Kooperativer Bibliotheksverbund

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Format: 1 online resource (xiii, 381 pages) : , digital, PDF file(s).

ISBN: 1-108-61724-7 , 1-108-62022-1 , 1-108-75507-0

Series Statement: Educational and psychological testing in a global context

Content: To look forward, it is necessary to look back and learn. History is more than just facts about the past; it is a narrative told from a particular perspective. A proverb from Africa, 'Until lions have their own historians, tales of the hunt shall always glorify the hunter,' captures this best. Most of the scholarship about psychological assessment comes from very specific nationalities and cultures, which does not truly reflect the diversity and breadth of histories pertaining to the field. Covering 50 countries, this collection gives voice to those that have previously been under represented and sometimes marginalized. This book not only describes important moments in psychological assessment from around the globe, but also equips readers with the tools to map the future of psychological assessment across nations. It advocates for a more globally inclusive science of assessment that holds promise for enhancing creativity and innovation in the field.

Note: Title from publisher's bibliographic system (viewed on 01 Aug 2022). , Cover -- Half-title -- Series information -- Title page -- Copyright information -- Contents -- List of Tables -- List of Contributors -- Series Editor's Foreword -- Chapter 1 Histories of Psychological Assessment: An Introduction -- 1.1 Introduction -- 1.2 Overview of the Book -- 1.3 Africa -- 1.4 The Arab Regions -- 1.5 Europe -- 1.6 Asia -- 1.7 Oceania -- 1.8 The Americas -- 1.9 Conclusion -- References -- Chapter 2 Psychological Assessment in Southern Africa -- 2.1 Introduction -- 2.2 Psychological Assessment in South Africa -- 2.3 Psychological Assessment in Botswana -- 2.3.1 Projective Tests Study -- 2.3.2 Regional Comparative or Benchmark Studies -- 2.3.3 Policy Formulation and Support Studies -- 2.4 Psychological Assessment in Zimbabwe -- 2.5 Psychological Assessment in Zambia -- 2.6 Conclusion -- References -- Chapter 3 Psychological Testing and Inclusive Schooling: Issues and Prospects in Central Africa -- 3.1 Introduction -- 3.2 Types of Psychological Tests and Inclusive Schooling in Central Africa -- 3.3 Issues/Problems Associated with the Current State of Psychological Testing in Central Africa -- 3.4 Prospects of Psychological Testing and School Reforms in Central Africa -- 3.5 Conclusion -- References -- Chapter 4 Psychological Assessment in West Africa -- 4.1 Introduction -- 4.2 Psychological Assessment in Ghana -- 4.3 Psychological Assessment in Nigeria -- 4.4 Psychological Assessment in Liberia and Sierra Leone -- 4.5 Current Challenges -- 4.6 Future Prospects -- 4.7 Conclusion -- References -- Chapter 5 Psychological Assessment in the Levant -- 5.1 Introduction -- 5.1.1 Historical Development -- 5.2 Psychological Assessment Research in Levant -- 5.2.1 Jordan -- 5.2.2 Lebanon -- 5.2.3 Palestine -- 5.2.4 Syria -- 5.3 The Current Impact of Sociocultural Factors on Assessment -- 5.3.1 Arabic Language -- 5.3.2 Bilingualism. , 5.3.3 Intellectual Dependency -- 5.3.4 Economic and Sociopolitical Context -- 5.3.5 Education, Training, and Professional Regulation -- 5.3.6 Collaboration -- 5.4 Conclusion and Recommendations -- References -- Chapter 6 The History of Assessment in the Nordic Countries -- 6.1 Introduction -- 6.2 Scandinavian Psychology Prior to the World Wars -- 6.3 Psychology and Assessment in Scandinavia during the World Wars (1923-1945) -- 6.4 Scandinavian Psychology Post the World Wars -- 6.5 Scandinavian Psychological Assessment: 1960s-1970s -- 6.6 Psychological Assessment: 2000-Present -- 6.7 Conclusion -- References -- Chapter 7 Key Episodes in The History of Testing in Central Western Europe -- 7.1 Introduction -- 7.2 Wilhelm Wundt, Experimental Psychological Laboratories, and Early Testing -- 7.3 Alfred Binet and the Measurement of Intelligence -- 7.4 William Stern and the Foundation of Differential Psychology -- 7.5 Hugo Münsterberg and the First Selection Tests -- 7.6 Otto Lipmann, William Stern, Institutes of Applied Psychology and the First Journal of Applied Psychology -- 7.7 The Exodus from Germany -- 7.8 Wehrmachtpsychologie Testing -- 7.9 Dutch Psychometrics and the Centraal Instituut voor Toetsontwikkeling -- 7.10 Internationalization and Critical Psychology -- 7.11 University Entry Selection in Belgium, Germany, and the Netherlands -- 7.12 Modern Use of Tests in Organizations -- 7.13 Outlook and Trends -- References -- Chapter 8 The Beginnings of Psychological Assessment in Spain and Portugal -- 8.1 Introduction -- 8.2 Huarte de San Juan, a Precursor -- 8.3 Psychological Assessment in the Nineteenth Century -- 8.4 Psychological Assessment in the Twentieth Century (1900-1949) -- 8.5 Further Developments in Psychological Assessment (1950-1969) -- 8.6 Psychological Assessment in Spain and Portugal (1970-1990). , 8.7 Psychological Assessment in Spain and Portugal Post 1990 -- 8.8 Conclusion -- References -- Chapter 9 Histories of Psychological Assessments in the United Kingdom -- 9.1 Introduction -- 9.2 The Early Development of Psychological Assessment (1859-1890) -- 9.3 From the 1890s to the Great War of 1914-1918 -- 9.4 The Development of Psychometrics -- 9.5 The Great 1914-1918 War -- 9.6 The Inter-war Years (1918-1939) -- 9.7 World War II and the Post-war Years (1940s-1970s) -- 9.8 The Development of Assessment Centers -- 9.9 The 1970s and 1980s: Assessment Centers in the Private Sector -- 9.10 Concerns over Bias and Fairness in Testing -- 9.11 The Cyril Burt Saga and the Continuing Eugenics Issue -- 9.12 The Growth in Use of Personality Assessment -- 9.13 The Growth of Occupational Assessment in the United Kingdom (1970s-1990s) -- 9.14 The Technological Revolution in the 1980s to the Late 1990s -- 9.15 Item Response Theory -- 9.16 The British Ability Scales -- 9.17 Item Generation and Test Generation -- 9.18 The Internet (Late 1990s to Now) -- 9.19 Conclusion -- References -- Chapter 10 The Early History of Psychological Testing in Eastern Europe and Russia -- 10.1 The General Context of Eastern Europe -- 10.2 Psychology in Eastern Europe: The Early Days -- 10.2.1 Russia -- 10.2.2 Romania -- 10.2.3 Poland -- 10.2.4 The Former Kingdom/Republic of Yugoslavia -- 10.2.5 Czechoslovakia -- 10.2.6 Hungary -- 10.3 The Dark Days -- 10.4 The Revival -- 10.5 Conclusion -- References -- Chapter 11 Hearing the Untold: A Review of Central Asia's Contribution to the Expansion of Psychological Assessment -- 11.1 Introduction -- 11.2 Iran -- 11.3 Pakistan -- 11.4 Afghanistan -- 11.5 Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, and Uzbekistan -- 11.6 Conclusion -- References -- Chapter 12 History of Psychological Assessment in Southern Asia -- 12.1 Introduction. , 12.2 Assessment in South Asia Pre-colonialism -- 12.3 Psychological Assessment in India -- 12.4 Assessment in Educational Settings -- 12.5 Assessment in Clinical Settings -- 12.6 Assessment in Social Settings -- 12.7 Assessment in Workplace Settings -- 12.8 Assessment in Military Settings -- 12.9 Psychological Assessment in Sri Lanka -- 12.10 Psychological Assessment in Bangladesh -- 12.11 Psychological Assessment in Nepal -- 12.12 Psychological Assessment in Bhutan -- 12.13 Conclusion -- References -- Chapter 13 The History of Psychological Testing in East Asia -- 13.1 Introduction -- 13.2 The History of Psychological Testing in China -- 13.2.1 The Idea and Practice of Psychological Testing in Ancient China -- 13.2.2 Development of Modern Psychological Testing in China (1915-1948) -- 13.2.3 Development of Psychological Testing in China after 1949 -- 13.2.4 cpai: One Representative Personality Test -- 13.3 Psychological Testing in Japan -- 13.4 Psychological Testing in South Korea -- 13.5 Challenges and Future Directions of Psychological Testing in East Asia -- References -- Chapter 14 Psychological Assessment and Testing in Malaysia and Singapore -- 14.1 Introduction -- 14.2 Contextualizing Malaysia -- 14.3 History of Psychology in Malaysia -- 14.4 The Development of Psychological Assessments in Malaysia -- 14.5 Contextualizing Singapore -- 14.6 History of Psychology in Singapore -- 14.7 The Development of Psychological Assessment in Singapore -- 14.8 Conclusion -- References -- Chapter 15 A Brief History of Testing and Assessment in Oceania -- 15.1 Introduction -- 15.2 Australia: Beginnings at the Turn of the Twentieth Century -- 15.3 World War I and the Interwar Years -- 15.4 World War II and the Postwar Years -- 15.5 Testing in Australia: 1960-1990 -- 15.6 Changes with the Coming of the Twenty-First Century. , 15.7 Recognizing Cultural Differences in Test Use -- 15.8 Aotearoa/New Zealand: The Early Years -- 15.9 Testing in Education, Industry, and the Clinics: 1940 Onwards -- 15.10 Testing in New Zealand: The Current Climate -- 15.11 Recognition of Cultural Differences -- 15.12 PNG and the Pacific Islands -- 15.13 Conclusion -- References -- Chapter 16 Psychological Assessment in South America: Perspectives from Brazil, Bolivia, Chile, and Peru -- 16.1 Introduction -- 16.2 Brazil -- 16.2.1 Historical Aspects of Test Use in Brazil -- 16.2.2 The Development of Psychological Assessment -- 16.2.3 Professional Regulations and Training -- 16.2.4 Increase of Research Groups and Production -- 16.2.5 Challenges and Vision of the Future -- 16.3 Bolivia -- 16.3.1 History of Psychological Assessment -- 16.3.2 Professional Training in Psychology -- 16.3.3 Assessment Practice -- 16.3.4 Challenges -- 16.4 Chile -- 16.4.1 Initial Historical Context -- 16.4.2 Deregulation and Attempts at Regulation -- 16.4.2.1 Training -- 16.4.2.2 Professional Practice -- 16.4.2.3 Research -- 16.4.3 Conclusions and Challenges for Assessment in Chile -- 16.5 Peru -- 16.5.1 History of Psychological Assessment in Peru -- 16.5.2 Training -- 16.5.3 Research -- 16.5.4 Challenges -- 16.6 Conclusion -- References -- Chapter 17 Historical Development of Psychological Assessment in the Caribbean -- 17.1 Introduction -- 17.2 Pre-Columbian Era to the Eighteenth Century -- 17.3 Slavery to the Nineteenth Century -- 17.4 Traditional Healers -- 17.5 Emancipation to the Twentieth Century -- 17.6 The Twenty-First Century and Cross-cultural Issues of Euro-American Assessment Methods -- 17.7 Conclusion -- Reference -- Chapter 18 The History of Psychological Assessment in North America -- 18.1 Introduction -- 18.2 Antecedents of Psychological Testing in North America -- 18.3 Intellectual Assessment. , 18.3.1 Adaptations of the Binet Scales.

Additional Edition: ISBN 1-108-48500-6

Language: English

URL: lizenzpflichtig

URL: https://doi.org/10.1017/9781108755078

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Format: 1 online resource (viii, 424 pages) : , digital, PDF file(s).

ISBN: 1-108-62032-9 , 1-108-61736-0 , 1-108-75552-6

Content: This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

Note: Title from publisher's bibliographic system (viewed on 29 Jan 2020). , Cover -- Half-title -- Title page -- Copyright information -- Contents -- 1 Introduction -- 2 High-Dimensional Space -- 2.1 Introduction -- 2.2 The Law of Large Numbers -- 2.3 The Geometry of High Dimensions -- 2.4 Properties of the Unit Ball -- 2.4.1 Volume of the Unit Ball -- 2.4.2 Volume near the Equator -- 2.5 Generating Points Uniformly at Random from a Ball -- 2.6 Gaussians in High Dimension -- 2.7 Random Projection and Johnson-Lindenstrauss Lemma -- 2.8 Separating Gaussians -- 2.9 Fitting a Spherical Gaussian to Data -- 2.10 Bibliographic Notes -- 2.11 Exercises -- 3 Best-Fit Subspaces and Singular Value Decomposition (SVD) -- 3.1 Introduction -- 3.2 Preliminaries -- 3.3 Singular Vectors -- 3.4 Singular Value Decomposition (SVD) -- 3.5 Best Rank-k Approximations -- 3.6 Left Singular Vectors -- 3.7 Power Method for Singular Value Decomposition -- 3.7.1 A Faster Method -- 3.8 Singular Vectors and Eigenvectors -- 3.9 Applications of Singular Value Decomposition -- 3.9.1 Centering Data -- 3.9.2 Principal Component Analysis -- 3.9.3 Clustering a Mixture of Spherical Gaussians -- 3.9.4 Ranking Documents and Web Pages -- 3.9.5 An Illustrative Application of SVD -- 3.9.6 An Application of SVD to a Discrete Optimization Problem -- 3.10 Bibliographic Notes -- 3.11 Exercises -- 4 Random Walks and Markov Chains -- 4.1 Stationary Distribution -- 4.2 Markov Chain Monte Carlo -- 4.2.1 Metropolis-Hasting Algorithm -- 4.2.2 Gibbs Sampling -- 4.3 Areas and Volumes -- 4.4 Convergence of Random Walks on Undirected Graphs -- 4.4.1 Using Normalized Conductance to Prove Convergence -- 4.5 Electrical Networks and Random Walks -- 4.6 Random Walks on Undirected Graphs with Unit Edge Weights -- 4.6.1 Hitting Time -- 4.6.2 Commute Time -- 4.6.3 Cover Time -- 4.7 Random Walks in Euclidean Space -- 4.7.1 Random Walks on Lattices -- 4.7.2 Two Dimensions. , 4.7.3 Three Dimensions -- 4.8 The Web as a Markov Chain -- 4.8.1 Pagerank -- 4.8.2 Relation to Hitting Time -- 4.8.3 Spam -- 4.8.4 Personalized Pagerank -- 4.8.5 Algorithm for Computing Personalized Pagerank -- 4.9 Bibliographic Notes -- 4.10 Exercises -- 5 Machine Learning -- 5.1 Introduction -- 5.1.1 The Core Problem -- 5.1.2 How to Learn -- 5.2 The Perceptron Algorithm -- 5.3 Kernel Functions and Nonlinearly Separable Data -- 5.4 Generalizing to New Data -- 5.4.1 Overfitting and Uniform Convergence -- 5.4.2 Occam's Razor -- 5.4.3 Regularization: Penalizing Complexity -- 5.5 VC-Dimension -- 5.5.1 Definitions and Key Theorems -- 5.5.2 VC-Dimension of Some Set Systems -- 5.5.3 Shatter Function for Set Systems of Bounded VC-Dimension -- 5.5.4 VC-Dimension of Combinations of Concepts -- 5.5.5 The Key Theorem -- 5.6 VC-Dimension and Machine Learning -- 5.7 Other Measures of Complexity -- 5.8 Deep Learning -- 5.8.1 Generative Adversarial Networks (GANs) -- 5.9 Gradient Descent -- 5.9.1 Stochastic Gradient Descent -- 5.9.2 Regularizer -- 5.10 Online Learning -- 5.10.1 An Example: Learning Disjunctions -- 5.10.2 The Halving Algorithm -- 5.10.3 The Perceptron Algorithm -- 5.10.4 Inseparable Data and Hinge Loss -- 5.10.5 Online to Batch Conversion -- 5.10.6 Combining (Sleeping) Expert Advice -- 5.11 Boosting -- 5.12 Further Current Directions -- 5.12.1 Semi-Supervised Learning -- 5.12.2 Active Learning -- 5.12.3 Multitask Learning -- 5.13 Bibliographic Notes -- 5.14 Exercises -- 6 Algorithms for Massive Data Problems: Streaming, Sketching, and Sampling -- 6.1 Introduction -- 6.2 Frequency Moments of Data Streams -- 6.2.1 Number of Distinct Elements in a Data Stream -- 6.2.2 Number of Occurrences of a Given Element -- 6.2.3 Frequent Elements -- 6.2.4 The Second Moment -- 6.3 Matrix Algorithms Using Sampling -- 6.3.1 Matrix Multiplication Using Sampling. , 6.3.2 Implementing Length Squared Sampling in Two Passes -- 6.3.3 Sketch of a Large Matrix -- 6.4 Sketches of Documents -- 6.5 Bibliographic Notes -- 6.6 Exercises -- 7 Clustering -- 7.1 Introduction -- 7.1.1 Preliminaries -- 7.1.2 Two General Assumptions on the Form of Clusters -- 7.1.3 Spectral Clustering -- 7.2 k-Means Clustering -- 7.2.1 A Maximum-Likelihood Motivation -- 7.2.2 Structural Properties of the k-Means Objective -- 7.2.3 Lloyd's Algorithm -- 7.2.4 Ward's Algorithm -- 7.2.5 k-Means Clustering on the Line -- 7.3 k-Center Clustering -- 7.4 Finding Low-Error Clusterings -- 7.5 Spectral Clustering -- 7.5.1 Why Project? -- 7.5.2 The Algorithm -- 7.5.3 Means Separated by Ω(1) Standard Deviations -- 7.5.4 Laplacians -- 7.5.5 Local Spectral Clustering -- 7.6 Approximation Stability -- 7.6.1 The Conceptual Idea -- 7.6.2 Making This Formal -- 7.6.3 Algorithm and Analysis -- 7.7 High-Density Clusters -- 7.7.1 Single Linkage -- 7.7.2 Robust Linkage -- 7.8 Kernel Methods -- 7.9 Recursive Clustering Based on Sparse Cuts -- 7.10 Dense Submatrices and Communities -- 7.11 Community Finding and Graph Partitioning -- 7.12 Spectral Clustering Applied to Social Networks -- 7.13 Bibliographic Notes -- 7.14 Exercises -- 8 Random Graphs -- 8.1 The G(n,p) Model -- 8.1.1 Degree Distribution -- 8.1.2 Existence of Triangles in G(n, d/n) -- 8.2 Phase Transitions -- 8.3 Giant Component -- 8.3.1 Existence of a Giant Component -- 8.3.2 No Other Large Components -- 8.3.3 The Case of p < -- 1/n -- 8.4 Cycles and Full Connectivity -- 8.4.1 Emergence of Cycles -- 8.4.2 Full Connectivity -- 8.4.3 Threshold for O(ln n) Diameter -- 8.5 Phase Transitions for Increasing Properties -- 8.6 Branching Processes -- 8.7 CNF-SAT -- 8.7.1 SAT-Solvers in Practice -- 8.7.2 Phase Transitions for CNF-SAT -- 8.8 Nonuniform Models of Random Graphs. , 8.8.1 Giant Component in Graphs with Given Degree Distribution -- 8.9 Growth Models -- 8.9.1 Growth Model without Preferential Attachment -- 8.9.2 Growth Model with Preferential Attachment -- 8.10 Small-World Graphs -- 8.11 Bibliographic Notes -- 8.12 Exercises -- 9 Topic Models, Nonnegative Matrix Factorization, Hidden Markov Models, and Graphical Models -- 9.1 Topic Models -- 9.2 An Idealized Model -- 9.3 Nonnegative Matrix Factorization -- 9.4 NMF with Anchor Terms -- 9.5 Hard and Soft Clustering -- 9.6 The Latent Dirichlet Allocation Model for Topic Modeling -- 9.7 The Dominant Admixture Model -- 9.8 Formal Assumptions -- 9.9 Finding the Term-Topic Matrix -- 9.10 Hidden Markov Models -- 9.11 Graphical Models and Belief Propagation -- 9.12 Bayesian or Belief Networks -- 9.13 Markov Random Fields -- 9.14 Factor Graphs -- 9.15 Tree Algorithms -- 9.16 Message Passing in General Graphs -- 9.16.1 Graphs with a Single Cycle -- 9.16.2 Belief Update in Networks with a Single Loop -- 9.16.3 Maximum Weight Matching -- 9.17 Warning Propagation -- 9.18 Correlation between Variables -- 9.19 Bibliographic Notes -- 9.20 Exercises -- 10 Other Topics -- 10.1 Ranking and Social Choice -- 10.1.1 Randomization -- 10.1.2 Examples -- 10.2 Compressed Sensing and Sparse Vectors -- 10.2.1 Unique Reconstruction of a Sparse Vector -- 10.2.2 Efficiently Finding the Unique Sparse Solution -- 10.3 Applications -- 10.3.1 Biological -- 10.3.2 Low-Rank Matrices -- 10.4 An Uncertainty Principle -- 10.4.1 Sparse Vector in Some Coordinate Basis -- 10.4.2 A Representation Cannot Be Sparse in Both Time and Frequency Domains -- 10.5 Gradient -- 10.6 Linear Programming -- 10.6.1 The Ellipsoid Algorithm -- 10.7 Integer Optimization -- 10.8 Semi-Definite Programming -- 10.9 Bibliographic Notes -- 10.10 Exercises -- 11 Wavelets -- 11.1 Dilation -- 11.2 The Haar Wavelet. , 11.3 Wavelet Systems -- 11.4 Solving the Dilation Equation -- 11.5 Conditions on the Dilation Equation -- 11.6 Derivation of the Wavelets from the Scaling Function -- 11.7 Sufficient Conditions for the Wavelets to Be Orthogonal -- 11.8 Expressing a Function in Terms of Wavelets -- 11.9 Designing a Wavelet System -- 11.10 Applications -- 11.11 Bibliographic Notes -- 11.12 Exercises -- 12 Background Material -- 12.1 Definitions and Notation -- 12.1.1 Integers -- 12.1.2 Substructures -- 12.1.3 Asymptotic Notation -- 12.2 Useful Relations -- 12.3 Useful Inequalities -- 12.4 Probability -- 12.4.1 Sample Space, Events, and Independence -- 12.4.2 Linearity of Expectation -- 12.4.3 Union Bound -- 12.4.4 Indicator Variables -- 12.4.5 Variance -- 12.4.6 Variance of the Sum of Independent Random Variables -- 12.4.7 Median -- 12.4.8 The Central Limit Theorem -- 12.4.9 Probability Distributions -- 12.4.10 Bayes Rule and Estimators -- 12.5 Bounds on Tail Probability -- 12.5.1 Chernoff Bounds -- 12.5.2 More General Tail Bounds -- 12.6 Applications of the Tail Bound -- 12.7 Eigenvalues and Eigenvectors -- 12.7.1 Symmetric Matrices -- 12.7.2 Relationship between SVD and Eigen Decomposition -- 12.7.3 Extremal Properties of Eigenvalues -- 12.7.4 Eigenvalues of the Sum of Two Symmetric Matrices -- 12.7.5 Norms -- 12.7.6 Important Norms and Their Properties -- 12.7.7 Additional Linear Algebra -- 12.7.8 Distance between Subspaces -- 12.7.9 Positive Semi-Definite Matrix -- 12.8 Generating Functions -- 12.8.1 Generating Functions for Sequences Defined by Recurrence Relationships -- 12.8.2 The Exponential Generating Function and the Moment Generating Function -- 12.9 Miscellaneous -- 12.9.1 Lagrange Multipliers -- 12.9.2 Finite Fields -- 12.9.3 Application of Mean Value Theorem -- 12.10 Exercises -- References -- Index.

Additional Edition: Online version: Blum, Avrim, 1966- Foundations of data science New York, NY : Cambridge University Press, 2020. ISBN 9781108755528

Additional Edition: ISBN 9781108485067

Additional Edition: ISBN 1108485065

Language: English

URL: Volltext  (lizenzpflichtig)

URL: https://doi.org/10.1017/9781108755528

UID:

Format: 1 online resource (281 p.)

ISBN: 1-282-28982-9 , 9786612289828 , 0-08-095571-1

Series Statement: Mathematics in science and engineering ; v. 61, 2

Content: Methods of nonlinear analysis

Note: Description based upon print version of record. , Front Cover; Methods of Nonlinear Analysis; Copyright Page; Preface; Contents; Contents of Volume I; Chapter 9. Upper and Lower Bounds via Duality; 9.1. Introduction; 9.2. Guiding Idea; 9.3. A Simple Identity; 9.4. Quadratic Functional: Scalar Case; 9.5. min u J = max v H; 9.6. The Functional l t o [u'2 + g(u)] dt; 9.7. Geometric Aspects; 9.8. Multidimensional Case; 9.9. The Rayleigh-Ritz Method; 9.10. Alternative Approach; 9.11. J(u) = lto [u'2 + f(t)u2] dt; General f(t); 9.12. Geometric Aspects; Miscellaneous Exercises; Bibliography and Comments , Chapter 10. Caplygin's Method and Differential Inequalities10.1. Introduction; 10.2. The Caplygin Method; 10.3. The Equation u' 〈 a(t)u + f (t); 10.4. The Linear Differential Inequality L(u) 〈 f ( t ); 10.5. Elementary Approach; 10.6. An Integral Identity; 10.7. Strengthening of Previous Result; 10.8. Factorization of the Operator; 10.9. Alternate Proof of Monotonicity; 10.10. A Further Condition; 10.11. Two-point Boundary Conditions; 10.12. Variational Approach; 10.13. A Related Parabolic Partial Differential Equation; 10.14. Nonnegativity of u(t, s); 10.15. Limiting Behavior , 10.16. Limiting Behavior: Energy Inequalities10.17. Monotonicity of Maximum; 10.18. Lyapunov Functions; 10.19. Factorization of the nth-order Linear Operator; 10.20. A Result for the nth-order Linear Differential Equation; 10.21. An Example; 10.22. Linear Systems; 10.23. Partial Differential Equation-I; 10.24. Partial Differential Equation-II; Miscellaneous Exercises; Bibliography and Comments; Chapter 11. Quasilinearization; 11.1. Introduction; 11.2. The Riccati Equation; 11.3. Explicit Representation; 11.4. Successive Approximations and Monotone Convergence , 11.5. Maximum Interval of Convergence11.6. Dini's Theorem and Uniform Convergence; 1 1.7. Newton-Raphson-Kantorovich Approximation; 11.8. Quadratic Convergence; 11.9. Upper Bounds; 11.10. u' = g(u, t ); 11.11. Random Equation; 11.12. Upper and Lower Bounds; 1 I. 13. Asymptotic Behavior; 11.14. Multidimensional Riccati Equation; 11.15. Two-point Boundary Value Problems; 11.16. Maximum Interval of Convergence; 11.1 7. Quadratic Convergence; 11.18. Discussion; 11.19. Computational Feasibility; 11.20. Elliptic Equations; 11.21. Parabolic Equations; 1 1.22. Minimum and Maximum Principles , Miscellaneous ExercisesBibliography and Comments; Chapter 12. Dynamic Programming; 12.1. Introduction; 12.2. Multistage Processes; 12.3. Continuous Version; 12.4. Multistage Decision Processes; 12.5. Stochastic and Adaptive Processes; 12.6. Functional Equations; 12.7. Infinite Stage Process; 12.8. Policy; 12.9. Approximation in Policy Space; 12.10. Discussion; 12.11. Calculus of Variations as a Multistage Decision Process; 12.12. A New Formalism; 12.13. The Principle of Optimality; 12.14. Quadratic Case; 12.15. Multidimensional Case; 12.1 6. Computational Feasibility; 12.17. Stability , 12.18. Computational Feasibility: General Case-I , English

Additional Edition: ISBN 0-12-084902-X

Language: English

UID:

Format: 1 online resource (246 p.)

ISBN: 1-84569-355-8

Series Statement: Woodhead Publishing Series in Welding and Other Joining Technologies

Content: Computational welding mechanics (CWM) provides an important technique for modelling welding processes. Welding simulations are a key tool in improving the design and control of welding processes and the performance of welded components or structures. CWM can be used to model phenomena such as heat generation, thermal stresses and large plastic deformations of components or structures. It also has a wider application in modelling thermomechanical and microstructural phenomena in metals. This important book reviews the principles, methods and applications of CWM.The book begins by discus

Note: Description based upon print version of record. , Cover; Computational welding mechanics: Thermomechanical and microstructural simulations; Copyright; Contents; Foreword; Preface; CWM_Lab software; 1 Introduction; 1.1 Computational welding mechanics; 1.2 Contents of the book; 1.3 The competent company; 1.4 Driving forces for increased use of welding simulations; 2 The multi-physics of welding; 3 Couplings and reference frames; 3.1 Coupled systems and solution procedures; 3.2 Linearised coupled thermoelasticity; 3.3 Decoupling of the subdomains of welding simulations; 4 Thermomechanics of welding , 4.1 The thermal cycle and microstructure evolution4.2 The Satoh test; 4.3 Welding of plate; 4.4 Welding of pipe; 5 Nonlinear heat flow; 5.1 Basic equations of nonlinear heat conduction; 5.2 Finite element formulation of nonlinear heat conduction; 6 Nonlinear deformation; 6.1 Basic choices in formulation of nonlinear deformation; 6.2 Finite element formulation of nonlinear deformation; 6.3 Constitutive model; 6.4 Stress updating algorithm for deviatoric plasticity; 7 Numerical methods and modelling for efficient simulations; 7.1 Element technologies; 7.2 Meshing , 7.3 Dynamic and adaptive meshing7.4 Substructuring; 7.5 Parallel computing; 7.6 Dimensional reduction; 7.7 Weld pass reduction; 7.8 Replacement of weld by simplified loads; 8 Calibration and validation strategy; 8.1 Definitions of concepts used; 8.2 Code verification; 8.3 Model refinement and qualification; 8.4 General approach for validation; 8.5 Calibration and validation strategy; 8.6 Validation using subsystems and complete systems; 9 Modelling options in computational welding mechanics (CWM); 9.1 A note about computability in CWM; 9.2 The importance of material modelling , 9.3 Effect of temperature and microstructure9.4 Density; 9.5 Thermal properties; 9.6 Elastic properties; 9.7 Plastic properties and models; 9.8 Thermomechanical properties; 9.9 Microstructure evolution; 9.10 Material modelling in the weld pool; 9.11 Surface properties; 9.12 Heat input models; 9.13 Geometric models; 10 Modelling strategy; 10.1 Accuracy and weld flexibility categories for CWM models; 10.2 Characteristics of different accuracy categories; 10.3 Motivation for proposed modelling strategy; 11 Robustness and stability; 11.1 Definitions concerned with robustness and stability , 11.2 Perturbation methods for investigation of robustness11.3 Methods for analysis of stability; 11.4 Application of robustness and stability analysis in CWM; 12 The current state of computational welding mechanics (CWM); 12.1 Heat input models; 12.2 Material models; 12.3 Models for fatigue and cracking; 12.4 Computational efficiency; 12.5 Simplified methods; 12.6 Reducing risk for buckling, deformations or residual stresses; 12.7 Improved life; 12.8 Repair welding; 12.9 Optimisation; 12.10 Simulation of welding and other manufacturing steps , 13 The Volvo Aero story in computational welding mechanics (CWM) , English

Additional Edition: ISBN 1-84569-221-7

Language: English

UID:

Format: 1 online resource (329 p.)

Edition: 2nd ed.

ISBN: 1-283-31107-0 , 9786613311078 , 1-4377-3529-0

Series Statement: PDL handbook series

Content: Stretch blow molding is the blow molding process used to produce bottles of the strength required for carbonated drinks. In this handbook, Ottmar Brandau introduces the technology of stretch blow molding, explores practical aspects of designing and running a production line and looks at practical issues for quality control and troubleshooting. As an experienced engineer, manager and consultant, Brandau's focus is on optimizing the production process, improving quality and reducing cycle time. This book is a thoroughly practical handbook that provides engineers and managers with the

Note: Includes index. , Previous edition: Stretch blow moulding : a hands-on guide. 2003. , Front Cover; Series Page; Stretch Blow Molding; Copyright; Contents; Preface; Acknowledgments; Introduction; Chapter 1 - A Short History of Stretch Blow Molding; Chapter 2 - Material Basics; 2.1 Manufacture and States of PET; 2.2 Crystallization of PET; 2.3 Drying of PET; 2.4 Behavior in the Injection Mold; 2.5 Behavior in the Blow Mold; 2.6 Acetaldehyde (AA) in PET Bottles; Chapter 3 - Reheat Stretch Blow Molding Machines; 3.1 Overview; 3.2 Semi-automatic Machines; 3.3 Linear Shuttle-type Machines; 3.4 Linear Continuous Motion Machines; 3.5 Rotary Machines; Chapter 4 - Machine Details , 4.1 Ovens4.2 T?ransfer Functions; 4.3 Blow Wheel/Blow Clamp; Chapter 5 - Blow Molds; 5.1 Design; 5.2 Making a Mold; 5.3 Venting; Chapter 6 - Fundamentals of the Blow Process; 6.1 Process Overview; 6.2 Stretch Ratios; 6.3 Types of Heat Transfer; 6.4 Light Absorption Characteristics of PET; 6.5 Optimum Preform Temperature; Chapter 7 - The Blowing Process; 7.1 Reheating Preforms; 7.2 Blowing Bottles; Chapter 8 - Injection Stretch Blow Molding Machines; 8.1 Four-station Machines; 8.2 Machine Controls; 8.3 Injection Controls; 8.4 Interaction between Injection and Blow; 8.5 Conditioning , 8.6 Container Blowing8.7 Hot Runners; 8.8 Integrated Two-stage Stretch Blow Molding; Chapter 9 - Special Applications; 9.1 Simulation of the Blow Process; 9.2 Stretch Blow Molding of Oriented Polypropylene; 9.3 Plant-based Plastics; 9.4 Blow Process for Hot-fill Applications; 9.5 Preferential Heating; 9.6 Direct Feeding of Preforms into the Blow Machine; 9.7 Vision Inspection; 9.8 Barrier-enhancing Technologies; 9.9 Blow-and-Trim Process; 9.10 CSD Bottle-base Failures; 9.11 Recycling of PET Bottles; 9.12 Preform Esthetics in the Two-stage Process , Chapter 10 - Troubleshooting of Blowing Problems10.1 General Guidelines; 10.2 Starting a New Process; 10.3 Troubleshooting of Specific Problems; 10.4 Defects Particular to Single-stage Molding; 10.5 Summary of Preform Quality Checks; Chapter 11 - Economics; 11.1 Container Types; 11.2 Business Models; 11.3 Tooling Costs; 11.4 Light-weighing of Bottles and Caps; 11.5 Resin Prices; 11.6 Bottle Production Costs; 11.7 Starting with a New Product; 11.8 Recommended Laboratory Equipment for RSBM Plants; 11.9 Western vs. Asian Machinery; Chapter 12 - Preform Design for Single and Two-stage Processing , 12.1 Two-stage Process Injection Molding12.2 Single-stage Process Injection Molding; 12.3 Goals and Conditions; 12.4 The Mechanics of Preform Design; 12.5 Putting it All T?ogether; Chapter 13 - Auxiliary Equipment; 13.1 Compressors; 13.2 Chillers; 13.3 Conveyors and Bottle Storage Devices; Chapter 14 Training of Operators; 14.1 Current State of Training; 14.2 Obstacles to Training Programs; 14.3 Re-thinking Abstract Concepts; 14.4 Language Structure; 14.5 Converting Formulas into Common English Sentences; 14.6 Substituting Uncommon Arithmetical Operators; 14.7 Presentation Style , 14.8 Translating Graphs into Common-day Language , English

Additional Edition: ISBN 1-4377-3527-4

Language: English

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Format: 1 online resource (571 p.)

Edition: 1st ed.

ISBN: 1-281-14518-1 , 9786611145187 , 0-08-054928-4

Content: Industries that use pumps, seals and pipes will also use valves and actuators in their systems. This key reference provides anyone who designs, uses, specifies or maintains valves and valve systems with all of the critical design, specification, performance and operational information they need for the job in hand. Brian Nesbitt is a well-known consultant with a considerable publishing record. A lifetime of experience backs up the huge amount of practical detail in this volume.* Valves and actuators are widely used across industry and this dedicated reference provides all the informati

Note: Published by Elsevier in association with Roles & Associates Ltd. , Front Cover; VALVES MANUAL International: Handbook of Valves and Actuators; Copyright Page; Contents; Chapter 1. Definitions and abbreviations; Chapter 2. Properties of fluids; 2.1 Explanation of terms; 2.2 Water; 2.3 Oils; 2.4 Liquid-solid mixtures; 2.5 Liquid-gas mixtures; 2.6 Gas laws and gas properties; 2.7 Useful references; Chapter 3. Isolating valves; 3.1 Isolating valves and the system; 3.2 Isolating valve design; 3.3 Isolating valve types; 3.4 Useful references; Chapter 4. Non-return valves; 4.1 Non-return valves and the system; 4.2 Non-return valve design; 4.3 Non-return valve types , 4.4 Useful referencesChapter 5. Regulators; 5.1 Regulators and the system; 5.2 Regulator design; 5.3 Regulator types; 5.4 Useful references; Chapter 6. Control valves; 6.1 Process control valves and the system; 6.2 Control valve design; 6.3 Process control valve types; 6.4 Useful references; Chapter 7. Safety relief valves; 7.1 Safety relief valves and the system; 7.2 Safety relief valve design; 7.3 Safety relief valve types; 7.4 Piping reactions; 7.5 Useful references; Chapter 8. Valve and piping sizing; 8.1 Sizing isolating valves; 8.2 Sizing non-return valves , 8.3 Sizing safety relief valves8.4 Sizing regulators and control valves; 8.6 Useful references; Chapter 9. Piping and connectors; 9.1 Pipework design principles; 9.2 Rigid piping systems; 9.3 Flexible piping systems; 9.4 Expansion joints; 9.5 Threaded connections; 9.6 Welded connections; 9.7 Soldered connections; 9.8 Cemented connections; 9.9 Flanges; 9.10 Gaskets; 9.11 Clamped connections; 9.12 Grooved connections; 9.13 Compression fittings; 9.14 Flared fittings; 9.15 Quick release couplings; 9.16 Approved connections; 9.17 Useful references; Chapter 10. Noise in valves , 10.1 The noise problem10.2 Noise analysis; 10.3 Sources of valve noise; 10.4 Noise prediction; 10.5 Noise attenuation; 10.6 Noise calculations; 10.7 Useful references; Chapter 11. Valve stem sealing; 11.1 Introduction; 11.2 Single seals; 11.3 Double seals; 11.4 Special designs; 11.5 Seal materials; 11.6 Lubrication; 11.7 Packing friction; 11.8 Packing box assembly; 11.9 Useful references; Chapter 12. Actuators; 12.1 Introduction; 12.2 Control signals; 12.3 Types of actuator; 12.4 Accessories; 12.5 Force/torque required in valve operation; 12.6 Setting-up; 12.7 Actuator selection , 12.8 Useful referencesChapter 13. Valve materials; 13.1 General; 13.2 The Pressure Equipment Directive (PED); 13.3 NACE; 13.4 Valve body material; 13.5 Trim materials; 13.6 Hard facing materials; 13.7 Pressure/temperature ratings for flanges; 13.8 Non-metallic coatings; 13.9 Bolting materials; 13.10 Useful references; Chapter 14. Instrumentation and ancillaries; 14.1 Instrumentation; 14.2 Ancillary equipment; 14.3 Useful references; Chapter 15. Quality, inspection and testing; 15.1 Introduction; 15.2 Mass-produced valves; 15.3 Custom-built valves; 15.4 Guidelines for testing and documentation , 15.5 Standards , English

Additional Edition: ISBN 1-4933-0388-0

Additional Edition: ISBN 1-85617-494-8

Language: English

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Format: X, 253 p. 2 illus. , online resource.

ISBN: 9783642557293

Series Statement: Universitext,

Content: The first fifteen chapters of these lectures (omitting four to six chapters each year) cover a one term course taken by a mixed group of senior undergraduate and junior graduate students specializing either in mathematics or physics. Typically, the mathematics students have some background in advanced anal­ ysis, while the physics students have had introductory quantum mechanics. To satisfy such a disparate audience, we decided to select material which is interesting from the viewpoint of modern theoretical physics, and which illustrates an interplay of ideas from various fields of mathematics such as operator theory, probability, differential equations, and differential geometry. Given our time constraint, we have often pursued mathematical content at the expense of rigor. However, wherever we have sacrificed the latter, we have tried to explain whether the result is an established fact, or, mathematically speaking, a conjecture, and in the former case, how a given argument can be made rigorous. The present book retains these features.

Note: 1 Physical Background -- 1.1 The Double-Slit Experiment -- 1.2 Wave Functions -- 1.3 State Space -- 1.4 The Schrödinger Equation -- 1.5 Mathematical Supplement: Operators on Hilbert Spaces -- 2 Dynamics -- 2.1 Conservation of Probability -- 2.2 Existence of Dynamics -- 2.3 The Free Propagator -- 2.4 Mathematical Supplement: Operator Adjoints -- 2.5 Mathematical Supplement: the Fourier Transform -- 3 Observables -- 3.1 Mean Values and the Momentum Operator -- 3.2 Observables -- 3.3 The Heisenberg Representation -- 3.4 Quantization -- 3.5 Pseudodifferential Operators -- 4 The Uncertainty Principle -- 4.1 The Heisenberg Uncertainty Principle -- 4.2 A Refined Uncertainty Principle -- 4.3 Application: Stability of Hydrogen -- 5 Spectral Theory -- 5.1 The Spectrum of an Operator -- 5.2 Functions of Operators and the Spectral Mapping Theorem -- 5.3 Applications to Schrödinger Operators -- 5.4 Spectrum and Evolution -- 5.5 Variational Characterization of Eigenvalues -- 5.6 Number of Bound States -- 5.7 Mathematical Supplement: Integral Operators -- 6 Scattering States -- 6.1 Short-range Interactions: µ 〉 1 -- 6.2 Long-range Interactions: µ ? 1 -- 6.3 Existence of Wave Operators -- 7 Special Cases -- 7.1 The Infinite Well -- 7.2 The Torus -- 7.3 A Potential Step -- 7.4 The Square Well -- 7.5 The Harmonic Oscillator -- 7.6 A Particle on a Sphere -- 7.7 The Hydrogen Atom -- 7.8 A Particle in an External EM Field -- 8 Many-particle Systems -- 8.1 Quantization of a Many-particle System -- 8.2 Separation of the Centre-of-mass Motion -- 8.3 Break-ups -- 8.4 The HVZ Theorem -- 8.5 Intra- vs. Inter-cluster Motion -- 8.6 Existence of Bound States for Atoms and Molecules -- 8.7 Scattering States -- 8.8 Mathematical Supplement: Tensor Products -- 9 Density Matrices -- 9.1 Introduction -- 9.2 States and Dynamics -- 9.3 Open Systems -- 9.4 The Thermodynamic Limit -- 9.5 Equilibrium States -- 9.6 The T ? 0 Limit -- 9.7 Example: a System of Harmonic Oscillators -- 9.8 A Particle Coupled to a Reservoir -- 9.9 Quantum Systems -- 9.10 Problems -- 9.11 Hilbert Space Approach -- 9.12 Appendix: the Ideal Bose Gas -- 9.13 Appendix: Bose-Einst ein Condensation -- 9.14 Mathematical Supplement: the Trace, and Trace Class Operators -- 10 The Feynman Path Integral -- 10.1 The Feynman Path Integral -- 10.2 Generalizations of the Path Integral -- 10.3 Mathematical Supplement: the Trotter Product Formula -- 11 Quasi-classical Analysis -- 11.1 Quasi-classical Asymptotics of the Propagator -- 11.2 Quasi-classical Asymptotics of Green’s Function -- 11.3 Bohr-Sommerfeld Semi-classical Quantization -- 11.4 Quasi-classical Asymptotics for the Ground State Energy -- 11.5 Mathematical Supplement: Operator Determinants -- 12 Mathematical Supplement: the Calculus of Variations -- 12.1 Functionals -- 12.2 The First Variation and Critical Points -- 12.3 Constrain ed Variational Problems -- 12.4 The Second Variation -- 12.5 Conjugate Points and Jacobi Fields -- 12.6 The Action of the Critical Path -- 12.7 Appendix: Connection to Geodesics -- 13 Resonances -- 13.1 Tunneling and Resonances -- 13.2 The Free Resonance Energy -- 13.3 Instantons -- 13.4 Positive Temperatures -- 13.5 Pre-exponential Factor for the Bounce -- 13.6 Contribution of the Zero-mode -- 13.7 Bohr-Sommerfeld Quantization for Resonances -- 14 Introduction to Quantum Field Theory -- 14.1 The Place of QFT -- 14.2 Klein-Gordon Theory as a Hamiltonian System -- 14.3 Maxwell’s Equations as a Hamiltonian System -- 14.4 Quantization of the Klein-Gordon and Maxwell Equations -- 14.5 Fock Space -- 14.6 Generalized Free Theory -- 14.7 Interactions -- 14.8 Quadratic Approximation -- 15 Quantum Electrodynamics of Non-relativistic Particles: the Theory of Radiation -- 15.1 The Hamiltonian -- 15.2 Perturbation Set-up -- 15.3 Results -- 15.4 Mathematical Supplements -- 16 Supplement: Renormalization Group -- 16.1 The Decimation Map -- 16.2 Relative Bounds -- 16.3 Elimination of Particle and High Photon Energy Degrees of Freedom -- 16.4 Generalized Normal Form of Operators on Fock Space -- 16.5 The Hamiltonian H0(?, z) -- 16.6 A Banach Space of Operators -- 16.7 Rescaling -- 16.8 The Renormalization Map -- 16.9 Linearized Flow -- 16.10 Central-stable Manifold for RG and Spectra of Hamiltonians -- 16.11 Appendix -- 17 Comments on Missing Topics, Literature, and Further Reading -- References.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9783540441601

Language: English

Keywords: Lehrbuch

DOI: 10.1007/978-3-642-55729-3

URL: http://dx.doi.org/10.1007/978-3-642-55729-3

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Format: XIII, 149 p. , online resource.

ISBN: 9781461220640

Content: This is a problem book on Hilbert space operators (Le. , on bounded linear transformations of a Hilbert space into itself) where theory and problems are investigated together. We tre!l:t only a part of the so-called single operator theory. Selected prob­ lems, ranging from standard textbook material to points on the boundary of the subject, are organized into twelve chapters. The book begins with elementary aspects of Invariant Subspaces for operators on Banach spaces 1. Basic properties of Hilbert Space Operators are introduced in in Chapter Chapter 2, Convergence and Stability are considered in Chapter 3, and Re­ ducing Subspaces is the theme of Chapter 4. Primary results about Shifts on Hilbert space comprise Chapter 5. These are introductory chapters where the majority of the problems consist of auxiliary results that prepare the ground for the next chapters. Chapter 6 deals with Decompositions for Hilbert space contractions, Chapter 7 focuses on Hyponormal Operators, and Chapter 8 is concerned with Spectral Properties of operators on Banach and Hilbert spaces. The next three chapters (as well as Chapter 6) carry their subjects from an introductory level to a more advanced one, including some recent results. Chapter 9 is about Paranormal Operators, Chapter 10 covers Proper Contractions, and Chapter 11 searches through Quasi­ reducible Operators. The final Chapter 12 commemorates three decades of The Lomonosov Theorem on nontrivial hyperinvariant subspaces for compact operators.

Note: 1 Invariant Subspaces -- Problem 1.1 Closure -- Problem 1.2 Kernel and Range -- Problem 1.3 Null Product -- Problem 1.4 Operator Equation -- Problem 1.5 Nilpotent and Algebraic -- Problem 1.6 Polynomials -- Problem 1.7 Totally Cyclic -- Problem 1.8 Densely Intertwined -- Problem 1.9 Hyperinvariant -- Problem 1.10 Quasiaffine Transform -- Solutions -- 2 Hilbert Space Operators -- Problem 2.1 Adjoint -- Problem 2.2 Nonnegative -- Problem 2.3 Contraction -- Problem 2.4 Normal -- Problem 2.5 Isometry -- Problem 2.6 Unitary -- Problem 2.7 Projection -- Problem 2.8 Mutually Orthogonal -- Problem 2.9 Increasing -- Solutions -- 3 Convergence and Stability -- Problem 3.1 Diagonal -- Problem 3.2 Product -- Problem 3.3 * -Preserving -- Problem 3.4 Nonnegative -- Problem 3.5 Monotone -- Problem 3.6 Self-Adjoint -- Problem 3.7 Commutant -- Problem 3.8 Convex Cone -- Problem 3.9 Absolute Value -- Solutions -- 4 Reducing Subspaces -- Problem 4.1 T-Invariant -- Problem 4.2 Matrix Form -- Problem 4.3 T*-Invariant -- Problem 4.4 T and T*-Invariant -- Problem 4.5 Commuting with T and T* -- Problem 4.6 Reducible -- Problem 4.7 Restriction -- Problem 4.8 Direct Sum -- Problem 4.9 Unitarily Equivalent -- Problem 4.10 Unitary Restriction -- Solutions -- 5 Shifts -- Problem 5.1 Unilateral -- Problem 5.2 Bilateral -- Problem 5.3 Multiplicity -- Problem 5.4 Unitarily Equivalent -- Problem 5.5 Reducible -- Problem 5.6 Irreducible -- Problem 5.7 Rotation -- Problem 5.8 Riemann-Lebesgue Lemma -- Problem 5.9 Weighted Shift -- Problem 5.10 Nonnegative Weights -- Solutions -- 6 Decompositions -- Problem 6.1 Strong Limit -- Problem 6.2 Projection -- Problem 6.3 Kernels -- Problem 6.4 Kernel Decomposition -- Problem 6.5 Intertwined to Isometry -- Problem 6.6 Dual Limits -- Problem 6.7 Nagy-Foia?-Langer Decomposition -- Problem 6.8 von Neumann-Wold Decomposition -- Problem 6.9 Another Decomposition -- Problem 6.10 Foguel Decomposition -- Problem 6.11 Isometry -- Problem 6.12 Coisometry -- Problem 6.13 Strongly Stable -- Problem 6.14 Property PF -- Problem 6.15 Direct Summand -- Solutions -- 7 Hyponormal Operators -- Problem 7.1 Quasinormal -- Problem 7.2 Strong Stability -- Problem 7.3 Hyponormal -- Problem 7.4 Direct Proof -- Problem 7.5 Invariant Subspace -- Problem 7.6 Restriction -- Problem 7.7 Normal -- Problem 7.8 Roots of Powers -- Problem 7.9 Normaloid -- Problem 7.10 Power Inequality -- Problem 7.11 Unitarily Equivalent -- Problem 7.12 Subnormal -- Problem 7.13 Not Subnormal -- Problem 7.14 Distinct Weights -- Solutions -- 8 Spectral Properties -- Problem 8.1 Spectrum -- Problem 8.2 Eigenspace -- Problem 8.3 Examples -- Problem 8.4 Residual Spectrum -- Problem 8.5 Weighted Shift -- Problem 8.6 Uniform Stability -- Problem 8.7 Finite Rank -- Problem 8.8 Stability for Compact -- Problem 8.9 Continuous Spectrum -- Problem 8.10 Compact Contraction -- Problem 8.11 Normal -- Problem 8.12 Square Root -- Problem 8.13 Fuglede Theorem -- Problem 8.14 Quasinormal -- Problem 8.15 Fuglede-Putnam Theorem -- Problem 8.16 Reducible -- Solutions -- 9 Paranormal Operators -- Problem 9.1 Quasihyponormal -- Problem 9.2 Semi-quasihyponormal -- Problem 9.3 Paranormal -- Problem 9.4 Square of Paranormal -- Problem 9.5 Alternative Definition -- Problem 9.6 Unitarily Equivalent -- Problem 9.7 Weighted Shift -- Problem 9.8 Equivalences -- Problem 9.9 Not Paranormal -- Problem 9.10 Projection ? Nilpotent -- Problem 9.11 Shifted Operators -- Problem 9.12 Shifted Projections -- Problem 9.13 Shifted Seif-Adjoints -- Problem 9.14 Examples -- Problem 9.15 Hyponormal -- Problem 9.16 Invertible -- Problem 9.17 Paranormal Inequality -- Problem 9.18 Normaloid -- Problem 9.19 Cohyponormal -- Problem 9.20 Strongly Stable -- Problem 9.21 Quasinormal -- Solutions -- 10 Proper Contractions -- Problem 10.1 Equivalences -- Problem 10.2 Diagonal -- Problem 10.3 Compact -- Problem 10.4 Adjoint -- Problem 10.5 Paranormal -- Problem 10.6 Nagy-Foia? Classes -- Problem 10.7 Weakly Stable -- Problem 10.8 Hyponormal -- Problem 10.9 Subnormal -- Problem 10.10 Quasinormal -- Problem 10.11 Direct Proof -- Problem 10.12 Invariant Subspace -- Solutions -- 11 Quasireducible Operators -- Problem 11.1 Alternative Definition -- Problem 11.2 Basic Properties -- Problem 11.3 Nilpotent -- Problem 11.4 Index 2 -- Problem 11.5 Higher Indices -- Problem 11.6 Product -- Problem 11.7 Unitarily Equivalent -- Problem 11.8 Similarity -- Problem 11.9 Unilateral Shift -- Problem 11.10 Isometry -- Problem 11.11 Quasinormal -- Problem 11.12 Weighted Shift -- Problem 11.13 Subnormal -- Problem 11.14 Commutator -- Problem 11.15 Reducible -- Problem 11.16 Normal -- Solutions -- 12 The Lomonosov Theorem -- Problem 12.1 Hilden’s Proof -- Problem 12.2 Lomonosov Lemma -- Problem 12.3 Lomonosov Theorem -- Problem 12.4 Extension -- Problem 12.5 Quasireducible -- Problem 12.6 Hyponormal -- Solutions -- References.

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Additional Edition: Printed edition: ISBN 9780817632427

Language: English

DOI: 10.1007/978-1-4612-2064-0

URL: http://dx.doi.org/10.1007/978-1-4612-2064-0

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Format: XII, 209 p. , online resource.

ISBN: 9781461301257

Series Statement: Springer Series in Statistics,

Content: Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This text explores a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric. It is the first book on this topic. The text is intended for first-year graduate students in statistics and learning theory, and offers a host of opportunities for further research and thesis topics. Each chapter corresponds roughly to one lecture, and is supplemented with many classroom exercises. A one year course in probability theory at the level of Feller's Volume 1 should be more than adequate preparation. Gabor Lugosi is Professor at Universitat Pompeu Fabra in Barcelona, and Luc Debroye is Professor at McGill University in Montreal. In 1996, the authors, together with Lászlo Györfi, published the successful text, A Probabilistic Theory of Pattern Recognition with Springer-Verlag. Both authors have made many contributions in the area of nonparametric estimation.

Note: 1. Introduction -- §1.1. References -- 2. Concentration Inequalities -- §2.1. Hoeffding’s Inequality -- §2.2. An Inequality for the Expected Maximal Deviation -- §2.3. The Bounded Difference Inequality -- §2.4. Examples -- §2.5. Bibliographic Remarks -- §2.6. Exercises -- §2.7. References -- 3. Uniform Deviation Inequalities -- §3.1. The Vapnik-Chervonenkis Inequality -- §3.2. Covering Numbers and Chaining -- §3.3. Example: The Dvoretzky-Kiefer-Wolfowitz Theorem -- §3.4. Bibliographic Remarks -- §3.5. Exercises -- §3.6. References -- 4. Combinatorial Tools -- §4.1. Shatter Coefficients -- §4.2. Vapnik-Chervonenkis Dimension and Shatter Coefficients -- §4.3. Vapnik-Chervonenkis Dimension and Covering Numbers -- §4.4. Examples -- §4.5. Bibliographic Remarks -- §4.6. Exercises -- §4.7. References -- 5. Total Variation -- §5.1. Density Estimation -- §5.2. The Total Variation -- §5.3. Invariance -- §5.4. Mappings -- §5.5. Convolutions -- §5.6. Normalization -- §5.7. The Lebesgue Density Theorem -- §5.8. LeCam’s Inequality -- §5.9. Bibliographic Remarks -- §5.10. Exercises -- §5.11. References -- 6. Choosing a Density Estimate -- §6.1. Choosing Between Two Densities -- §6.2. Examples -- §6.3. Is the Factor of Three Necessary? -- §6.4. Maximum Likelihood Does not Work -- §6.5. L2 Distances Are To Be Avoided -- §6.6. Selection from k Densities -- §6.7. Examples Continued -- §6.8. Selection from an Infinite Class -- §6.9. Bibliographic Remarks -- §6.10. Exercises -- §6.11. References -- 7. Skeleton Estimates -- §7.1. Kolmogorov Entropy -- §7.2. Skeleton Estimates -- §7.3. Robustness -- §7.4. Finite Mixtures -- §7.5. Monotone Densities on the Hypercube -- §7.6. How To Make Gigantic Totally Bounded Classes -- §7.7. Bibliographic Remarks -- §7.8. Exercises -- §7.9. References -- 8. The Minimum Distance Estimate: Examples -- §8.1. Problem Formulation -- §8.2. Series Estimates -- §8.3. Parametric Estimates: Exponential Families -- §8.4. Neural Network Estimates -- §8.5. Mixture Classes, Radial Basis Function Networks -- §8.6. Bibliographic Remarks -- §8.7. Exercises -- §8.8. References -- 9. The Kernel Density Estimate -- §9.1. Approximating Functions by Convolutions -- §9.2. Definition of the Kernel Estimate -- §9.3. Consistency of the Kernel Estimate -- §9.4. Concentration -- §9.5. Choosing the Bandwidth -- §9.6. Choosing the Kernel -- §9.7. Rates of Convergence -- §9.8. Uniform Rate of Convergence -- §9.9. Shrinkage, and the Combination of Density Estimates -- §9.10. Bibliographic Remarks -- §9.11. Exercises -- §9.12. References -- 10. Additive Estimates and Data Splitting -- §10.1. Data Splitting -- §10.2. Additive Estimates -- §10.3. Histogram Estimates -- §10A. Bibliographic Remarks -- §10.5. Exercises -- §10.6. References -- 11. Bandwidth Selection for Kernel Estimates -- §11.1. The Kernel Estimate with Riemann Kernel -- §11.2. General Kernels, Kernel Complexity -- §11.3. Kernel Complexity: Univariate Examples -- §11.4. Kernel Complexity: Multivariate Kernels -- §11.5. Asymptotic Optimality -- §11.6. Bibliographic Remarks -- §11.7. Exercises -- §11.8. References -- 12. Multiparameter Kernel Estimates -- §12.1. Multivariate Kernel Estimates—Product Kernels -- §12.2. Multivariate Kernel Estimates—Ellipsoidal Kernels -- §12.3. Variable Kernel Estimates -- §12.4. Tree-Structured Partitions -- §12.5. Changepoints and Bump Hunting -- §12.6. Bibliographic Remarks -- §12.7. Exercises -- §12.8. References -- 13. Wavelet Estimates -- §13.1. Definitions -- §13.2. Smoothing -- §13.3. Thresholding -- §13.4. Soft Thresholding -- §13.5. Bibliographic Remarks -- §13.6. Exercises -- §13.7. References -- 14. The Transformed Kernel Estimate -- §14.1. The Transformed Kernel Estimate -- §14.2. Box-Cox Transformations -- §14.3. Piecewise Linear Transformations -- §14.4. Bibliographic Remarks -- §14.5. Exercises -- §14.6. References -- 15. Minimax Theory -- §15.1. Estimating a Density from One Data Point -- §15.2. The General Minimax Problem -- §15.3. Rich Classes -- §15.4. Assouad’s Lemma -- §15.5. Example: The Class of Convex Densities -- §15.6. Additional Examples -- §15.7. Tuning the Parameters of Variable Kernel Estimates -- §15.8. Sufficient Statistics -- §15.9. Bibliographic Remarks -- §15.10. Exercises -- §15.11. References -- 16. Choosing the Kernel Order -- §16.1. Introduction -- §16.2. Standard Kernel Estimate: Riemann Kernels -- §16.3. Standard Kernel Estimates: General Kernels -- §16.4. An Infinite Family of Kernels -- §16.5. Bibliographic Remarks -- §16.6. Exercises -- §16.7. References -- 17. Bandwidth Choice with Superkernels -- §17.1. Superkernels -- §17.2. The Trapezoidal Kernel -- §17.3. Bandwidth Selection -- §17.4. Bibliographic Remarks -- §17.5. Exercises -- §17.6. References -- Author Index.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9781461265276

Language: English

DOI: 10.1007/978-1-4613-0125-7

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Format: 1 online resource (xxx, 650 p. ) , ill.

ISBN: 1-281-79351-5 , 9786611793517 , 0-08-086794-4

Series Statement: Annals of discrete mathematics Submodular functions and electrical networks

Note: Bibliographic Level Mode of Issuance: Monograph , Front Cover -- Submodular Functions and Electrical Networks -- Copyright Page -- Contents -- Chapter 1. Introduction -- Chapter 2. Mathematical Preliminaries -- 2.1 Sets -- 2.2 Vectors and Matrices -- 2.3 Linear Inequality Systems -- 2.4 Solutions of Exercises -- 2.5 Solutions of Problems -- Chapter 3. Graphs -- 3.1 Introduction -- 3.2 Graphs: Basic Notions -- 3.3 Graphs and Vector Spaces -- 3.4 Basic Operations on Graphs and Vector Spaces -- 3.5 Problems -- 3.6 Graph Algorithms -- 3.7 Duality -- 3.8 Notes -- 3.9 Solutions of Exercises -- 3.10 Solutions of Problems -- Chapter 4. Matroids -- 4.1 Introduction -- 4.2 Axiom Systems for Matroids -- 4.3 Dual of a Matroid -- 4.4 Minors of Matroids -- 4.5 Connectedness in Matroids -- 4.6 Matroids and the Greedy Algorithm -- 4.7 Notes -- 4.8 Solutions of Exercises -- Chapter 5. Electrical Networks -- 5.1 Introduction -- 5.2 In Terms of Multiterminal Devices -- 5.3 In Terms of 2-Terminal Devices -- 5.4 Standard Devices -- 5.5 Common Methods of Analysis -- 5.6 Procedures used in Circuit Simulators -- 5.7 State Equations for Dynamic Networks -- 5.8 Multiports in Electrical Networks -- 5.9 Some Elementary Results of Network Theory -- 5.10 Notes -- 5.11 Solutions of Exercises -- Chapter 6. Topological Hybrid Analysis -- 6.1 Introduction -- 6.2 Electrical Network: A Formal Description -- 6.3 Some Basic Topological Results -- 6.4 A Theorem on Topological Hybrid Analysis -- 6.5 Structure of Constraints and Optimization -- 6.6 Notes -- 6.7 Solutions of Exercises -- Chapter 7. The Implicit Duality Theorem and Its Applications -- 7.1 The Vector Space Version -- 7.2 *Quasi Orthogonality -- 7.3 Applications of the Implicit Duality Theorem -- 7.4 *Linear Inequality Systems -- 7.5 *Integrality Systems -- 7.6 Problems -- 7.7 Notes -- 7.8 Solutions of Exercises -- 7.9 Solutions of Problems. , Chapter 8. Multiport Decomposition -- 8.1 Introduction -- 8.2 Multiport Decomposition of Vector Spaces -- 8.3 Analysis through Multiport Decomposition -- 8.4 Port Minimization -- 8.5 *Multiport Decomposition for Network Reduction -- 8.6 Problems -- 8.7 Solutions of Exercises -- 8.8 Solutions of Problems -- Chapter 9. Submodular Functions -- 9.1 Introduction -- 9.2 Submodularity -- 9.3 Basic Operations on Semimodular Functions -- 9.4 *Other Operations on Semimodular Functions -- 9.5 Polymatroid and Matroid Rank Functions -- 9.6 Connectedness for Semimodular Functions -- 9.7 *Semimodular Polyhedra -- 9.8 Symmetric Submodular functions -- 9.9 Problems -- 9.10 Notes -- 9.11 Solutions of Exercises -- 9.12 Solutions of Problems -- Chapter 10. Convolution of Submodular Functions -- 10.1 Introduction -- 10.2 Convolution -- 10.3 Matroids, Polymatroids and Convolution -- 10.4 The Principal Partition -- 10.5 *The Refined Partial Order of the Principal Partition -- 10.6 Algorithms for PP -- 10.7 *Aligned Polymatroid Rank Functions -- 10.8 Notes -- 10.9 Solutions of Exercises -- 10.10 Solutions of Problems -- Chapter 11. Matroid Union -- 11.1 Introduction -- 11.2 Submodular Functions induced through a Bipartite Graph -- 11.3 Matroid Union: Algorithm and Structure -- 11.4 PP of the Rank Function of a Matroid -- 11.5 Notes -- 11.6 Solutions of Exercises -- Chapter 12. Dilworth Truncation of Submodular Functions -- 12.1 Introduction -- 12.2 Dilworth Truncation -- 12.3 The Principal Lattice of Partitions -- 12.4 *Approximation Algorithms through PLP for the Min Cost Partition Problem -- 12.5 The PLP of Duals and Truncations -- 12.6 *The Principal Lattice of Partitions associated with Special Fusions -- 12.7 Building Submodular Functions with desired PLP -- 12.8 Notes -- 12.9 Solutions of Exercises -- 12.10 Solutions of Problems. , Chapter 13. Algorithms for the PLP of a Submodular Function -- 13.1 Introduction -- 13.2 Minimizing the Partition Associate of a Submodular function -- 13.3 Construction of the P-sequence of Partitions -- 13.4 Construction of the DTL -- 13.5 Complexity of construction of the PLP -- 13.6 Construction of the PLP of the dual -- 13.7 PLP Algorithms for (wRΓ)(·) and -(wREL)(·) -- 13.8 Structural Changes in Minimizing Partitions -- 13.9 Relation between PP and PLP -- 13.10 Fast Algorithms for Principal Partition of the rank function of a graph -- 13.11 Solutions of Exercises -- Chapter 14. The Hybrid Rank Problem -- 14.1 Introduction -- 14.2 The Hybrid Rank Problem - First Formulation -- 14.3 The Hybrid Rank Problem - Second Formulation -- 14.4 The Hybrid Rank Problem - Third Formulation -- 14.5 The Hybrid Rank Problem - Fourth Formulation -- 14.6 Solutions of Exercises -- Bibliography -- Index. , English

Additional Edition: ISBN 0-444-82523-1

Language: English

Keywords: Electronic books. ; Electronic books.