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  • 1
    UID:
    almafu_BV009110277
    Format: XII, 240 S. : , Illustrationen.
    ISBN: 3-540-94161-4 , 0-387-94161-4
    Content: This book comprises a collection of 125 problems and snapshots from discrete probability. The problems are selected on the basis of their elegance and utility whereas the snapshots are intended to provide a quick overview of topics in probability. These include combinatorics, Poisson approximation, patterns in random sequences, Markov chains, random walks, cover times, and embedding procedures
    Content: A wide range of readers will enjoy this diverse selection of topics. Students will find this a helpful and stimulating companion to their probability courses. The snapshots will leave the students with an expanded knowledge about topics not generally covered by textbooks. Other than a basic exposure to probabilistic ideas, such as might be gained from a first course in probability, it is self-contained
    Content: Consequently, almost all of the problems can be tackled by undergraduate students as well as appeal to those who enjoy the challenge of constructing and solving problems
    Note: Literaturverz. S. 230 - 235
    Language: English
    Subjects: Mathematics
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    Keywords: Wahrscheinlichkeitsrechnung ; Wahrscheinlichkeit ; Beispielsammlung ; Beispielsammlung ; Beispielsammlung
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  • 2
    UID:
    almahu_9947363070002882
    Format: XVI, 240 p. , online resource.
    Edition: Second Edition.
    ISBN: 9781475768046
    Series Statement: Graduate Texts in Mathematics, 203
    Content: I have been very gratified by the response to the first edition, which has resulted in it being sold out. This put some pressure on me to come out with a second edition and now, finally, here it is. The original text has stayed much the same, the major change being in the treatment of the hook formula which is now based on the beautiful Novelli-Pak-Stoyanovskii bijection (NPS 97]. I have also added a chapter on applications of the material from the first edition. This includes Stanley's theory of differential posets (Stn 88, Stn 90] and Fomin's related concept of growths (Fom 86, Fom 94, Fom 95], which extends some of the combinatorics of Sn-representations. Next come a couple of sections showing how groups acting on posets give rise to interesting representations that can be used to prove unimodality results (Stn 82]. Finally, we discuss Stanley's symmetric function analogue of the chromatic polynomial of a graph (Stn 95, Stn ta]. I would like to thank all the people, too numerous to mention, who pointed out typos in the first edition. My computer has been severely reprimanded for making them. Thanks also go to Christian Krattenthaler, Tom Roby, and Richard Stanley, all of whom read portions of the new material and gave me their comments. Finally, I would like to give my heartfelt thanks to my editor at Springer, Ina Lindemann, who has been very supportive and helpful through various difficult times.
    Note: 1 Group Representations -- 2 Representations of the Symmetric Group -- 3 Combinatorial Algorithms -- 4 Symmetric Functions -- 5 Applications and Generalizations.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9781441928696
    Language: English
    Subjects: Mathematics
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  • 3
    UID:
    almahu_9947362941902882
    Format: XXIII, 470 p. , online resource.
    ISBN: 9781468403022
    Series Statement: Graduate Texts in Mathematics, 113
    Content: Two of the most fundamental concepts in the theory of stochastic processes are the Markov property and the martingale property. * This book is written for readers who are acquainted with both of these ideas in the discrete-time setting, and who now wish to explore stochastic processes in their continuous­ time context. It has been our goal to write a systematic and thorough exposi­ tion of this subject, leading in many instances to the frontiers of knowledge. At the same time, we have endeavored to keep the mathematical prerequisites as low as possible, namely, knowledge of measure-theoretic probability and some familiarity with discrete-time processes. The vehicle we have chosen for this task is Brownian motion, which we present as the canonical example of both a Markov process and a martingale. We support this point of view by showing how, by means of stochastic integration and random time change, all continuous-path martingales and a multitude of continuous-path Markov processes can be represented in terms of Brownian motion. This approach forces us to leave aside those processes which do not have continuous paths. Thus, the Poisson process is not a primary object of study, although it is developed in Chapter 1 to be used as a tool when we later study passage times and local time of Brownian motion.
    Note: 1 Martingales, Stopping Times, and Filtrations -- 1.1. Stochastic Processes and ?-Fields -- 1.2. Stopping Times -- 1.3. Continuous-Time Martingales -- 1.4. The Doob-Meyer Decomposition -- 1.5. Continuous, Square-Integrable Martingales -- 1.6. Solutions to Selected Problems -- 1.7. Notes -- 2 Brownian Motion -- 2.1. Introduction -- 2.2. First Construction of Brownian Motion -- 2.3. Second Construction of Brownian Motion -- 2.4. The Space C [0, ?), Weak Convergence, and Wiener Measure -- 2.5. The Markov Property -- 2.6. The Strong Markov Property and the Reflection Principle -- 2.7. Brownian Filtrations -- 2.8. Computations Based on Passage Times -- 2.9. The Brownian Sample Paths -- 2.10. Solutions to Selected Problems -- 2.11. Notes -- 3 Stochastic Integration -- 3.1. Introduction -- 3.2. Construction of the Stochastic Integral -- 3.3. The Change-of-Variable Formula -- 3.4. Representations of Continuous Martingales in Terms of Brownian Motion -- 3.5. The Girsanov Theorem -- 3.6. Local Time and a Generalized Itô Rule for Brownian Motion -- 3.7. Local Time for Continuous Semimartingales -- 3.8. Solutions to Selected Problems -- 3.9. Notes -- 4 Brownian Motion and Partial Differential Equations -- 4.1. Introduction -- 4.2. Harmonic Functions and the Dirichlet Problem -- 4.3. The One-Dimensional Heat Equation -- 4.4. The Formulas of Feynman and Kac -- 4.5. Solutions to selected problems -- 4.6. Notes -- 5 Stochastic Differential Equations -- 5.1. Introduction -- 5.2. Strong Solutions -- 5.3. Weak Solutions -- 5.4. The Martingale Problem of Stroock and Varadhan -- 5.5. A Study of the One-Dimensional Case -- 5.6. Linear Equations -- 5.7. Connections with Partial Differential Equations -- 5.8. Applications to Economics -- 5.9. Solutions to Selected Problems -- 5.10. Notes -- 6 P. Lévy’s Theory of Brownian Local Time -- 6.1. Introduction -- 6.2. Alternate Representations of Brownian Local Time -- 6.3. Two Independent Reflected Brownian Motions -- 6.4. Elastic Brownian Motion -- 6.5. An Application: Transition Probabilities of Brownian Motion with Two-Valued Drift -- 6.6. Solutions to Selected Problems -- 6.7. Notes.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9781468403046
    Language: English
    Subjects: Economics , Mathematics
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  • 4
    Online Resource
    Online Resource
    New York, NY :Springer US :
    UID:
    almahu_9949198276502882
    Format: XIV, 206 p. , online resource.
    Edition: 1st ed. 1997.
    ISBN: 9781461562054
    Series Statement: International Series in Operations Research & Management Science, 7
    Content: 3. 2 The Busy Period 43 3. 3 The M 1M IS System with Last Come, First Served 50 3. 4 Comparison of FCFS and LCFS 51 3. 5 Time-Reversibility of Markov Processes 52 The Output Process 54 3. 6 3. 7 The Multi-Server System in a Series 55 Problems for Solution 3. 8 56 4 ERLANGIAN QUEUEING SYSTEMS 59 4. 1 Introduction 59 4. 2 The System M I E/c/1 60 4. 3 The System E/cl Mil 67 4. 4 The System MIDI1 72 4. 5 Problems for Solution 74 PRIORITY SYSTEMS 79 5 5. 1 Description of a System with Priorities 79 Two Priority Classes with Pre-emptive Resume Discipline 5. 2 82 5. 3 Two Priority Classes with Head-of-Line Discipline 87 5. 4 Summary of Results 91 5. 5 Optimal Assignment of Priorities 91 5. 6 Problems for Solution 93 6 QUEUEING NETWORKS 97 6. 1 Introduction 97 6. 2 A Markovian Network of Queues 98 6. 3 Closed Networks 103 Open Networks: The Product Formula 104 6. 4 6. 5 Jackson Networks 111 6. 6 Examples of Closed Networks; Cyclic Queues 112 6. 7 Examples of Open Networks 114 6. 8 Problems for Solution 118 7 THE SYSTEM M/G/I; PRIORITY SYSTEMS 123 7. 1 Introduction 123 Contents ix 7. 2 The Waiting Time in MIGI1 124 7. 3 The Sojourn Time and the Queue Length 129 7. 4 The Service Interval 132 7.
    Note: 1 Introduction -- 1.1 Description of a Queueing System -- 1.2 The Basic Model GI/G/S -- 1.3 Processes of Interest -- 1.4 The Nature of Congestion -- 1.5 Little's Formula L = ?W -- 1.6 Control of Queueing Systems -- 1.7 Historical Remarks -- 2 Markovian Queueing Systems -- 2.1 Introduction -- 2.2 The System M/M/1 -- 2.3 The System M/M/s -- 2.4 A Design Problem -- 2.5 M/M/s System with Finite Source -- 2.6 The Machine Interference Problem -- 2.7 The System M/M/s with Finite Capacity -- 2.8 Loss Systems -- 2.9 Social Versus Self-Optimization -- 2.10 The System M/M/s with Balking -- 2.11 The System M/M/s with Reneging -- 2.12 Problems for Solution -- 3 The Busy Period, Output and Queues in Series -- 3.1 Introduction -- 3.2 The Busy Period -- 3.3 The M/M/S System with Last Come, First Served -- 3.4 Comparison of FCFS and LCFS -- 3.5 Time-Reversibility of Markov Processes -- 3.6 The Output Process -- 3.7 The Multi-Server System in a Series -- 3.8 Problems for Solution -- 4 Erlangian Queueing Systems -- 4.1 Introduction -- 4.2 The System M/Ek/1 -- 4.3 The System Ek/M/1 -- 4.4 The System M/D/1 -- 4.5 Problems for Solution -- 5 Priority Systems -- 5.1 Description of a System with Priorities -- 5.2 Two Priority Classes with Pre-emptive Resume Discipline -- 5.3 Two Priority Classes with Head-of-Line Discipline -- 5.4 Summary of Results -- 5.5 Optimal Assignment of Priorities -- 5.6 Problems for Solution -- 6 Queueing Networks -- 6.1 Introduction -- 6.2 A Markovian Network of Queues -- 6.3 Closed Networks -- 6.4 Open Networks: The Product Formula -- 6.5 Jackson Networks -- 6.6 Examples of Closed Networks; Cyclic Queues -- 6.7 Examples of Open Networks -- 6.8 Problems for Solution -- 7 The System M/G/1; Priority Systems -- 7.1 Introduction -- 7.2 The Waiting Time in M/G/1 -- 7.3 The Sojourn Time and the Queue Length -- 7.4 The Service Interval -- 7.5 The M/G/1 System with Exceptional Service -- 7.6 The Busy Period in M/G/1 -- 7.7 Completion Times in Priority Systems -- 7.8 Low Priority Waiting Time -- 7.9 Problems for Solution -- 8 The System GI/G/1; Imbedded Markov Chains -- 8.1 Imbedded Markov Chains -- 8.2 The System GI/G/1 -- 8.3 The Wiener-Hopf Technique; Examples -- 8.4 Set-up Times; Server Vacations -- 8.5 The Queue Length and Waiting Time in GI/M/1 -- 8.6 The Queue Length in M/G/1 -- 8.7 Time Sharing Systems -- 8.8 The M/M/1 System with RR Discipline -- 8.9 Problems for Solution -- A Appendix -- A.1 The Poisson Process -- A.2 Renewal Theory -- A.3 The Birth-And-Death Process -- A.4 Markov Processes with a Countable State Space -- A.5 Markov Chains -- A.6 Two Theorems on Functional Equations -- A.7 Review Problems in Probability and Stochastic Processes -- B Bibliography.
    In: Springer Nature eBook
    Additional Edition: Printed edition: ISBN 9780792399629
    Additional Edition: Printed edition: ISBN 9781461378457
    Additional Edition: Printed edition: ISBN 9781461562061
    Language: English
    Subjects: Economics , Mathematics
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  • 5
    UID:
    almahu_9949198282102882
    Format: X, 215 p. , online resource.
    Edition: 1st ed. 1997.
    ISBN: 9781461563297
    Content: The factory scheduling problem, that of allocating machines to competing jobs in manufacturing facilities to optimize or at least improve system performance, is encountered in many different manufacturing environments. Given the competitive pressures faced by many companies in today's rapidly changing global markets, improved factory scheduling should contribute to a flrm's success. However, even though an extensive body of research on scheduling models has been in existence for at least the last three decades, most of the techniques currently in use in industry are relatively simplistic, and have not made use of this body of knowledge. In this book we describe a systematic, long-term research effort aimed at developing effective scheduling algorithms for complex manufacturing facilities. We focus on a speciflc industrial context, that of semiconductor manufacturing, and try to combine knowledge of the physical production system with the methods and results of scheduling research to develop effective approximate solution procedures for these problems. The class of methods we suggest, decomposition methods, constitute a broad family of heuristic approaches to large, NP-hard scheduling problems which can be applied in other environments in addition to those studied in this book.
    Note: 1 Introduction -- 1.1 Introduction -- 1.2 The Scheduling Problem in the Organization -- 1.3 The Nature of the Factory Scheduling Problem -- 1.4 Deterministic Formulation of the Factory Scheduling -- Problem -- 1.5 Outline of Book -- 2 Industrial Context and Motivation for Decomposition Methods -- 2.1 Introduction -- 2.2 Semiconductor Manufacturing -- 2.3 Formulation as a Job Shop Scheduling Problem -- 2.4 Decomposition Methods -- 2.5 Summary -- 3 Review of Decomposition Methods for Factory Scheduling Problems -- 3.1 Introduction -- 3.2 A Taxonomy of Decomposition Methods for Factory 31 Scheduling Problems -- 3.3 Temporal Decomposition Schemes -- 3.4 Entity Decomposition Schemes -- 3.5 Hybrid Decomposition Schemes -- 3.6 Discussion -- 3.7 Conclusions -- 4 Modelling Interactions Between Subproblems: the Disjunctive Graph Representation and Extensions -- 4.1 Introduction -- 4.2 Disjunctive Graph Representation of the Classical Job Shop 48 Problem -- 4.3 Delayed Precedence Constraints -- 4.4 Extensions to Disjunctive Graph Representation -- 4.5 Summary -- 5 Workcenter-Based Decomposition Procedures for The Classical Job Shop Environment -- 5.1 Introduction -- 5.2 The Shifting Bottleneck Procedure -- 5.3 Dispatching Rules Used in Experiments -- 5.4 Results for Benchmark J//Cmax Problems -- 5.5 Results for Small Job Shop Problems -- 5.6 Results for Large Problems -- 5.7 Evaluation of Shifting Bottleneck using Other Performance -- Measures -- 5.8 Summary -- 6 A Generic Decomposition Procedure for Semiconductor Testing Facilities -- 6.1 Introduction -- 6.2 The Generic Decomposition Procedure -- 6.3 Computational Experiments -- 6.4 Results -- 6.5 Conclusions -- 7 Time-Based Decomposition Procedures for Single-Machine Subproblems with Sequence-Dependent Setup Times -- 7.1 Introduction -- 7.2 Previous Related Work -- 7.3 Rolling Horizon Procedures -- 7.4 Branch and Bound Algorithm -- 7.5 Experimental Design -- 7.6 Results -- 7.7 Conclusions -- 8 Time-Based Decomposition Procedures for Parallel Machine Subproblems with Sequence-Dependent Setup Times -- 8.1 Introduction -- 8.2 Previous Related Work -- 8.3 Rolling Horizon Procedures for Parallel Machines -- 8.4 Use of RHP to Improve on LIST(EDD) -- 8.5 Computational Experiments -- 8.6 Results -- 8.7 Conclusions and Future Directions -- 9 Naive Rolling Horizon Procedures for Job Shop Scheduling -- 9.1 Introduction -- 9.2 Scheduling Approach -- 9.3 Implementation and Computational Experiments -- 9.4 Results -- 9.5 Summary and Conclusions -- 10 Tailored Decomposition Procedures for Semiconductor Testing Facilities -- 10.1 Introduction -- 10.2 Subproblem Formulations -- 10.3 Modifications to the Rolling Horizon Procedures -- 10.4 Local Search Procedures for Single and Parallel Machine -- Problems -- 10.5 Operation-Based Decomposition -- 10.6 Tailored Control Structures for Semiconductor Testing -- Facilities -- 10.7 Summary -- 11. Computational Results for Job Shops with Single and Parallel Machine Workcenters -- 11.1 Introduction -- 11.2 Algorithms Compared in Experiments -- 11.3 Results for Shops with Single Machine Workcenters -- 11.4 Results for Shops with Parallel Machine Workcenters -- 11.5 Conclusions -- 12 The Effects of Subproblem Solution Procedures and Control Structures -- 12.1 Introduction -- 12.2 Two Additional Decomposition Procedures -- 12.3 Results for Semiconductor Testing Problems -- 12.4 Results for Reentrant Flow Shops -- 12.5 Summary and Conclusions -- 13 Conclusions and Future Directions -- 13.1 Introduction -- 13.2 Summary -- 13.3 Conclusions and Future Directions -- Author Index.
    In: Springer Nature eBook
    Additional Edition: Printed edition: ISBN 9780792398356
    Additional Edition: Printed edition: ISBN 9781461379065
    Additional Edition: Printed edition: ISBN 9781461563303
    Language: English
    Subjects: Economics , Mathematics
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  • 6
    UID:
    almahu_9949285172302882
    Format: XXI, 489 p. , online resource.
    Edition: 1st ed. 2002.
    ISBN: 9781461508359
    Content: After a decade of development, genetic algorithms and genetic programming have become a widely accepted toolkit for computational finance. Genetic Algorithms and Genetic Programming in Computational Finance is a pioneering volume devoted entirely to a systematic and comprehensive review of this subject. Chapters cover various areas of computational finance, including financial forecasting, trading strategies development, cash flow management, option pricing, portfolio management, volatility modeling, arbitraging, and agent-based simulations of artificial stock markets. Two tutorial chapters are also included to help readers quickly grasp the essence of these tools. Finally, a menu-driven software program, Simple GP, accompanies the volume, which will enable readers without a strong programming background to gain hands-on experience in dealing with much of the technical material introduced in this work.
    Note: 1 An Overview -- I Introduction -- 2 Genetic Algorithms in Economics and Finance -- 3 Genetic Programming: A Tutorial -- II Forecasting -- 4 GP and the Predictive Power of Internet Message Traffic -- 5 Genetic Programming of Polynomial Models for Financial Forecasting -- 6 NXCS: Hybrid Approach to Stock Indexes Forecasting -- III Trading -- 7 EDDIE for Financial Forecasting -- 8 Forecasting Market Indices Using Evolutionary Automatic Programming -- 9 Genetic Fuzzy Expert Trading System for NASDAQ Stock Market Timing -- IV Miscellaneous Applications Domains -- 10 Portfolio Selection and Management -- 11 Intelligent Cash Flow: Planning and Optimization Using GA -- 12 The Self-Evolving Logic of Financial Claim Prices -- 13 Using GP to Predict Exchange Rate Volatility -- 14 EDDIE for Stock Index Options and Futures Arbitrage -- V Agent-Based Computational Finance -- 15 A Model of Boundedly Rational Consumer Choice -- 16 Price Discovery in Agent-Based Computational Modeling of the Artificial Stock Market -- 17 Individual Rationality as a Partial Impediment to Market Efficiency -- 18 A Numerical Study on the Evolution of Portfolio Rules -- 19 Adaptive Portfolio Managers in Stock Markets -- 20 Learning and Convergence to Pareto Optimality -- VI Retrospect and Prospect -- 21 The New Evolutionary Computational Paradigm.
    In: Springer Nature eBook
    Additional Edition: Printed edition: ISBN 9780792376019
    Additional Edition: Printed edition: ISBN 9781461352624
    Additional Edition: Printed edition: ISBN 9781461508366
    Language: English
    Subjects: Computer Science , Mathematics
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    Keywords: Konferenzschrift
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  • 7
    UID:
    almahu_9949198379002882
    Format: XIII, 395 p. , online resource.
    Edition: 1st ed. 2000.
    ISBN: 9781461544593
    Series Statement: International Series in Operations Research & Management Science, 25
    Content: Multicriterion Decision in Management: Principles and Practice is the first multicriterion analysis book devoted exclusively to discrete multicriterion decision making. Typically, multicriterion analysis is used in two distinct frameworks: Firstly, there is multiple criteria linear programming, which is an extension of the results of linear programming and its associated algorithms. Secondly, there is discrete multicriterion decision making, which is concerned with choices among a finite number of possible alternatives such as projects, investments, decisions, etc. This is the focus of this book. The book concentrates on the basic principles in the domain of discrete multicriterion analysis, and examines each of these principles in terms of their properties and their implications. In multicriterion decision analysis, any optimum in the strict sense of the term does not exist. Rather, multicriterion decision making utilizes tools, methods, and thinking to examine several solutions, each having their advantages and disadvantages, depending on one's point of view. Actually, various methods exist for reaching a good choice in a multicriterion setting and even a complete ranking of the alternatives. The book describes and compares these methods, so-called `aggregation methods', with their advantages and their shortcomings. Clearly, organizations are becoming more complex, and it is becoming harder and harder to disregard complexity of points of view, motivations, and objectives. The day of the single objective (profit, social environment, etc. ) is over and the wishes of all those involved in all their diversity must be taken into account. To do this, a basic knowledge of multicriterion decision analysis is necessary. The objective of this book is to supply that knowledge and enable it to be applied. The book is intended for use by practitioners (managers, consultants), researchers, and students in engineering and business.
    Note: 1 What is multicriterion decision making? -- 1.1 Choice in the presence of multiple criteria -- 1.2 Historical background -- 1.3 The role of multicriterion analysis in organizations -- 1.4 An example to introduce some basic notions -- 1.5 Continuous multicriterion decision-making -- 1.6 How to use the book -- 2 Basic principles and tools -- 2.1 The discrete multicriterion decision (DMD) paradigm -- 2.2 The decision maker's preferences and order relations -- 2.3 Preorders and utility functions -- 2.4 Ordinal and cardinal utility functions and evaluation of alternatives -- 2.5 Semi-criteria and pseudo-criteria -- 2.6 Models and aims of multicriterion decision making -- 2.7 Evaluation of alternatives and normalization -- 3 Analysis of dominance and satisfaction -- 3.1 Product preorders and dominance -- 3.2 Cones and preorders -- 3.3 Pre-analysis of dominance -- 3.4 Pre-analysis of satisfaction -- 3.5 Methods of discrete multicriterion decision -- 4 Weighting methods and associated problems -- 4.1 Weights and weighted sums -- 4.2 Geometrical interpretation -- 4.3 Determining weights -- 4.4 The entropy method -- 4.5 Direct evaluation methods -- 4.6 Eigenvalue methods -- 4.7 Methods of comparison of alternatives -- 4.8 Other problems -- 5 Ordinal multicriterion methods -- 5.1 Introduction -- 5.2 Borda's method -- 5.3 The Condorcet method -- 5.4 Social choice and Arrow's theorem -- 5.5 The method of Bowman and Colantoni -- 5.6 Lexicographic methods -- 6 Additive utility functions and associated methods -- 6.1 Introduction -- 6.2 The problem of comparing utilities -- 6.3 Definition and cardinality of additive utility functions -- 6.4 Difference additivity models -- 6.5 The existence of additively separable utility functions -- 6.6 Constructing additive utilities -- 6.7 The UTA method -- 7 Outranking methods -- 7.1 Introduction -- 7.2 Outranking relations -- 7.3 The Electre method -- 7.4 The Promethee method -- 7.5 Other methods -- 8 Other multicriterion decision methods -- 8.1 Introduction -- 8.2. Alternative comparison methods -- 8.3. Methods involving distance from an ideal alternative -- 8.4 Permutation methods -- 8.5 Miscellaneous methods -- 9 Computers, Artificial Intelligence, Interactivity and Multicriterion Decision -- 9.1 The complexity of calculations -- 9.2 Artificial intelligence (AI) and multicriterion decision -- 9.3 Interactivity -- 9.4 Interactive multicriterion methods -- 9.5 Incorporation of multicriterion methods in DSS -- 9.6 Conclusion -- 10 Software for discrete multicriterion decision -- 10.1 Introduction -- 10.2 Logical Decisions -- 10.3 Promcalc -- 10.4 Expert Choice -- 10.5 Qualiflex -- 10.6 Brief review of DMD software -- 11 Multicriterion decision in practice -- 11.1 The role of multicriterion decision in descriptive models of human decision -- 11.2 People and timing in multicriterion decision -- 11.3 On modeling -- 11.4 From aggregation to choice -- 11.5 Reactions of decision makers to multicriterion decision -- 11.6 Applications -- 12 Multicriterion methods: features and comparisons -- 12.1 Introduction -- 12.2 A theoretical framework for analyzing the desirable properties of choice functions -- 12.3 Empirical comparison of practical properties -- 12.4 Comparison of multicriterion aggregation procedures: the various factors to be considered -- 12.5 The specialist's point of view: choice of a method in terms of information available and terms of reference -- 12.6 Choice of method: the user's point of view -- 12.7 Conclusion -- References -- Author Inde.
    In: Springer Nature eBook
    Additional Edition: Printed edition: ISBN 9781461370086
    Additional Edition: Printed edition: ISBN 9780792377566
    Additional Edition: Printed edition: ISBN 9781461544609
    Language: English
    Subjects: Economics , Mathematics
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  • 8
    Online Resource
    Online Resource
    New York, NY :Springer New York :
    UID:
    almahu_9949198292102882
    Format: XII, 394 p. , online resource.
    Edition: 1st ed. 1997.
    ISBN: 9781461240549
    Content: This book is intended as a text covering the central concepts and techniques of Competitive Markov Decision Processes. It is an attempt to present a rig­ orous treatment that combines two significant research topics: Stochastic Games and Markov Decision Processes, which have been studied exten­ sively, and at times quite independently, by mathematicians, operations researchers, engineers, and economists. Since Markov decision processes can be viewed as a special noncompeti­ tive case of stochastic games, we introduce the new terminology Competi­ tive Markov Decision Processes that emphasizes the importance of the link between these two topics and of the properties of the underlying Markov processes. The book is designed to be used either in a classroom or for self-study by a mathematically mature reader. In the Introduction (Chapter 1) we outline a number of advanced undergraduate and graduate courses for which this book could usefully serve as a text. A characteristic feature of competitive Markov decision processes - and one that inspired our long-standing interest - is that they can serve as an "orchestra" containing the "instruments" of much of modern applied (and at times even pure) mathematics. They constitute a topic where the instruments of linear algebra, applied probability, mathematical program­ ming, analysis, and even algebraic geometry can be "played" sometimes solo and sometimes in harmony to produce either beautifully simple or equally beautiful, but baroque, melodies, that is, theorems.
    Note: 1 Introduction -- 1.0 Background -- 1.1 Raison d'Etre and Limitations -- 1.2 A Menu of Courses and Prerequisites -- 1.3 For the Cognoscenti -- 1.4 Style and Nomenclature -- I Mathematical Programming Perspective -- 2 Markov Decision Processes: The Noncompetitive Case -- 3 Stochastic Games via Mathematical Programming -- II Existence, Structure and Applications -- 4 Summable Stochastic Games -- 5 Average Reward Stochastic Games -- 6 Applications and Special Classes of Stochastic Games -- Appendix G Matrix and Bimatrix Games and Mathematical Programming -- G.1 Introduction -- G.2 Matrix Game -- G.3 Linear Programming -- G.4 Bimatrix Games -- G.5 Mangasarian-Stone Algorithm for Bimatrix Games -- G.6 Bibliographic Notes -- Appendix H A Theorem of Hardy and Littlewood -- H.1 Introduction -- H.2 Preliminaries, Results and Examples -- H.3 Proof of the Hardy-Littlewood Theorem -- Appendix M Markov Chains -- M.1 Introduction -- M.2 Stochastic Matrix -- M.3 Invariant Distribution -- M.4 Limit Discounting -- M.5 The Fundamental Matrix -- M.6 Bibliographic Notes -- Appendix P Complex Varieties and the Limit Discount Equation -- P.1 Background -- P.2 Limit Discount Equation as a Set of Simultaneous Polynomials -- P.3 Algebraic and Analytic Varieties -- P.4 Solution of the Limit Discount Equation via Analytic Varieties -- References.
    In: Springer Nature eBook
    Additional Edition: Printed edition: ISBN 9781461284819
    Additional Edition: Printed edition: ISBN 9780387948058
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    Subjects: Mathematics
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  • 9
    Online Resource
    Online Resource
    New York, NY :Springer US :
    UID:
    almahu_9949198286702882
    Format: VIII, 490 p. , online resource.
    Edition: 1st ed. 2000.
    ISBN: 9781475748284
    Series Statement: International Series in Operations Research & Management Science, 24
    Content: Great advances have been made in recent years in the field of computational probability. In particular, the state of the art - as it relates to queuing systems, stochastic Petri-nets and systems dealing with reliability - has benefited significantly from these advances. The objective of this book is to make these topics accessible to researchers, graduate students, and practitioners. Great care was taken to make the exposition as clear as possible. Every line in the book has been evaluated, and changes have been made whenever it was felt that the initial exposition was not clear enough for the intended readership. The work of major research scholars in this field comprises the individual chapters of Computational Probability. The first chapter describes, in nonmathematical terms, the challenges in computational probability. Chapter 2 describes the methodologies available for obtaining the transition matrices for Markov chains, with particular emphasis on stochastic Petri-nets. Chapter 3 discusses how to find transient probabilities and transient rewards for these Markov chains. The next two chapters indicate how to find steady-state probabilities for Markov chains with a finite number of states. Both direct and iterative methods are described in Chapter 4. Details of these methods are given in Chapter 5. Chapters 6 and 7 deal with infinite-state Markov chains, which occur frequently in queueing, because there are times one does not want to set a bound for all queues. Chapter 8 deals with transforms, in particular Laplace transforms. The work of Ward Whitt and his collaborators, who have recently developed a number of numerical methods for Laplace transform inversions, is emphasized in this chapter. Finally, if one wants to optimize a system, one way to do the optimization is through Markov decision making, described in Chapter 9. Markov modeling has found applications in many areas, three of which are described in detail: Chapter 10 analyzes discrete-time queues, Chapter 11 describes networks of queues, and Chapter 12 deals with reliability theory.
    Note: 1 Computational Probability: Challenges and Limitations -- 2 Tools for Formulating Markov Models -- 3 Transient Solutions for Markov Chains -- 4 Numerical Methods for Computing Stationary Distributions of Finite Irreducible Markov Chains -- 5 Stochastic Automata Networks -- 6 Matrix Analytic Methods -- 7 Use of Characteristic Roots for Solving Infinite State Markov Chains -- 8 An Introduction to Numerical Transform Inversion and Its Application to Probability Models -- 9 Optimal Control of Markov Chains -- 10 On Numerical Computations of Some Discrete-Time Queues -- 11 The Product Form Tool for Queueing Networks -- 12 Techniques for System Dependability Evaluation.
    In: Springer Nature eBook
    Additional Edition: Printed edition: ISBN 9781441951007
    Additional Edition: Printed edition: ISBN 9780792386179
    Additional Edition: Printed edition: ISBN 9781475748291
    Language: English
    Subjects: Computer Science , Mathematics
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  • 10
    Online Resource
    Online Resource
    New York, NY :Springer New York :
    UID:
    almahu_9947363012302882
    Format: XII, 236 p. , online resource.
    ISBN: 9781461209072
    Series Statement: Universitext,
    Content: A book on the subject of normal families more than sixty years after the publication of Montel's treatise Ler;ons sur les familles normales de fonc­ tions analytiques et leurs applications is certainly long overdue. But, in a sense, it is almost premature, as so much contemporary work is still being produced. To misquote Dickens, this is the best of times, this is the worst of times. The intervening years have seen developments on a broad front, many of which are taken up in this volume. A unified treatment of the classical theory is also presented, with some attempt made to preserve its classical flavour. Since its inception early this century the notion of a normal family has played a central role in the development of complex function theory. In fact, it is a concept lying at the very heart of the subject, weaving a line of thought through Picard's theorems, Schottky's theorem, and the Riemann mapping theorem, to many modern results on meromorphic functions via the Bloch principle. It is this latter that has provided considerable impetus over the years to the study of normal families, and continues to serve as a guiding hand to future work. Basically, it asserts that a family of analytic (meromorphic) functions defined by a particular property, P, is likely to be a normal family if an entire (meromorphic in.
    Note: 1 Preliminaries -- 2 Analytic Functions -- 3 Meromorphic Functions -- 4 Bloch Principle -- 5 General Applications -- Appendix Quasi-Normal Families -- References.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9780387979670
    Language: English
    Subjects: Mathematics
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