Hippe / Kulikowski Human-Computer Systems Interaction

Backgrounds and Applications
1. Auflage 2009
ISBN: 978-3-642-03202-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 60, 570 Seiten

Reihe: Advances in Intelligent and Soft Computing

For the last decades, as the computer technology has been developing, the importance of human-computer systems interaction problems was growing. This is not only because the computer systems performance characteristics have been im-proved but also due to the growing number of computer users and of their expectations about general computer systems capabilities as universal tools for human work and life facilitation. The early technological problems of man-computer information exchange - which led to a progress in computer programming languages and input/output devices construction - have been step by step dominated by the more general ones of human interaction with-and-through computer systems, shortly denoted as H-CSI problems. The interest of scientists and of any sort specialists to the H-CSI problems is very high as it follows from an increasing number of scientific conferences and publications devoted to these topics. The present book contains selected papers concerning various aspects of H-CSI. They have been grouped into five Parts: I. General H-CSI problems (7 papers), II. Disabled persons helping and medical H-CSI applications (9 papers), III. Psychological and linguistic H-CSI aspects (9 papers), IV. Robots and training systems (8 papers), V. Various H-CSI applications (11 papers).

Autoren/Hrsg.

Hippe, Zdzislaw S.

Kulikowski, Juliusz Lech

Inhaltsverzeichnis

1;Foreword;6
2;Preface;8
3;Contents;10
4;Part I General Problems of H-CSI;15
4.1;From Research on the Decision-Making in Ill-Structured Situation Control and the Problem of Risks;16
4.1.1;Introduction;16
4.1.2;About Trends in Development of the Cognitive Approach in Decision-Making;17
4.1.2.1;Two Directions of the Cognitive Approach;18
4.1.2.2;Clarification of Concept of the {\it Cognitive} Map in Decision-Making;19
4.1.3;The Problem of Risks due to the Human Factor;19
4.1.3.1;Cognitive Risks in Subjective-Formal Searching and Making Solutions: Two Kinds of Risk Factors;21
4.1.4;A Family of Risks Concerned with Causal Influence Transitivity;22
4.1.4.1;Practical Example of Causal Influence Transitivity Violation;23
4.1.4.2;The Analysis of Revealed Cognitive Risks;24
4.1.4.3;Some Criteria for the Early Detection of False Transitivity Risks;25
4.1.5;Conclusions;26
4.1.6;References;26
4.2;Emulating the Perceptual System of the Brain for the Purpose of Sensor Fusion;29
4.2.1;Introduction;29
4.2.2;The Research Field of Sensor Fusion;30
4.2.3;Characteristics of Human Perception;30
4.2.4;Bionic Model for Perception;32
4.2.4.1;Neuro-Symbolic Information Processing;32
4.2.4.2;Interaction between Neuro-Symbolic Network, Knowledge, and Focus of Attention;35
4.2.5;Results and Discussion;37
4.2.6;Conclusions;38
4.2.7;References;38
4.3;Knowledge Acquisition in Conceptual Ontological Artificial Intelligence System;40
4.3.1;Introduction;40
4.3.2;Method;40
4.3.2.1;Conversion from Natural Language;40
4.3.2.2;Polysemy of Natural Language Statements;41
4.3.2.3;Ontological Core Knowledge Acquisition;42
4.3.2.4;The Search of Similar Concepts;42
4.3.2.5;Separation of Concepts;45
4.3.2.6;Basic Concepts Search;47
4.3.2.7;Information Scope Presented with Questions Generated by the System;47
4.3.3;Conclusions;47
4.3.3.1;Active Knowledge Acquisition Role;47
4.3.3.2;Further Development;48
4.3.4;References;48
4.4;Problems of Knowledge Representation in Computer-Assisted Decision Making Systems;49
4.4.1;Introduction;49
4.4.2;Knowledge Representing Statements;51
4.4.2.1;Factual Statements;52
4.4.2.2;Implicative Statements;53
4.4.2.3;Deontic Statements;54
4.4.2.4;Evaluating Meta-statements;55
4.4.3;Structural and Semantic Redundancy in Knowledgebases;56
4.4.4;Knowledge Representation by Ontological Models;58
4.4.5;Conclusions;63
4.4.6;References;64
4.5;A Dialogue-Based Interaction System for Human-Computer Interfaces;65
4.5.1;Introduction;65
4.5.2;A Dialogue-Based Interaction System;66
4.5.3;An Example;71
4.5.4;Final Remarks;74
4.5.5;References;75
4.6;Consistency-Based vs. Similarity-Based Prediction Using Extensions of Information Systems – An Experimental Study;76
4.6.1;Introduction;76
4.6.2;Theoretical Background;77
4.6.2.1;Extensions of Information Systems;77
4.6.2.2;Consistency Measure;79
4.6.2.3;Similarity Measure;82
4.6.3;Experiments;82
4.6.3.1;Macroeconomics Data;83
4.6.3.2;Weather Data;86
4.6.3.3;Summary;89
4.6.4;Conclusions;89
4.6.5;References;90
4.7;Image Annotation Based on Semantic Rules;91
4.7.1;Introduction;91
4.7.2;The Image Segmentation;92
4.7.3;From Visual Features to Semantic Descriptors;94
4.7.4;Rule-Based Image Annotation;95
4.7.4.1;Generation of Semantic Association Rules;96
4.7.4.2;Image Categorization;98
4.7.5;Databases with Images for Learning and Annotation;99
4.7.6;Conclusions;101
4.7.7;References;102
5;Part II Disabled Persons Helping and Medical H-CSI Applications;103
5.1;A Prototype Mobility and Navigation Tele-Assistance System for Visually Disabled;104
5.1.1;Introduction;104
5.1.1.1;Existing Tele-Assitance Systems;105
5.1.1.2;The Electronic Travel Aid;106
5.1.2;Experimental Setup and Procedures;106
5.1.2.1;The Prototypes;106
5.1.2.2;Trial Rationale and Goals;107
5.1.2.3;Indoor Trial Description;108
5.1.2.4;Data Collection;110
5.1.2.5;Outdoor Trial Description;110
5.1.3;Trial Results and Analysis;112
5.1.3.1;Performance Review;112
5.1.3.2;Operator Conclusions;113
5.1.3.3;Survey Results;113
5.1.4;Present and Future Work;113
5.1.4.1;Enhancing GPS Navigation;113
5.1.4.2;Adjustable Video Quality;114
5.1.4.3;Target Platform;114
5.1.5;Conclusions;114
5.1.6;References;115
5.2;Eye-Mouse for Disabled;116
5.2.1;Introduction;116
5.2.2;Methods;117
5.2.3;Discussion;126
5.2.4;Conclusions;127
5.2.5;References;128
5.3;Eye-Blink Controlled Human-Computer Interface for the Disabled;130
5.3.1;Introduction;130
5.3.2;Eye-Blink Monitoring;131
5.3.3;Eye-Blink Monitoring System;132
5.3.3.1;System Overview;132
5.3.3.2;Face Detection and Eye Localization;133
5.3.3.3;Eye Tracking and Eye Blink Detection;135
5.3.4;The Developed Software;136
5.3.4.1;BlinkWriter;136
5.3.4.2;BlinkBrowser;136
5.3.5;Results;137
5.3.6;Conclusions;139
5.3.7;References;139
5.4;HMM-Based System for Recognizing Gestures in Image Sequences and Its Application in Continuous Gesture Recognition;141
5.4.1;Introduction;141
5.4.2;Methodology;142
5.4.2.1;Image Preprocessing and Color Segmentation;143
5.4.2.2;Feature Extraction;143
5.4.2.3;Dimensionality Reduction;144
5.4.2.4;Statistical Classifier;144
5.4.2.5;Recognition of Gestures;145
5.4.2.6;Gesture Detection and Segmentation in Time;146
5.4.3;Experimental Results;146
5.4.3.1;Recognition of Isolated Gestures;146
5.4.3.2;Comparison with Other Methods;146
5.4.4;Conclusions;151
5.4.5;References;152
5.5;Machine Learning of Melanocytic Skin Lesion Images;153
5.5.1;Introduction;153
5.5.2;Procedure;155
5.5.3;Results and Discussion;159
5.5.4;Conclusions and Outlook;162
5.5.5;References;163
5.6;A Preliminary Attempt to Validation of Glasgow Outcome Scale for Describing Severe Brain Damages;166
5.6.1;Introduction;166
5.6.2;The Main Goal of the Research;167
5.6.3;General Methodology of the Research;167
5.6.4;Results of Experiments;169
5.6.5;Discussion and Conclusions;174
5.6.6;References;175
5.7;Segmentation of Anatomical Structure by Using a Local Classifier Derived from Neighborhood Information;176
5.7.1;Introduction;176
5.7.2;Segmentation Framework with a Local Classifier;177
5.7.3;Experimental Analyses and Discussion;179
5.7.3.1;Advantages of Our Local Classifier;179
5.7.3.2;Segmentation on Test CT Images;180
5.7.3.3;Deliverables of Successful Segmentation;183
5.7.4;Conclusions;184
5.7.5;References;185
5.8;An Application of Detection Function for the Eye Blinking Detection;186
5.8.1;Introduction;186
5.8.2;The Detection Function for Eye-Blink Detection;188
5.8.3;Location of Blinks in Time Domain;192
5.8.4;Conclusions;195
5.8.5;References;195
5.9;Self-directed Training in an Evidence-Based Medicine Experiment;197
5.9.1;Introduction;197
5.9.2;Material and Method;198
5.9.2.1;Training and Evaluation System;198
5.9.2.2;System Evaluation Methodology: Evidence-Based Medicine;199
5.9.3;Results;200
5.9.3.1;Study Participants;200
5.9.3.2;Intervention Group: Pre- and Post-test Assessment of EBM Knowledge;202
5.9.3.3;Intervention Group: Usability Analysis of the Training and Evaluation System;203
5.9.3.4;Comparison between Control and Intervention Groups;203
5.9.4;Discussion;204
5.9.5;Conclusions;206
5.9.6;References;206
6;Part III Psychological and Linguistic Aspects of H-CSI;209
6.1;Emotion Recognition from Facial Expression Using Neural Networks;210
6.1.1;Introduction;210
6.1.2;Facial Expression Database;211
6.1.3;Feature Extraction;211
6.1.4;Neural Networks for Emotion Recognition;212
6.1.4.1;SVM for Emotion Recognition;212
6.1.4.2;MLP for Emotion Recognition;215
6.1.4.3;PCA for Emotion Recognition;217
6.1.4.4;GFFNN for Emotion Recognition;219
6.1.5;Conclusions;221
6.1.6;References;222
6.2;Emotion Eliciting and Decision Making by Psychodynamic Appraisal Mechanism;223
6.2.1;Introduction;223
6.2.2;Psychodynamic Appraisal Mechanism;224
6.2.2.1;Emotion Synthesis;224
6.2.2.2;Psychodynamic Appraisal Mechanism;224
6.2.2.3;System Architecture;225
6.2.2.4;Emotion as a Motivation Mechanism;227
6.2.3;Modules for Psychodynamic Cognitive Construction;227
6.2.3.1;Sensori-Motor Apparatus;227
6.2.3.2;Innate Need Module;228
6.2.3.3;Emotion Appraisal Module;228
6.2.3.4;G-Net;229
6.2.4;qViki System and Experiments;230
6.2.5;Conclusion and Future Work;232
6.2.6;References;233
6.3;Positing a Growth-Centric Approach in Empathic Ambient Human-System Interaction;235
6.3.1;Introduction;235
6.3.2;Making the Case for a Growth-Centric Empathic System;237
6.3.3;Making the Case for an Empathic Ambient Intelligent System;240
6.3.4;Conclusions;242
6.3.5;References;242
6.4;Toward Daydreaming Machines;247
6.4.1;Introduction;247
6.4.2;Synaptic-State Theory (SST);248
6.4.3;Machine Psychodynamics (M.D);249
6.4.3.1;Pleasure Principle;250
6.4.3.2;Freud in Machine;250
6.4.3.3;Machine Adventurousness;251
6.4.3.4;Constructive Ambivalence;252
6.4.4;Quest of Machine Consciousness;253
6.4.4.1;Hard-Requirement C253
6.4.4.2;Modest-Requirement C254
6.4.5;Concluding Remarks;255
6.4.6;References;256
6.5;Eliminate People’s Expressive Preference in the Mood of Fuzzy Linguistics;259
6.5.1;Introduction;259
6.5.2;Expressive Preference in Fuzzy Mood;260
6.5.2.1;Mood Operator;261
6.5.2.2;Attitude Preference;261
6.5.2.3;Degree Preference;262
6.5.3;Method;263
6.5.3.1;Process;263
6.5.3.2;Mathematical Translation;264
6.5.4;Experiments;265
6.5.5;Results;268
6.5.6;Conclusions;269
6.5.7;References;269
6.6;VoiceXML Platform for Minority Languages;271
6.6.1;Introduction;271
6.6.2;W3C Speech Interface Framework;272
6.6.2.1;VXML;273
6.6.2.2;VXML Platform Architecture;273
6.6.3;Dialogue Modeling;275
6.6.3.1;Weather Forecast Dialogues;276
6.6.3.2;VXML Syntax Basics;276
6.6.4;CROVREP System;279
6.6.5;Conclusions;280
6.6.6;References;281
6.7;Polish Speech Processing Expert System Incorporated into the EDA Tool;283
6.7.1;Introduction;283
6.7.2;The Idea and the Expert System Architecture;284
6.7.2.1;The Speech Recognition Module;284
6.7.2.2;Implementation of the Speech Recognition Module;285
6.7.2.3;Speech Synthesis Methodology;286
6.7.2.4;Examples of Polish Language Processing;288
6.7.2.5;System Knowledge Bases;289
6.7.2.6;Semantic Rules of the System Menu Commands;290
6.7.2.7;Management of the Information in the System – Inference Engine;290
6.7.3;The Implementation and Examples;292
6.7.4;Conclusions and Summary;293
6.7.5;References;294
6.8;A Web-Oriented Java3D Talking Head;296
6.8.1;Introduction;296
6.8.2;State of the Art;297
6.8.3;An Overview the Talking Head;301
6.8.3.1;Talking Head Features;301
6.8.4;The Proposed Architecture;303
6.8.4.1;The Server Side;304
6.8.4.2;Client Side;305
6.8.5;Interaction with the System;309
6.8.6;Conclusions;309
6.8.7;References;310
6.9;A VR-Based Visualization Framework for Effective Information Perception and Cognition;313
6.9.1;Introduction;313
6.9.2;Literature Review;314
6.9.2.1;Perception of Complex Data;314
6.9.2.2;Current HCI Approaches for Data Visualization;315
6.9.2.3;Minimizing Semantic Gap between the Data and the Reality;316
6.9.2.4;Focused Attention to Avoid Distraction;317
6.9.2.5;Mental Workload;317
6.9.3;Proposed Visualization Approach;318
6.9.3.1;Preparation of Raw System Data;318
6.9.3.2;Data Classification;319
6.9.3.3;Transformation of System Data;320
6.9.3.4;Visualization of Transformed Information in the VR Platform;321
6.9.4;Case Study – Implementation of the Framework to Visualize the Operation of an Express Cargo Handling Center;322
6.9.5;Information Visualization Using the ImseCAVE VR System;327
6.9.6;Discussion and Future Work;329
6.9.7;References;330
7;Part IV Robots and Training Systems;333
7.1;From Research on the Virtual Reality Installation;334
7.1.1;Introduction;334
7.1.2;Virtual Reality and Presence;334
7.1.2.1;The Role of Presence;334
7.1.2.2;The Pillars of Presence;335
7.1.2.3;Virtual Reality Installations;336
7.1.3;About the Developed Virtual Reality Installation;337
7.1.3.1;Outlook;337
7.1.3.2;Description of the Installation;338
7.1.3.3;Importance of the Content;341
7.1.3.4;Financial Details;341
7.1.4;Evaluation;342
7.1.5;Conclusions;342
7.1.6;References;343
7.2;High-Level Hierarchical Semantic Processing Framework for Smart Sensor Networks;345
7.2.1;Introduction;345
7.2.2;Architecture Overview;346
7.2.3;Description of Layers;348
7.2.3.1;Low-Level Feature Extraction;348
7.2.3.2;Preprocessing Including Plausibility Checks;348
7.2.3.3;Tracking;349
7.2.3.4;Sensor Fusion;351
7.2.3.5;Parameter Inference;351
7.2.3.6;Trajectories;352
7.2.3.7;Inter-Node Communication;353
7.2.3.8;Alarm Generator;353
7.2.3.9;User Notification Filter;354
7.2.4;Conclusions;354
7.2.5;References;354
7.3;A Human-System Interaction Framework and Algorithm for UbiComp-Based Smart Home;357
7.3.1;Introduction;357
7.3.2;Related Works;358
7.3.3;System Overview;359
7.3.4;Framework for Human-System Interaction;360
7.3.4.1;The Requirements of Services;360
7.3.4.2;The Status of Environment;360
7.3.5;Algorithm for Human-System Interaction;362
7.3.5.1;Find QS and CS from the Environment;363
7.3.5.2;List of CS;363
7.3.5.3;Configuration of Services;364
7.3.5.4;Notification;364
7.3.6;Analysis and Discussion;365
7.3.6.1;Comfort;365
7.3.6.2;Convenience;365
7.3.6.3;Security;365
7.3.7;Experiment Results and Evaluations;366
7.3.7.1;Experiments;366
7.3.7.2;Evaluations;367
7.3.8;Conclusion;367
7.3.9;References;367
7.4;Biologically Reasoned Point-of-Interest Image Compression for Mobile Robots;369
7.4.1;Introduction;369
7.4.2;Object Recognition;370
7.4.3;Yellow Spot;371
7.4.4;Compression;372
7.4.5;Practical Realization;372
7.4.6;Active Vision vs. Yellow Spot;374
7.4.7;Inference;374
7.4.8;Election of a Next Fixation Point;376
7.4.9;Mobile Robots and Computer Clusters;377
7.4.10;Conclusion and Future Work;379
7.4.11;References;379
7.5;Surgical Training System with a Novel Approach to Human-Computer Interaction;381
7.5.1;Introduction;381
7.5.2;Description of the System;383
7.5.2.1;System Outline;383
7.5.2.2;Training Model;384
7.5.2.3;Processing;385
7.5.3;Conclusions;389
7.5.4;References;390
7.6;Kinematics Analysis and Design of 3 DOF Medical Parallel Robots;392
7.6.1;Introduction;392
7.6.2;Kinematics Analysis for 3 DOF Parallel Robots;393
7.6.2.1;Mathematical Model;393
7.6.3;Virtual Reality Model;398
7.6.4;Design of TRIGLIDE Parallel Robot;401
7.6.5;Conclusion;401
7.6.6;References;402
7.7;Graphical Human-Machine Interface for QB Systems;404
7.7.1;Introduction;404
7.7.2;Trajectory Planer and Trajectory Generator;405
7.7.2.1;Parts of the Application;405
7.7.3;Trajectory Generation;408
7.7.3.1;Procedure of Trajectory Generation;408
7.7.3.2;Command List;409
7.7.4;Test Results;412
7.7.5;Conclusions;413
7.7.6;References;413
7.8;Visualization of Two Parameters in a Three-Dimensional Environment;415
7.8.1;Introduction;415
7.8.2;Related Work;416
7.8.3;Effective Visualization of Two Parameters;417
7.8.3.1;Semantic Analytics Visualization;417
7.8.3.2;Semantic Event Tracker;419
7.8.3.3;Health of US States;421
7.8.4;Conclusions;422
7.8.5;References;423
8;Part V Various H-CSI Applications;425
8.1;An Evaluation Tool for End-User Computing Competency in an Organizational Computing Environment;426
8.1.1;Introduction;426
8.1.2;Computing Competency;426
8.1.3;Research Methods;428
8.1.3.1;Analysis and Results;428
8.1.4;Evaluation Tool;429
8.1.4.1;Evaluation Factors and Items;431
8.1.5;Evaluation Systems;431
8.1.5.1;Evaluation Method;433
8.1.6;Case Study and Analysis Results;434
8.1.6.1;Application and Analysis of overall Organization;434
8.1.6.2;Application and Analysis of a Business Department;434
8.1.6.3;Application and Analysis of an Individual;435
8.1.7;Conclusions;436
8.1.8;References;436
8.2;Enterprsise Ontology for Knowledge-Based System;438
8.2.1;Introduction;438
8.2.2;Enterprise Model – A Diagnostic Approach;441
8.2.3;A-E-AE Enterprise Ontology – A Diagnostic Approach;449
8.2.4;Knowledge Base Model According to A-E-AE Ontology;449
8.2.5;Conclusions;451
8.2.6;References;452
8.3;Constructing Ensemble-Based Classifiers Based on Feature Transformation: Application in Hand Recognition;454
8.3.1;Introduction;454
8.3.2;Preprocessing and Feature Extraction;456
8.3.2.1;Aligning the Elements of Feature Vectors;457
8.3.3;Classifier Ensemble Based on Feature Transformation;459
8.3.3.1;Diversity Creation Method;460
8.3.4;Experimental Results;461
8.3.5;Conclusions;463
8.3.6;References;463
8.4;A New and Improved Skin Detection Method Using Mixed Color Space;465
8.4.1;Introduction;465
8.4.2;Pervious Works;467
8.4.3;Proposed Method;468
8.4.4;Experimental Results;470
8.4.5;Conclusions;473
8.4.6;References;473
8.5;A Formal Model for Supporting the Adaptive Access to Virtual Museums;475
8.5.1;Introduction;475
8.5.2;Concept Space and Map;476
8.5.2.1;Zz-Structures;477
8.5.2.2;A-Space and a-Map;481
8.5.3;Displaying and Changing Views;482
8.5.4;Conclusion;485
8.5.5;References;485
8.6;3D Molecular Interactive Modeling;487
8.6.1;Introduction;487
8.6.2;Importance of the Molecular Spatial Structure;487
8.6.2.1;When Biology Becomes Molecular;488
8.6.2.2;Molecular Biology Is Rewarding;488
8.6.3;Contributions of Molecular Modeling;489
8.6.4;Three-Dimensional Structures: Visualization and Interaction;489
8.6.4.1;Three-Dimensional Modeling Approaches;490
8.6.4.2;Molecular Visualization Systems;490
8.6.4.3;Interactive Systems for Molecular Modeling;490
8.6.4.4;Molecular Dynamics Modeling;494
8.6.5;Conclusions;495
8.6.6;References;496
8.7;Shape Recognition of Film Sequence with Application of Sobel Filter and Backpropagation Neural Network;499
8.7.1;Introduction;499
8.7.2;Description of the System;499
8.7.3;Shape Recognition Process;499
8.7.3.1;Video Recording;500
8.7.3.2;Digital Video Signal Conversion;501
8.7.3.3;Filtration;502
8.7.3.4;Thinning Algorithm;503
8.7.3.5;Creation of Shape Token;504
8.7.3.6;Backpropagation Neural Network;505
8.7.4;Shape Recognition Results;507
8.7.5;Conclusions;508
8.7.6;References;509
8.8;Dynamic Changes of Population Size in Training of Artificial Neural Networks;511
8.8.1;Introduction;511
8.8.2;Differential Evolution Algorithm;512
8.8.3;Proposed Method DPS-DE-ANNT;513
8.8.4;Structure of Assumed Neural Networks and Neuron Model;516
8.8.5;Experiments;517
8.8.6;Conclusions;520
8.8.7;References;520
8.9;New Approach to Diagnostics of DC Machines by Sound Recognition Using Linear Predictive Coding;522
8.9.1;Introduction;522
8.9.2;Sound Recognition Process;523
8.9.2.1;Acoustic Signal Recording;524
8.9.2.2;Sound Track Dividing;525
8.9.2.3;Sampling;525
8.9.2.4;Quantization;526
8.9.2.5;Amplitude Normalization;526
8.9.2.6;Filtration;526
8.9.2.7;Windowing;526
8.9.2.8;Linear Predictive Coding;526
8.9.2.9;Classification;529
8.9.3;Sound Recognition Results;530
8.9.4;Conclusions;532
8.9.5;References;532
8.10;Diagnosis Based on Fuzzy IF-THEN Rules and Genetic Algorithms;534
8.10.1;Introduction;534
8.10.2;Fuzzy Model of Diagnosis;535
8.10.3;Solving Fuzzy Logical Equations;537
8.10.3.1;Optimization Problem;537
8.10.3.2;Genetic Algorithm;538
8.10.4;Fuzzy Model Tuning;539
8.10.5;Computer Experiment;539
8.10.6;Example of Technical Diagnosis;544
8.10.7;Conclusions and Future Work;548
8.10.8;References;549
8.11;Necessary Optimality Conditions for Fractional Bio-economic Systems: The Problem of Optimal Harvest Rate;550
8.11.1;Introduction;550
8.11.2;Some Required Transformations;552
8.11.3;Necessary Optimality Conditions;553
8.11.3.1;Statement of the Problem;553
8.11.3.2;Solution for 0