bi-Hamiltonian Systems.- Recursion Operators.- Notes.- Exercises.- References.- Symbol Index.- Author Index.

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Book SynopsisThis volume deals with controllability and observability properties of nonlinear systems, as well as various ways to obtain input-output representations. The emphasis is on fundamental notions as (controlled) invariant distributions and submanifolds, together with algorithms to compute the required feedbacks. Table of Contents1 Introduction.- 2 Manifolds, Vectorfields, Lie Brackets, Distributions.- 3 Controllability and Observability, Local Decompositions.- 4 Input-Output Representations.- 5 State Space Transformation and Feedback.- 6 Feedback Linearization of Nonlinear Systems.- 7 Controlled Invariant Distribution and the Disturbance Decoupling Problem.- 8 The Input-Output Decoupling Problem.- 9 The Input-Output Decoupling Problem.- 10 Local Stability and Stabilization of Nonlinear Systems.- 11 Controlled Invariant Submanifolds and Nonlinear Zero Dynamics.- 12 Mechanical Nonlinear Control Systems.- 13 Controlled Invariance and Decoupling for General Nonlinear Systems.- 14 Discrete-Time Nonlinear Control Systems.

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Book SynopsisThis book is the result of our teaching over the years an undergraduate course on Linear Optimal Systems to applied mathematicians and a first-year graduate course on Linear Systems to engineers.Table of Contents1 Introduction.- 1.1 Science and Engineering.- 1.2 Physical Systems, Models, and Representations.- 1.3 Robustness.- 2 The System RepresentationR(•) = [A(•),B(•),C(•),D(•)].- 2.1 Fundamental Properties ofR(•).- 2.1.1 Definitions.- 2.1.2 Structure ofR(•).- 2.1.3 State Transition Matrix.- 2.1.4 State Transition Map and Response Map.- 2.1.5 Impulse Response Matrix.- 2.1.6 Adjoint Equations.- 2.1.7 Linear-Quadratic Optimization.- 2.2 Applications.- 2.2.1 Variational Equation.- 2.2.2 Control Correction Example.- 2.2.3 Optimization Example.- 2.2.4 Periodically Varying Differential Equations.- 2d The Discrete-Time System RepresentationRd(•) = [A(•),B(•),C(•),D(•)].- 2d.1 Fundamental Properties ofRd(•).- 2d.2 Application: Periodically Varying Recursion Equations.- 3 The System RepresentationR= [A,B,C,D], Part I.- 3.1 Preliminaries.- 3.2 General Properties ofR= [A,B,C,D].- 3.2.1 Definition.- 3.2.2 State Transition Matrix.- 3.2.3 The State Transition and Response Map of R.- 3.3 Properties of R when A has a Basis of Eigenvectors.- 3d The Discrete-Time System Representation Rd = [A,B,C,D].- 3d.1 Preliminaries.- 3d.2 General Properties of Rd.- 3d.3 Properties of Rd when A has a Basis of Eigenvectors.- 4 The System Representation R = [A,B,C,D], Part II.- 4.1 Preliminaries.- 4.2 Minimal Polynomial.- 4.3 Decomposition Theorem.- 4.4 The Decomposition of a Linear Map.- 4.5 Jordan Form.- 4.6 Function of a Matrix.- 4.7 Spectral Mapping Theorem.- 4.8 The Linear Map X ? AX+XB.- 5 General System Concepts.- 5.1 Dynamical Systems.- 5.2 Time-Invariant Dynamical Systems.- 5.3 Linear Dynamical Systems.- 5.4 Equivalence.- 6 Sampled Data Systems.- 6.1 Relation BetweenL- and z-Transforms.- 6.2 D/A Converter.- 6.3 A/D Converter.- 6.4 Sampled-Data System.- 6.5 Example.- 7 Stability.- 7.1 I/O Stability.- 7.2 State Related Stability Concepts and Applications.- 7.2.1 Stability of x = A(t)x.- 7.2.2 Bounded Trajectories and Regulation.- 7.2.3 Response to T-Periodic Inputs.- 7.2.4 Periodically Varying System with Periodic Input.- 7.2.5 Slightly Nonlinear Systems.- 7d Stability: The Discrete-Time Case.- 7d.1 I/O Stability.- 7d.2 State Related Stability Concepts.- 7d.2.1 Stability of x(k+1) = A(k)x(k).- 7d.2.2 Bounded Trajectories and Regulation.- 7d.2.3 Response to q-Periodic Inputs.- 8 Controllability and Observability.- 8.1 Controllability and Observability of Dynamical Systems.- 8.2 Controllability of the Pair (A(•),B(•)).- 8.2.1 Controllability of the Pair (A(•),B(•)).- 8.2.2 The Cost of Control.- 8.2.3 Stabilization by Linear State Feedback.- 8.3 Observability of the Pair (C(•),A(•)).- 8.4 Duality.- 8.5 Linear Time-Invariant Systems.- 8.5.1 Observability Properties of the Pair (C,A).- 8.5.2 Controllability of the Pair (A,B).- 8.6 Kalman Decomposition Theorem.- 8.7 Hidden Modes, Stabilizability, and Detectability.- 8.8 Balanced Representations.- 8.9 Robustness of Controllability.- 8d Controllability and Observability: The Discrete-Time Case.- 8d.1 Controllability and Observability of Dynamical Systems.- 8d.2 Reachability and Controllability of the Pair (A(•),B(•)).- 8d.2.1 Controllability of the Pair (A(•),B(•)).- 8d.2.2 The Cost of Control.- 8d.3 Observability of the Pair (C(•),A(•)).- 8d.4 Duality.- 8d.5 Linear Time-Invariant Systems.- 8d.5.1 Observability of the Pair (C,A).- 8d.5.2 Reachability and Controllability of the Pair(A,B).- 8d.6 Kalman Decomposition Theorem.- 8d.7 Stabilizability and Detectability.- 9 Realization Theory.- 9.1 Minimal Realizations.- 9.2 Controllable Canonical Form.- 10 Linear State Feedback and Estimation.- 10.1 Linear State Feedback.- 10.2 Linear Output Injection and State Estimation.- 10.3 State Feedback of the Estimated State.- 10.4 Infinite Horizon Linear Quadratic Optimization.- 10d.4 Infinite Horizon Linear Quadratic Optimization. The Discrete-Time Case.- 11 Unity Feedback Systems.- 11.1 The Feedback System ?c.- 11.1.1 State Space Analysis.- 11.1.2 Special Case:R1andR2have no Unstable Hidden Modes.- 11.1.3 The Discrete-Time Case.- 11.2 Nyquist Criterion.- 11.2.1 The Nyquist Criterion.- 11.2.2 Remarks on the Nyquist Criterion.- 11.2.3 Proof of Nyquist Criterion.- 11.2.4 The Discrete-Time Case.- 11.3 Robustness.- 11.3.1 Robustness With Respect to Plant Perturbations.- 11.3.2 Robustness With Respect to Exogenous Disturbances.- 11.3.3 Robust Regulation.- 11.3.4 Bandwidth-Robustness Tradeoff.- 11.3.5 The Discrete-Time Case.- 11.4 Kharitonov’s Theorem.- 11.4.1 Hurwitz Polynomials.- 11.4.2 Kharitonov’s Theorem.- 11.5 Robust Stability Under Structured Perturbations.- 11.5.1 General Robustness Theorem.- 11.5.2 Special Case: Affine Maps and Convexity.- 11.5.3 The Discrete Time Case.- 11.6 Stability Under Arbitrary Additive Plant Perturbations.- 11.7 Transmission Zeros.- 11.7.1 Single-Input Single-Output Case.- 11.7.2 Multi-Input Multi-Output Case: Assumptions and Definitions.- 11.7.3 Characterization of the Zeros.- 11.7.4 Application to Unity Feedback Systems.- Appendix A Linear Maps and Matrix Analysis.- A.1 Preliminary Notions.- A.2 Rings and Fields.- A.3 Linear Spaces.- A4. Linear Maps.- AS. Matrix Representation.- A.5.1 The Concept of Matrix Representation.- A.5.2 Matrix Representation and Change of Basis.- A.5.3 Range and Null Space: Rank and Nullity.- A.5.4 Echelon Forms of a Matrix.- A.6 Notmed Linear Spaces.- A.6.1 Norms.- A.6.2 Convergence.- A.6.3 Equivalent Norms.- A.6.4 The Lebesgue Spaces 1P and LP [Tay.1].- A.6.5 Continuous Linear Transformations.- A.7 The Adjoint of a Linear Map.- A.7.1 Inner Products.- A.7.2 Adjoints of Continuous Linear Maps.- A.7.3 Properties of the Adjoint.- A.7.4 The Finite Rank Operator Fundamental Lemma.- A.7.5 Singular Value Decomposition (SVD).- Appendix B Differential Equations.- BA Existence and Uniqueness of Solutions.- B.1.1 Assumptions.- B.1.2 Fundamental Theorem.- B.1.3 Construction of a Solution by Iteration.- B.1.4 The Bellman-Gronwall Inequality.- B.1.5 Uniqueness.- B.2 Initial Conditions and Parameter Perturbations.- B.3 Geometric Interpretation and Numerical Calculations.- Appendix C Laplace Transforms.- C.1 Definition of the Laplace Transform.- C.2 Properties of Laplace Transforms.- Appendix D the z-Transform.- D.1 Definition of the z-Transform.- D.2 Properties of the z-Transform.- References.- Abbreviations.- Mathematical Symbols.

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Book SynopsisThis is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory.Table of Contents1 Geometry in Regions of a Space. Basic Concepts.- §1. Co-ordinate systems.- 1.1. Cartesian co-ordinates in a space.- 1.2. Co-ordinate changes.- §2. Euclidean space.- 2.1. Curves in Euclidean space.- 2.2. Quadratic forms and vectors.- §3. Riemannian and pseudo-Riemannian spaces.- 3.1. Riemannian metrics.- 3.2. The Minkowski metric.- §4. The simplest groups of transformations of Euclidean space.- 4.1. Groups of transformations of a region.- 4.2. Transformations of the plane.- 4.3. The isometries of 3-dimensional Euclidean space.- 4.4. Further examples of transformation groups.- 4.5. Exercises.- §5. The Serret—Frenet formulae.- 5.1. Curvature of curves in the Euclidean plane.- 5.2. Curves in Euclidean 3-space. Curvature and torsion.- 5.3. Orthogonal transformations depending on a parameter.- 5.4. Exercises.- §6. Pseudo-Euclidean spaces.- 6.1. The simplest concepts of the special theory of relativity.- 6.2. Lorentz transformations.- 6.3. Exercises.- 2 The Theory of Surfaces.- §7. Geometry on a surface in space.- 7.1. Co-ordinates on a surface.- 7.2. Tangent planes.- 7.3. The metric on a surface in Euclidean space.- 7.4. Surface area.- 7.5. Exercises.- §8. The second fundamental form.- 8.1. Curvature of curves on a surface in Euclidean space.- 8.2. Invariants of a pair of quadratic forms.- 8.3. Properties of the second fundamental form.- 8.4. Exercises.- §9. The metric on the sphere.- §10. Space-like surfaces in pseudo-Euclidean space.- 10.1. The pseudo-sphere.- 10.2. Curvature of space-like curves in $$ \mathbb{R}_1^3 $$.- §11. The language of complex numbers in geometry.- 11.1. Complex and real co-ordinates.- 11.2. The Hermitian scalar product.- 11.3. Examples of complex transformation groups.- §12. Analytic functions.- 12.1. Complex notation for the element of length, and for the differential of a function.- 12.2. Complex co-ordinate changes.- 12.3. Surfaces in complex space.- §13. The conformal form of the metric on a surface.- 13.1. Isothermal co-ordinates. Gaussian curvature in terms of conformal co-ordinates.- 13.2. Conformal form of the metrics on the sphere and the Lobachevskian plane.- 13.3. Surfaces of constant curvature.- 13.4. Exercises.- §14. Transformation groups as surfaces in N-dimensional space.- 14.1. Co-ordinates in a neighbourhood of the identity.- 14.2. The exponential function with matrix argument.- 14.3. The quaternions.- 14.4. Exercises.- §15. Conformal transformations of Euclidean and pseudo-Euclidean spaces of several dimensions.- 3 Tensors: The Algebraic Theory.- §16. Examples of tensors.- §17. The general definition of a tensor.- 17.1. The transformation rule for the components of a tensor of arbitrary rank.- 17.2. Algebraic operations on tensors.- 17.3. Exercises.- §18. Tensors of type (0, k).- 18.1. Differential notation for tensors with lower indices only.- 18.2. Skew-symmetric tensors of type (0, k).- 18.3. The exterior product of differential forms. The exterior algebra.- 18.4. Skew-symmetric tensors of type (k, 0) (polyvectors). Integrals with respect to anti-commuting variables.- 18.5. Exercises.- §19. Tensors in Riemannian and pseudo-Riemannian spaces.- 19.1. Raising and lowering indices.- 19.2. The eigenvalues of a quadratic form.- 19.3. The operator ?.- 19.4. Tensors in Euclidean space.- 19.5. Exercises.- §20. The crystallographic groups and the finite subgroups of the rotation group of Euclidean 3-space. Examples of invariant tensors.- §21. Rank 2 tensors in pseudo-Euclidean space, and their eigenvalues.- 21.1. Skew-symmetric tensors. The invariants of an electromagnetic field.- 21.2. Symmetric tensors and their eigenvalues. The energy-momentum tensor of an electromagnetic field.- §22. The behaviour of tensors under mappings.- 22.1. The general operation of restriction of tensors with lower indices.- 22.2. Mappings of tangent spaces.- §23. Vector fields.- 23.1. One-parameter groups of diffeomorphisms.- 23.2. The exponential function of a vector field.- 23.3. The Lie derivative.- 23.4. Exercises.- §24. Lie algebras.- 24.1. Lie algebras and vector fields.- 24.2. The fundamental matrix Lie algebras.- 24.3. Linear vector fields.- 24.4. Left-invariant fields defined on transformation groups.- 24.5. Invariant metrics on a transformation group.- 24.6. The classification of the 3-dimensional Lie algebras.- 24.7. The Lie algebras of the conformal groups.- 24.8. Exercises.- 4 The Differential Calculus of Tensors.- §25. The differential calculus of skew-symmetric tensors.- 25.1. The gradient of a skew-symmetric tensor.- 25.2. The exterior derivative of a form.- 25.3. Exercises.- §26. Skew-symmetric tensors and the theory of integration.- 26.1. Integration of differential forms.- 26.2. Examples of integrals of differential forms.- 26.3. The general Stokes formula. Examples.- 26.4. Proof of the general Stokes formula for the cube.- 26.5. Exercises.- §27. Differential forms on complex spaces.- 27.1. The operators d? and d?.- 27.2. Kählerian metrics. The curvature form.- §28. Covariant differentiation.- 28.1. Euclidean connexions.- 28.2. Covariant differentiation of tensors of arbitrary rank.- §29. Covariant differentiation and the metric.- 29.1. Parallel transport of vector fields.- 29.2. Geodesics.- 29.3. Connexions compatible with the metric.- 29.4. Connexions compatible with a complex structure (Hermitian metric).- 29.5. Exercises.- §30. The curvature tensor.- 30.1. The general curvature tensor.- 30.2. The symmetries of the curvature tensor. The curvature tensor defined by the metric.- 30.3. Examples: The curvature tensor in spaces of dimensions 2 and 3; the curvature tensor of transformation groups.- 30.4. The Peterson—Codazzi equations. Surfaces of constant negative curvature, and the “sine—Gordon” equation.- 30.5. Exercises.- 5 The Elements of the Calculus of Variations.- §31. One-dimensional variational problems.- 31.1. The Euler—Lagrange equations.- 31.2. Basic examples of functional.- §32. Conservation laws.- 32.1. Groups of transformations preserving a given variational problem.- 32.2. Examples. Applications of the conservation laws.- §33. Hamiltonian formalism.- 33.1. Legendre’s transformation.- 33.2. Moving co-ordinate frames.- 33.3. The principles of Maupertuis and Fermat.- 33.4. Exercises.- §34. The geometrical theory of phase space.- 34.1. Gradient systems.- 34.2. The Poisson bracket.- 34.3. Canonical transformations.- 34.4. Exercises.- §35. Lagrange surfaces.- 35.1. Bundles of trajectories and the Hamilton—Jacobi equation.- 35.2. Hamiltonians which are first-order homogeneous with respect to the momentum.- §36. The second variation for the equation of the geodesics.- 36.1. The formula for the second variation.- 36.2. Conjugate points and the minimality condition.- 6 The Calculus of Variations in Several Dimensions. Fields and Their Geometric Invariants.- §37. The simplest higher-dimensional variational problems.- 37.1. The Euler—Lagrange equations.- 37.2. The energy-momentum tensor.- 37.3. The equations of an electromagnetic field.- 37.4. The equations of a gravitational field.- 37.5. Soap films.- 37.6. Equilibrium equation for a thin plate.- 37.7. Exercises.- §38. Examples of Lagrangians.- §39. The simplest concepts of the general theory of relativity.- §40. The spinor representations of the groups SO(3) and O(3, 1). Dirac’s equation and its properties.- 40.1. Automorphisms of matrix algebras.- 40.2. The spinor representation of the group SO(3).- 40.3. The spinor representation of the Lorentz group.- 40.4. Dirac’s equation.- 40.5. Dirac’s equation in an electromagnetic field. The operation of charge conjugation.- §41. Covariant differentiation of fields with arbitrary symmetry.- 41.1. Gauge transformations. Gauge-invariant Lagrangians.- 41.2. The curvature form.- 41.3. Basic examples.- §42. Examples of gauge-invariant functionals. Maxwell’s equations and the Yang—Mills equation. Functionals with identically zero variational derivative (characteristic classes).

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Book SynopsisDuring the 90s robust control theory has seen major advances and achieved a new maturity, centered around the notion of convexity.Trade ReviewFrom the reviews"Because progress in LMI robust control theory has been explosive, only books published in the past 3 or 4 years can hope to adequatetely document the phenomenon. The textbook of Dullerud and Paganini rises admirably to the challenge, starting from the basics of linear algebra and system theory and leading the reader through the key 1990s breakthroughs in LMI robust control theory. To keep things simple, the authors relegate the issue of robustness against nonlinear uncertainties to the citations, focusing attention squarely on the linear case. (...)The book would make an excellent text for a two-semester or two-quarter course for first year graduate students beginning with no prior knowledge of state-space methods. Alternatively, for control students who already have a state-space background."IEEE Transactions on Automatics Control, Vol. 46, No. 9, September 2001Table of Contents0 Introduction.- 1 Preliminaries in Finite Dimensional Space.- 2 State Space System Theory.- 3 Linear Analysis.- 4 Model Realizations and Reduction.- 5 Stabilizing Controllers.- 6 H2 Optimal Control.- 7 H? Synthesis.- 8 Uncertain Systems.- 9 Feedback Control of Uncertain Systems.- 10 Further Topics: Analysis.- 11 Further Topics: Synthesis.- A Some Basic Measure Theory.- A.1 Sets of zero measure.- A.2 Terminology.- Notes and references.- B Proofs of Strict Separation.- Notes and references.- Notes and references.- Notation.- References.

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Book SynopsisThis book addresses the many important problems in service operations management, which can be analyzed using two core methodologies: optimization and queueing theory (including numerical simulation of queues).Trade Review"The book is well written and very easy to follow. The reviewer highly recommends the book to be considered as a textbook for courses on service operations at the senior-undergraduate and graduate levels." (A Journal for the Worldwide Service Science Community, 2011) Table of ContentsPreface. Acknowledgements. 1. Why study services? 1.1 What are services. 1.2 Services as a percent of the economy. 1.3 Public versus private service delivery. 1.4 Why model services? 1.5 Key service decisions. 1.6 Philosophy about models. 1.7 Outline of the book. 1.8 Problems. 1.9 References. METHODOLOGICAL FOUNDATIONS. 2 Optimization. 2.1 Introduction. 2.2 Five key elements of optimization. 2.3 Taxonomy of optimization models. 2.4 You probably have seen one already. 2.5 Linear programming. 2.6 Special network form. 2.7 Integer problems. 2.8 Multiple objective problems. 2.9 Mark’s ten rules of formulating problems. 2.10 Problems. 2.11 References. 3 Queueing theory. 3.1 Introduction. 3.2 What is a queueing theory? 3.3 Key performance metrics for queues and Little’s formula. 3.4 A framework for Markovian queues. 3.5 Key results for non-Markovian queues. 3.6 Solving queueing models numerically. 3.7 When conditions change over time. 3.8 Conclusions. 3.9 Problems. 3.10 References. APPLICATION AREAS. 4 Location and districting problems in services. 4.1 Example applications. 4.2 Taxonomy of location problems. 4.3 Covering problems. 4.4 Median problems - minimizing the demand-weighted average distance. 4.5 Multi-objective models. 4.6 Districting problems. 4.7 Franchise location problems. 4.8 Summary and software. 4.9 Problems. 4.10 References. 5 Inventory decisions in services. 5.1 Why is inventory in a service modeling book? 5.2 EOQ - a basic inventory model. 5.3 Extensions of the EOQ model. 5.4 Time varying demand. 5.5 Uncertain demand and lead times. 5.6 Newsvendor problem and applications. 5.7 Summary. 5.8 Problems. 5.9 References. 6 Resource allocation problems and decisions in services. 6.1 Example resource allocation problems. 6.2 How to formulate an assignment or resource allocation problem. 6.3 Infeasible solutions. 6.4 Assigning students to freshman seminars. 6.5 Assigning students to intersession courses. 6.6 Improving the assignment of zip codes to Congressional districts. 6.7 Summary. 6.8 Problems. 6.9 References. 7 Short-term workforce scheduling. 7.1 Overview of scheduling. 7.2 Simple model. 7.3 Extensions of the simple model. 7.4 More difficult extensions. 7.5 Linking scheduling to service. 7.6 Time-dependent queueing analyzer. 7.7 Assigning specific employees to shifts. 7.8 Summary. 7.9 Problems. 7.10 References. 8 Long-term workforce planning. 8.1 Why is long-term workforce planning an issue? 8.2 Basic model. 8.3 Grouping of skills. 8.4 Planning over time. 8.5 Linking to project scheduling. 8.6 Linking to personnel training and planning in general. 8.7 Simple model of training. 8.8 Summary. 8.9 Problems. 8.10 References. 9 Priority services, call center design and customer scheduling. 9.1 Examples. 9.2 Priority queueing for emergency and other services. service in each class with non-preemptive priorities. 9.2.3 Priority service with Poisson arrivals, multiple servers and identically distributed exponential service times.. 9.2.4 Preemptive queueing. 9.3 Call center design. 9.4 Scheduling in services. 9.5 Summary. 9.6 Problems. 9.7 References. 10 Vehicle routing and services. 10.1 Example routing problems. 10.2 Classification of routing problems. 10.3 Arc routing. 10.4 The traveling salesman problem. 10.5 Vehicle routing problems. 10.6 Summary. 10.7 Problems. 10.8 References. 11 Where to from here? 11.1 Introduction. 11.2 Other methodologies. 11.3 Other applications in services. 11.4 Summary. 11.5 References. APPENDICES. A. Sums of series - basic formulae. B. Overview of probability. B.1. Introduction and basic definitions. B.2 Axioms of probability .. B.3 Joint, marginal and conditional probabilities and Bayes’ theorem. B.4 Counting, ordered pairs, permutations and combinations. B.5 Random variables. B.6 Discrete random variables. B.7 Continuous random variables. B.8 Moment and probability generating functions. B.9 Generating random variables. B.10 Random variables in Excel. C. References.

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Book SynopsisThis is an engaging and informative book on the modern practice of experimental design. The authors'' writing style is entertaining, the consulting dialogs are extremely enjoyable, and the technical material is presented brilliantly but not overwhelmingly. The book is a joy to read. Everyone who practices or teaches DOE should read this book. - Douglas C. Montgomery, Regents Professor, Department of Industrial Engineering, Arizona State University It''s been said: ''Design for the experiment, don''t experiment for the design.'' This book ably demonstrates this notion by showing how tailor-made, optimal designs can be effectively employed to meet a client''s actual needs. It should be required reading for anyone interested in using the design of experiments in industrial settings. Christopher J. Nachtsheim, Frank A Donaldson Chair in Operations Management, Carlson School of Management, University of Minnesota This book demonstraTable of ContentsPreface. Acknowledgments. 1 A simple comparative experiment. 1.1 Key concepts. 1.2 The setup of a comparative experiment. 1.3 Summary. 2 An optimal screening experiment. 2.1 Key concepts. 2.2 Case: an extraction experiment. 2.2.1 Problem and design. 2.2.2 Data analysis. 2.3 Peek into the black box. 2.3.1 Main-effects models. 2.3.2 Models with two-factor interaction effects. 2.3.3 Factor scaling. 2.3.4 Ordinary least squares estimation. 2.3.5 Significance tests and statistical power calculations. 2.3.6 Variance inflation. 2.3.7 Aliasing. 2.3.8 Optimal design. 2.3.9 Generating optimal experimental designs. 2.3.10 The extraction experiment revisited. 2.3.11 Principles of successful screening: sparsity, hierarchy, and heredity. 2.4 Background reading. 2.4.1 Screening. 2.4.2 Algorithms for finding optimal designs. 2.5 Summary. 3 Adding runs to a screening experiment. 3.1 Key concepts. 3.2 Case: an augmented extraction experiment. 3.2.1 Problem and design. 3.2.2 Data analysis. 3.3 Peek into the black box. 3.3.1 Optimal selection of a follow-up design. 3.3.2 Design construction algorithm. 3.3.3 Foldover designs. 3.4 Background reading. 3.5 Summary. 4 A response surface design with a categorical factor. 4.1 Key concepts. 4.2 Case: a robust and optimal process experiment. 4.2.1 Problem and design. 4.2.2 Data analysis. 4.3 Peek into the black box. 4.3.1 Quadratic effects. 4.3.2 Dummy variables for multilevel categorical factors. 4.3.3 Computing D-efficiencies. 4.3.4 Constructing Fraction of Design Space plots. 4.3.5 Calculating the average relative variance of prediction. 4.3.6 Computing I-efficiencies. 4.3.7 Ensuring the validity of inference based on ordinary least squares. 4.3.8 Design regions. 4.4 Background reading. 4.5 Summary. 5 A response surface design in an irregularly shaped design region. 5.1 Key concepts. 5.2 Case: the yield maximization experiment. 5.2.1 Problem and design. 5.2.2 Data analysis. 5.3 Peek into the black box. 5.3.1 Cubic factor effects. 5.3.2 Lack-of-fit test. 5.3.3 Incorporating factor constraints in the design construction algorithm. 5.4 Background reading. 5.5 Summary. 6 A "mixture" experiment with process variables. 6.1 Key concepts. 6.2 Case: the rolling mill experiment. 6.2.1 Problem and design. 6.2.2 Data analysis. 6.3 Peek into the black box. 6.3.1 The mixture constraint. 6.3.2 The effect of the mixture constraint on the model. 6.3.3 Commonly used models for data from mixture experiments. 6.3.4 Optimal designs for mixture experiments. 6.3.5 Design construction algorithms for mixture experiments. 6.4 Background reading. 6.5 Summary. 7 A response surface design in blocks. 7.1 Key concepts. 7.2 Case: the pastry dough experiment. 7.2.1 Problem and design. 7.2.2 Data analysis. 7.3 Peek into the black box. 7.3.1 Model. 7.3.2 Generalized least squares estimation. 7.3.3 Estimation of variance components. 7.3.4 Significance tests. 7.3.5 Optimal design of blocked experiments. 7.3.6 Orthogonal blocking. 7.3.7 Optimal versus orthogonal blocking. 7.4 Background reading. 7.5 Summary. 8 A screening experiment in blocks. 8.1 Key concepts. 8.2 Case: the stability improvement experiment. 8.2.1 Problem and design. 8.2.2 Afterthoughts about the design problem. 8.2.3 Data analysis. 8.3 Peek into the black box. 8.3.1 Models involving block effects. 8.3.2 Fixed block effects. 8.4 Background reading. 8.5 Summary. 9 Experimental design in the presence of covariates. 9.1 Key concepts. 9.2 Case: the polypropylene experiment. 9.2.1 Problem and design. 9.2.2 Data analysis. 9.3 Peek into the black box. 9.3.1 Covariates or concomitant variables. 9.3.2 Models and design criteria in the presence of covariates. 9.3.3 Designs robust to time trends. 9.3.4 Design construction algorithms. 9.3.5 To randomize or not to randomize. 9.3.6 Final thoughts. 9.4 Background reading. 9.5 Summary. 10 A split-plot design. 10.1 Key concepts. 10.2 Case: the wind tunnel experiment. 10.2.1 Problem and design. 10.2.2 Data analysis. 10.3 Peek into the black box. 10.3.1 Split-plot terminology. 10.3.2 Model. 10.3.3 Inference from a split-plot design. 10.3.4 Disguises of a split-plot design. 10.3.5 Required number of whole plots and runs. 10.3.6 Optimal design of split-plot experiments. 10.3.7 A design construction algorithm for optimal split-plot designs. 10.3.8 Difficulties when analyzing data from split-plot experiments. 10.4 Background reading. 10.5 Summary. 11 A two-way split-plot design. 11.1 Key concepts. 11.2 Case: the battery cell experiment. 11.2.1 Problem and design. 11.2.2 Data analysis. 11.3 Peek into the black box. 11.3.1 The two-way split-plot model. 11.3.2 Generalized least squares estimation. 11.3.3 Optimal design of two-way split-plot experiments. 11.3.4 A design construction algorithm for D-optimal two-way split-plot designs. 11.3.5 Extensions and related designs. 11.4 Background reading. 11.5 Summary. Bibliography. Index.

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Book SynopsisEngineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems.Table of ContentsLinear Spaces. Hilbert Space. Least-Squares Estimation. Dual Spaces. Linear Operators and Adjoints. Optimization of Functionals. Global Theory of Constrained Optimization. Local Theory of Constrained Optimization. Iterative Methods of Optimization. Indexes.

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Book SynopsisAn up-close look at the theory behind and application of extremum seeking Originally developed as a method of adaptive control for hard-to-model systems, extremum seeking solves some of the same problems as today''s neural network techniques, but in a more rigorous and practical way. Following the resurgence in popularity of extremum-seeking control in aerospace and automotive engineering, Real-Time Optimization by Extremum-Seeking Control presents the theoretical foundations and selected applications of this method of real-time optimization. Written by authorities in the field and pioneers in adaptive nonlinear control systems, this book presents both significant theoretic value and important practical potential. Filled with in-depth insight and expert advice, Real-Time Optimization by Extremum-Seeking Control: * Develops optimization theory from the points of dynamic feedback and adaptation * Builds a solid bridge between the classical optimization theory and Trade Review"The subject matter is hard; this short book is therefore presented as an overview." (Computing Reviws.com, March 26, 2004) "…a well-written and authoritative book…an essential resource for learning about extremum-seeking control and for motivating further developments in this subject area." (IEEE Control Systems Magazine, April 2004) “...recommended..” (Choice, Vol. 41, No. 7, March 2004)Table of ContentsPreface ix I Theory 1 II Applications 91 Appendices 199 Bibliography 223 Index 235

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Book SynopsisThis textbook provides a thorough treatment of standard methods such as linear and quadratic programming, Newton-like methods and the conjugate gradient method. The theoretical aspects of the subject include a treatment of optimality conditions and the significance of Lagrange multipliers.Table of ContentsUNCONSTRAINED OPTIMIZATION. Structure of Methods. Newton-like Methods. Conjugate Direction Methods. Restricted Step Methods. Sums of Squares and Nonlinear Equations. CONSTRAINED OPTIMIZATION. Linear Programming. The Theory of Constrained Optimization. Quadratic Programming. General Linearly Constrained Optimization. Nonlinear Programming. Other Optimization Problems. Non-Smooth Optimization. References. Subject Index.

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Book SynopsisA complete, highly accessible introduction to one of today's most exciting areas of applied mathematics One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms.Table of ContentsProblems and Algorithms. Optimal Trees and Paths. Maximum Flow Problems. Minimum-Cost Flow Problems. Optimal Matchings. Integrality of Polyhedra. The Traveling Salesman Problem. Matroids. NP and NP-Completeness. Appendix. Bibliography. Index.

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Book SynopsisUnique in that it focuses on formulation and case studies rather than solutions procedures covering applications for pure, generalized and integer networks, equivalent formulations plus successful techniques of network models.Table of ContentsNetform Origins and Uses: Why Modeling and Netforms AreImportant. Fundamental Models for Pure Networks. Additional Pure Network Formulation Techniques. Dynamic Network Models. Generalized Networks. Netforms with Discrete Requirements. Appendices. Index.

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Book SynopsisTwo-sided matching provides a model of search processes such as those between firms and workers in labor markets or between buyers and sellers in auctions. This book gives a comprehensive account of recent results concerning the game-theoretic analysis of two-sided matching. The focus of the book is on the stability of outcomes, on the incentives that different rules of organization give to agents, and on the constraints that these incentives impose on the ways such markets can be organized. The results for this wide range of related models and matching situations help clarify which conclusions depend on particular modeling assumptions and market conditions, and which are robust over a wide range of conditions. 'This book chronicles one of the outstanding success stories of the theory of games, a story in which the authors have played a major role: the theory and practice of matching markets â The authors are to be warmly congratulated for this fine piece of work, which is quite uniqTrade Review"This book chronicles one of the outstanding success stories of the theory of games, a story in which the authors have played a major role: the theory and practice of matching markets....The authors are to be warmly congratulated for this fine piece of work, which is quite unique in the game-theoretic literature." From the Foreword by Robert Aumann"An expertly guided tour through an unfamiliar and beautiful region of equilibrium theory would be quite enough incentive for most economic theorists to buy and read this book. But perhaps the greatest treat offred is Roth's discovery of a happy coincidence between theory and practical affairs." Journal of Economic LiteratureTable of ContentsForeword Robert Auman; Acknowledgment; 1. Introduction; Part I. One-To-One Matching: the Marriage Model: 2. Stable matchings; 3. The structure of the set of stable matchings; 4. Strategic questions; Part II. Many-To-One Matching: Models in which Firms May Employ Many Workers: 5. The college admissions model and the labor market for medical interns; 6. Discrete models with money, and more complex preferences; Part III. Models of One-To-One Matching with Money as a Continuous Variable: 7. A simple model of one seller and many buyers; 8. The assignment game; 9. The generalization of the assignment model; Part IV. Epilogue: 10. Open questions and research directions; Bibliography; Indexes.

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Book SynopsisThis book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-contaTrade Review'… the book is an excellent reference for self-studies, especially for students in business and economics.' H. Noltemeier, WürzbergTable of Contents1. Mathematical preliminaries; 2. Optimization in Rn; 3. Existence of solutions: the Weierstrass theorem; 4. Unconstrained optima; 5. Equality constraints and the theorem of Lagrange; 6. Inequality constraints and the theorem of Kuhn and Tucker; 7. Convex structures in optimization theory; 8. Quasi-convexity and optimization; 9. Parametric continuity: the maximum theorem; 10. Supermodularity and parametric monotonicity; 11. Finite-horizon dynamic programming; 12. Stationary discounted dynamic programming; Appendix A. Set theory and logic: an introduction; Appendix B. The real line; Appendix C. Structures on vector spaces; Bibliography.

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Book SynopsisShimon Even''s Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the field. This thoroughly revised second edition, with a foreword by Richard M. Karp and notes by Andrew V. Goldberg, continues the exceptional presentation from the first edition and explains algorithms in a formal but simple language with a direct and intuitive presentation. The book begins by covering basic material, including graphs and shortest paths, trees, depth-first-search and breadth-first search. The main part of the book is devoted to network flows and applications of network flows, and it ends with chapters on planar graphs and testing graph planarity.Trade Review'[This book] provides an intensive study of the main topics of the field, with [a] list of problems following each topic and explains algorithms in a formal but simple language with a direct and intuitive presentation. Its usage is not limited to being a textbook for an upper-level undergraduate or a graduate course in mathematics. Thanks to the rich set of results covered it can also be used as a reference book for postgraduate students and researchers in the area of Graph algorithms … Besides being extremely useful to those who are interested in theory of graphs and design of graph algorithms, instructors can also benefit from the easy way it presents various ideas and approaches to problem solutions.' Vladimir Lacko, Zentralblatt MATH'The book is an excellent introduction to (algorithmic) graph theory, and seems to be a good choice for a class on the topic, or for self-study. Each chapter comes with its own selected bibliography, and ends with a collection of problems to help the reader check his or her understanding of the material presented in that chapter. Proofs are always provided and are also the topic of a few selected exercises.' Anthony Labarre, SIGACT NewsTable of Contents1. Paths in graphs; 2. Trees; 3. Depth-first search; 4. Ordered trees; 5. Flow in networks; 6. Applications of network flow techniques; 7. Planar graphs; 8. Testing graph planarity.

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Book SynopsisExplores a range of entertaining questions about urban life such as: How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? And, more.Trade Review"[Adam's] writing is fun and accessible... College or even advanced high school mathematics instructors will find plenty of great examples here to supplement the standard calculus problem sets."--Library Journal "For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis."--Choice "Read this book and come away with a fresh view of how cities work. Enjoy it for the connections between mathematics and the real world. Share it with your friends, family, and maybe even a municipal planning commissioner or two!"--Sandra L. Arlinghaus, Mathematical Reviews Clippings "It goes without saying that the exposition is very friendly and lucid: this makes the vast majority of material accessible to a general audience interested in mathematical modeling and real life applications. This excellent book may well complement standard texts on engineering mathematics, mathematical modeling, applied mathematics, differential equations; it is a delightful and entertaining reading itself. Thank you, Vickie Kearn, the editor of A Mathematical Nature Walk, for suggesting the idea of this book to Professor Adam--your idea has been delightfully implemented!"--Svitlana P. Rogovchenko, Zentralblatt MATH "[Y]ou'll find this book quite extensive in how many different areas you can apply mathematics in the city and just how revealing even a simple model can be... A Mathematical Nature Walk opened my eyes to nature and now Adam has done the same for cities."--David S. Mazel, MAA Reviews "The author has an entertaining style, interweaving clever stories with the process of mathematical modeling. This book is not designed as a textbook, although it could certainly be used as an interesting source of real-world problems and examples for advanced high school mathematics courses."--Theresa Jorgensen, Mathematics TeacherTable of ContentsPreface xiii Acknowledgments xvii Chapter 1 Introduction: Cancer, Princess Dido, and the city 1 Chapter 2 Getting to the city 7 Chapter 3 Living in the city 15 Chapter 4 Eating in the city 35 Chapter 5 Gardening in the city 41 Chapter 6 Summer in the city 47 Chapter 7 Not driving in the city! 63 Chapter 8 Driving in the city 73 Chapter 9 Probability in the city 89 Chapter 10 Traffic in the city 97 Chapter 11 Car following in the city--I 107 Chapter 12 Car following in the city--II 113 Chapter 13 Congestion in the city 121 Chapter 14 Roads in the city 129 Chapter 15 Sex and the city 135 Chapter 16 Growth and the city 149 Chapter 17 The axiomatic city 159 Chapter 18 Scaling in the city 167 Chapter 19 Air pollution in the city 179 Chapter 20 Light in the city 191 Chapter 21 Nighttime in the city--I 209 Chapter 22 Nighttime in the city--II 221 Chapter 23 Lighthouses in the city? 233 Chapter 24 Disaster in the city? 247 Chapter 25 Getting away from the city 255 Appendix 1 Theorems for Princess Dido 261 Appendix 2 Dido and the sinc function 263 Appendix 3 Taxicab geometry 269 Appendix 4 The Poisson distribution 273 Appendix 5 The method of Lagrange multipliers 277 Appendix 6 A spiral braking path 279 Appendix 7 The average distance between two random points in a circle 281 Appendix 8 Informal "derivation" of the logistic differential equation 283 Appendix 9 A miniscule introduction to fractals 287 Appendix 10 Random walks and the diffusion equation 291 Appendix 11 Rainbow/halo details 297 Appendix 12 The Earth as vacuum cleaner? 303 Annotated references and notes 309 Index 317

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Book SynopsisTrade Review"Are you a video game enthusiast who is getting tired of being asked 'How can you waste time on such stuff?' This book is your answer! Matthew Lane skillfully weaves a tale of how video games can be important tools for teaching mathematics and physics. As a long-time video gamer, I highly recommend Power-Up."—Paul J. Nahin, author of In Praise of Simple Physics"What a delightful journey through the math of hidden worlds! This is much more than a book about video games. It's an exploration of interconnectedness and an invitation for the perpetually curious."—Karim Ani, founder of Mathalicious"A fun survey."—Paul Taylor, Aperiodical"A very readable book."—Computing Reviews

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Book SynopsisA comprehensive exposition of the properties of semiconcave functions and their various applications, particularly to optimal control problems. It is suitable for graduate students and researchers in optimal control, the calculus of variations, and PDEs.Trade Review"The main purpose of this book is to provide a systematic study of the notion of semiconcave functions, as well as a presentation of mathematical fields in which this notion plays a fundamental role. Many results are extracted from articles by the authors and their collaborators, with simplified—and often new—presentation and proofs.... One of the most attractive features of this book is the interplay between several fields of mathematical analysis.... Despite the many topics addressed in the book, the required mathematical background for reading it is limited because all the necessary notions are not only recalled, but also carefully explained, and the main results proved. The book will be found very useful by experts in nonsmooth analysis, nonlinear control theory and PDEs, in particular, as well as by advanced graduate students in this field. They will appreciate the many detailed examples, the clear proofs and the elegant style of presentation, the fairly comprehensive and up-to-date bibliography and the very pertinent historical and bibliographical comments at the end of each chapter." —Mathematical ReviewsTable of ContentsA Model Problem.- Semiconcave Functions.- Generalized Gradients and Semiconcavity.- Singularities of Semiconcave Functions.- Hamilton-Jacobi Equations.- Calculus of Variations.- Optimal Control Problems.- Control Problems with Exit Time.

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Book SynopsisOutline of the main ideas on a model problem.- Continuous viscosity solutions of Hamilton-Jacobi equations.- Optimal control problems with continuous value functions: unrestricted state space.- Optimal control problems with continuous value functions: restricted state space.- Discontinuous viscosity solutions and applications.- Approximation and perturbation problems.- Asymptotic problems.- Differential Games.Trade Review"The exposition is self-contained, clearly written and mathematically precise. The exercises and open problems…will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area. The book may be used by graduate students and researchers in control theory both as an introductory textbook, and as an up-to-date reference book." —Mathematical Reviews "The work is self-contained and is written in an accessible style with discussions of difficult questions on simplified model problems, with useful sections of bibliographical and historical notes and rich sets of proposed exercises at the end of each section. It may be easily used for graduate courses on various topics in control theory. We recommend it to both students and researchers interested in this area of applied mathematics." —Revue Roumaine de Mathématiques Pures et Appliquées "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my oppinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." —Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)... In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." —Acta Applicandae Mathematicae "The book originated from the lecture notes of courses taught by the authors, which is reflected in the style of presentation. Each chapter is enriched with a section of bibliographical and historical notes. The book can be recommended to specialists in PDEs, control theory, differential games, and related topics." —Mathematica Bohemica "As an outgrowth of lecture notes, this monograph purports to introduce and pursue the concept of viscosity solutions of the Hamilton-Jacobo-Bellman equations. It does so requiring but a relative modicum of mathematical knowledge... The book is written in a largely self-contained manner. In addition to bibliographical notes, exercises are provided as well." —Monatshefte für Mathematik "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercises exciting to self control and active collaboration. Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." —ZAATable of ContentsPreface.- Basic notations.- Outline of the main ideas on a model problem.- Continuous viscosity solutions of Hamilton-Jacobi equations.- Optimal control problems with continuous value functions: unrestricted state space.- Optimal control problems with continuous value functions: restricted state space.- Discontinuous viscosity solutions and applications.- Approximation and perturbation problems.- Asymptotic problems.- Differential Games.- Numerical solution of Dynamic Programming.- Nonlinear H-infinity control by Pierpaolo Soravia.- Bibliography.- Index

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Book SynopsisA collection of some of the work of Frederick J Almgren, Jr, the man most noted for defining the shape of geometric variational problems and for his role in founding The Geometry Center. It includes a summary by Sheldon Chang of the famous 1,700 page paper on singular sets of area-minimizing $m$-dimensional surfaces in $R^n$.Table of ContentsThe mathematics of F. J. Almgren, Jr. by B. White On Almgren's regularity result by S. X. Chang The homotopy groups of the integral cycle groups by F. J. Almgren, Jr. An isoperimetric inequality by F. J. Almgren, Jr. Three theorems on manifolds with bounded mean curvature by F. J. Almgren, Jr. Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure by F. J. Almgren, Jr. Measure theoretic geometry and elliptic variational problems by F. J. Almgren, Jr. The structure of limit varifolds associated with minimizing sequences of mappings by F. J. Almgren, Jr. Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints by F. J. Almgren, Jr. The structure of stationary one dimensional varifolds with positive density by W. K. Allard and F. J. Almgren, Jr. The geometry of soap films and soap bubbles by F. J. Almgren, Jr. and J. E. Taylor Examples of unknotted curves which bound only surfaces of high genus within their convex hulls by F. J. Almgren, Jr. and W. P. Thurston Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals by R. Schoen, L. Simon, and F. J. Almgren, Jr. Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents by F. J. Almgren, Jr. Liquid crystals and geodesics by R. N. Thurston and F. J. Almgren $\mathbf{Q}$ valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two by F. J. Almgren, Jr. Optimal isoperimetric inequalities by F. Almgren Co-area, liquid crystals, and minimal surfaces by F. Almgren, W. Browder, and E. Lieb Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds by F. J. Almgren, Jr. and E. H. Lieb Symmetric decreasing rearrangement is sometimes continuous by F. J. Almgren, Jr. and E. H. Lieb Questions and answers about area-minimizing surfaces and geometric measure theory by F. Almgren Curvature-driven flows: A variational approach by F. Almgren, J. E. Taylor, and L. Wang Questions and answers about geometric evolution processes and crystal growth by F. Almgren.

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Book SynopsisCovers the key topics of numerical methods. This work covers topics including interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory and computer arithmetic.Table of ContentsInterpolation by polynomials Spline functions The discrete Fourier transform and its applications Solution of linear systems of equations Nonlinear systems of equations The numerical integration of functions Explicit one-step methods for initial value problems in ordinary differential equations Multistep methods for initial value problems of ordinary differential equations Boundary value problems for ordinary differential equations Jacobi, Gauss-Seidel and relaxation methods for the solution of linear systems of equations The conjugate gradient and GMRES methods Eigenvalue problems Numerical methods for eigenvalue problems Peano's error representation Approximation theory Computer arithmetic Bibliography Index.

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Book SynopsisCovers key topics of numerical methods. This book includes such topics as interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic.Table of ContentsInterpolation by polynomials; Spline functions; The discrete Fourier transform and its applications; Solution of linear systems of equations; Nonlinear systems of equations; The numerical integration of functions; Explicit one-step methods for initial value problems in ordinary differential equations; Multistep methods for initial value problems of ordinary differential equations; Boundary value problems for ordinary differential equations; Jacobi, Gauss-Seidel and relaxation methods for the solution of linear systems of equations; The conjugate gradient and GMRES methods; Eigenvalue problems; Numerical methods for eigenvalue problems; Peano's error representation; Approximation theory; Computer arithmetic; Bibliography; Index; Interpolation by polynomials; Spline functions; The discrete Fourier transform and its applications; Solution of linear systems of equations; Nonlinear systems of equations; The numerical integration of functions; Explicit one-step methods for initial value problems in ordinary differential equations; Multistep methods for initial value problems of ordinary differential equations; Boundary value problems for ordinary differential equations; Jacobi, Gauss-Seidel and relaxation methods for the solution of linear systems of equations; The conjugate gradient and GMRES methods; Eigenvalue problems; Numerical methods for eigenvalue problems; Peano's error representation; Approximation theory; Computer arithmetic; Bibliography; Index

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Book SynopsisThanks to recent advancements, optimization is now recognized as a crucial component in research and decision-making across a number of fields. Through optimization, scientists have made tremendous advances in cancer treatment planning, disease control, and drug development, as well as in sequencing DNA, and identifying protein structures. Optimization in Medicine and Biology provides researchers with a comprehensive, single-source reference that will enable them to apply the very latest optimization techniques to their work. With contributions from pioneering international experts this volume integrates strong foundational theory, good modeling techniques, and efficient and robust algorithms with relevant applications Divided into two sections, the first begins with mathematical programming techniques for medical decision making processes and demonstrates their application to optimizing pediatric vaccine formularies, kidney paired donation, and the cost-effectiveness Table of ContentsMedicine. Classification and Disease Prediction via Mathematical Programming. Using Influence Diagrams in Cost Effectiveness Analysis for Medical Decisions. Non-Bayesian Classification to Obtain High Quality Clinical Decisions. Optimizing Pediatric Vaccine Formularies. . Optimization Over Graphs for Kidney Paired Donation. Introduction to Radiation Therapy Planning Optimization. Beam Orientation Optimization Methods in Intensity Modulated Radiation Therapy Treatment Planning. Multileaf collimator shape matrix decomposition. Optimal Planning for Radiation Therapy. Biology. An Introduction to Systems Biology for Mathematical Programmers. Algorithms for Genomics Analysis. Computational Methods for Probe Design and Selection. An Implementation of Logical Analysis of Data for Oligo Probe Selection. A New Dihedral Angle Measure for Protein Secondary Prediction. Optimization of Tumor Virotherapy with Recombinant Measles Viruses. Combating Microbial Resistance to Antimicrobial Agents through Dosing Regimen Optimization. Appendix.

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Book SynopsisThis self-contained textbook introduces students and researchers of AI to the key mathematical concepts and techniques necessary to learn and analyze machine learning algorithms. Readers will gain the technical knowledge needed to understand research papers in theoretical machine learning, without much difficulty.Trade Review'This graduate-level text gives a thorough, rigorous and up-to-date treatment of the main mathematical tools that have been developed for the analysis and design of machine learning methods. It is ideal for a graduate class, and the exercises at the end of each chapter make it suitable for self-study. An excellent addition to the literature from one of the leading researchers in this area, it is sure to become a classic.' Peter Bartlett, University of California, Berkeley'This book showcases the breadth and depth of mathematical ideas in learning theory. The author has masterfully synthesized techniques from the many disciplines that have contributed to this subject, and presented them in an accessible format that will be appreciated by both newcomers and experts alike. Readers will learn the tools-of-the-trade needed to make sense of the research literature and to express new ideas with clarity and precision.' Daniel Hsu, Columbia University'Tong Zhang shares in this book his deep and broad knowledge of machine learning, writing an impressively comprehensive and up-to-date reference text, providing a rigorous and rather advanced treatment of the most important topics and approaches in the mathematical study of machine learning. As an authoritative reference and introduction, his book will be a great asset to the field.' Robert Schapire, Microsoft Research'This book gives a systematic treatment of the modern mathematical techniques that are commonly used in the design and analysis of machine learning algorithms. Written by a key contributor to the field, it is a unique resource for graduate students and researchers seeking to gain a deep understanding of the theory of machine learning.' Shai Shalev-Shwartz, Hebrew University of JerusalemTable of Contents1. Introduction; 2. Basic probability inequalities for sums of independent random variables; 3. Uniform convergence and generalization analysis; 4. Empirical covering number analysis and symmetrization; 5. Covering number estimates; 6. Rademacher complexity and concentration inequalities; 7. Algorithmic stability analysis; 8. Model selection; 9. Analysis of kernel methods; 10. Additive and sparse models; 11. Analysis of neural networks; 12. Lower bounds and minimax analysis; 13. Probability inequalities for sequential random variables; 14. Basic concepts of online learning; 15. Online aggregation and second order algorithms; 16. Multi-armed bandits; 17. Contextual bandits; 18. Reinforcement learning; A. Basics of convex analysis; B. f-Divergence of probability measures; References; Author index; Subject index.

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Book SynopsisThis is a graduate-level introduction to the key ideas and theoretical foundation of the vibrant field of optimal mass transport in the Euclidean setting. Taking a pedagogical approach, it introduces concepts gradually and in an accessible way, while also remaining technically and conceptually complete.Trade Review'Francesco Maggi's book is a detailed and extremely well written explanation of the fascinating theory of Monge-Kantorovich optimal mass transfer. I especially recommend Part IV's discussion of the 'linear' cost problem and its subtle mathematical resolution.' Lawrence C. Evans, University of California, Berkeley'Over the last three decades, optimal transport has revolutionized the mathematical analysis of inequalities, differential equations, dynamical systems, and their applications to physics, economics, and computer science. By exposing the interplay between the discrete and Euclidean settings, Maggi's book makes this development uniquely accessible to advanced undergraduates and mathematical researchers with a minimum of prerequisites. It includes the first textbook accounts of the localization technique known as needle decomposition and its solution to Monge's centuries old cutting and filling problem (1781). This book will be an indispensable tool for advanced undergraduates and mathematical researchers alike.' Robert McCann, University of TorontoTable of ContentsPreface; Notation; Part I. The Kantorovich Problem: 1. An introduction to the Monge problem; 2. Discrete transport problems; 3. The Kantorovich problem; Part II. Solution of the Monge Problem with Quadratic Cost: the Brenier-McCann Theorem: 4. The Brenier theorem; 5. First order differentiability of convex functions; 6. The Brenier-McCann theorem; 7. Second order differentiability of convex functions; 8. The Monge-Ampère equation for Brenier maps; Part III. Applications to PDE and the Calculus of Variations and the Wasserstein Space: 9. Isoperimetric and Sobolev inequalities in sharp form; 10. Displacement convexity and equilibrium of gases; 11. The Wasserstein distance W2 on P2(Rn); 12. Gradient flows and the minimizing movements scheme; 13. The Fokker-Planck equation in the Wasserstein space; 14. The Euler equations and isochoric projections; 15. Action minimization, Eulerian velocities and Otto's calculus; Part IV. Solution of the Monge Problem with Linear Cost: the Sudakov Theorem: 16. Optimal transport maps on the real line; 17. Disintegration; 18. Solution to the Monge problem with linear cost; 19. An introduction to the needle decomposition method; Appendix A: Radon measures on Rn and related topics; Appendix B: Bibliographical Notes; Bibliography; Index.

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Book SynopsisThis textbook offers a guided tutorial that reviews the theoretical fundamentals while going through the practical examples used for constructing the computational frame, applied to various real-life models.Computational Optimization: Success in Practice will lead the readers through the entire process. They will start with the simple calculus examples of fitting data and basics of optimal control methods and end up constructing a multi-component framework for running PDE-constrained optimization. This framework will be assembled piece by piece; the readers may apply this process at the levels of complexity matching their current projects or research needs.By connecting examples with the theory and discussing the proper communication between them, the readers will learn the process of creating a big house. Moreover, they can use the framework exemplified in the book as the template for their research or course problems they will know how to change theTable of ContentsChapter 1. Introduction to Optimization. Chapter 2. Minimization Approaches for Functions of One Variable. Chapter 3. Generalized Optimization Framework. Chapter 4. Exploring Optimization Algorithms. Chapter 5. Line Search Algorithms. Chapter 6. Choosing Optimal Step Size. Chapter 7. Trust Region and Derivative-Free Methods. Chapter 8. Large-Scale and Constrained Optimization. Chapter 9. ODE-based Optimization. Chapter 10. Implementing Regularization Techniques. Chapter 11. Moving to PDE-based Optimization. Chapter 12. Sharing Multiple Software Environments.

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Book SynopsisThis engineering textbook is designed to introduce advanced control systems for vehicles, including advanced automotive concepts and the next generation of vehicles for ITS. For each automotive control problem considered, the authors emphasise the physics and underlying principles behind the control system concept and design.Table of ContentsPreface; Part I. Introduction and Background: 1. Introduction; 2. Automotive control system design process; 3. Review of engine modeling; 4. Review of vehicle dynamics; 5. Human factors and driver modeling; Part II. Powertrain Control Systems: 6. Air-to-fuel ratio control; 7. Control of spark timing; 8. Idle speed control; 9. Transmission control; 10. Control of hybrid vehicles; 11. Modeling and control of fuel cells for vehicles; Part III. Vehicle Control Systems: 12. Cruise and headway control; 13. Antilock brake systems and traction control; 14. Vehicle stability control; 15. Four wheel steering; 16. Active suspensions; Part IV. Intelligent Transportation Systems (ITS): 17. Overview of ITS; 18. Preventing collisions; 19. Automated highway systems (AHS) and platooning; 20. Lateral active safety systems and automated steering; Appendix A. Review of control theory fundamentals; Appendix B. Two-mass three DOF vehicle lateral/yaw/roll model.

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Book SynopsisThis book discusses aircraft flight performance, focusing on commercial aircraft but also considering examples of high-performance military aircraft. The framework is a multidisciplinary engineering analysis, fully supported by flight simulation, with software validation at several levels. The book covers topics such as geometrical configurations, configuration aerodynamics and determination of aerodynamic derivatives, weight engineering, propulsion systems (gas turbine engines and propellers), aircraft trim, flight envelopes, mission analysis, trajectory optimisation, aircraft noise, noise trajectories and analysis of environmental performance. A unique feature of this book is the discussion and analysis of the environmental performance of the aircraft, focusing on topics such as aircraft noise and carbon dioxide emissions.Trade Review'The book represents a useful reference for practising performance engineers and it would be a good starting point for anyone tasked with carrying out a performance analysis of an aircraft …' The Aeronautical JournalTable of Contents1. Prolegomena; 2. Aircraft models; 3. Weight and balance performance; 4. Aerodynamic performance; 5. Engine performance; 6. Propeller performance; 7. Aeroplane trim; 8. Flight envelopes; 9. Take-off and field performance; 10. Climb performance; 11. Descent and landing performance; 12. Cruise performance; 13. Manoeuvre performance; 14. Thermo-structural performance; 15. Mission analysis; 16. Aircraft noise: noise sources; 17. Aircraft noise: propagation; 18. Aircraft noise: flight trajectories; 19. Environmental performance; 20. Epilogue.

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Book SynopsisPresenting a fresh look at process control, this new text demonstrates state-space approach shown in parallel with the traditional approach to explain the strategies used in industry today. Modern time-domain and traditional transform-domain methods are integrated throughout and explain the advantages and limitations of each approach; the fundamental theoretical concepts and methods of process control are applied to practical problems. To ensure understanding of the mathematical calculations involved, MATLAB is included for numeric calculations and MAPLE for symbolic calculations, with the math behind every method carefully explained so that students develop a clear understanding of how and why the software tools work. Written for a one-semester course with optional advanced-level material, features include solved examples, cases that include a number of chemical reactor examples, chapter summaries, key terms, and concepts, as well as over 240 end-of-chapter problems, focused computatiTrade Review'Provides a fresh perspective through the integrated coverage of modern state-space and traditional transfer function approaches. The mathematical derivations are detailed and accessible, aiding clear understanding of the basic as well as the more advanced topics.' Prodromos Daoutidis, University of Minnesota'Breaking new ground in the crowded field of process control textbooks, this book provides the foundation for teaching a modern undergraduate process control course in the twenty-first century. It is exceptionally well written and organized, and includes numerous examples, making it a must-have for all process control researchers, students and engineers.' Panagiotis D. Christofides, University of California, Los AngelesTable of ContentsContents; Preface; 1. Introduction; 2. Dynamic Models for Chemical Process Systems; 3. First Order Systems; 4. Connections of First Order Systems; 5. Second Order Systems; 6. Linear Higher Order Systems; 7. Eigenvalue Analysis – Asymptotic Stability; 8. Transfer Function Analysis of the Input/Output Behavior; 9. Frequency Response; 10. The Feedback Control System; 11. Block Diagram Reduction and Transient Response Calculation in a Feedback Control System; 12. Steady-State and Stability Analysis of the Closed Loop System; 13. State Space Description and Analysis of the Closed Loop System; 14. Systems with Dead Time; 15. Parametric Analysis of Closed Loop Dynamics – Root Locus Diagrams; 16. Optimal Selection of Controller Parameters; 17. Bode and Nyquist Stability Criteria – Gain and Phase Margins; 18. Multiple-Input-Multiple-Output Systems; 19. Synthesis of Model-Based Feedback Controllers; 20. Cascade, Ratio and Feedforward Control; Appendix A; Appendix B.

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