Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
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ISBN-13
978-94-009-5422-9 (9789400954229)
DOI
10.1007/978-94-009-5422-9
Schweitzer Klassifikation
1 Introduction.- 1.1 The Nature of the Problem.- 1.2 Examples of Spatially Random Material.- 1.3 Notes.- 2 Deterministic Design I: Conceptual Formulation.- 2.1 Relative Mass Resolution.- 2.2 Response Functions.- 2.3 Point-Source Response Sets.- 2.4 The Convexity Theorem: Complete Response Sets.- 2.5 Relative Mass Resolution and the Concept of Expansion.- 2.6 Example: Pu Assay With One Detector.- 2.7 Example: Pu Assay With Two Detectors.- 2.8 Example: Coincidence Measurements.- 2.9 Computation of the Relative Mass Resolution.- 2.10 Example: Pu Assay With Four Detectors.- 2.11 The Inclusion of Statistical Uncertainty.- 2.12 Example: Radioactive Waste Assay.- 2.13 Summary.- 2.14 Notes.- 3 Deterministic Design II: General Formulation.- 3.1 Motivation.- 3.2 Unconstrained Spatial Distributions.- 3.3 Constrained Spatial Distributions.- 3.4 Example: Simple Constrained Distributions.- 3.5 Example: Constrained Normal Distributions.- 3.6 Example: Meteorological Measurements.- 3.7 Example: Assay of a Pulmonary Aerosol.- 3.8 Example: Thickness Measurement.- 3.9 Example: Enrichment Assay.- 3.10 Auxiliary Parameters.- 3.11 Example: Variable Matrix Structure.- 3.12 Variable Spatial Distributions and Auxiliary Parameters.- 3.13 Constrained Time-Varying Distributions.- 3.14 Example: Flow-Rate Measurement.- 3.15 Notes.- 4 Probabilistic Interpretation of Measurement.- 4.1 Probability Density of the Measurement.- 4.2 Probability Density of the Total Source Mass.- 4.3 Bayes' Decision Theory.- 4.4 Neyman-Pearson Decision Theory.- 4.5 Direct Probabilistic Calibration.- 4.6 Summary.- 4.7 Notes.- 5 Probabilistic Design.- 5.1 Motivation.- 5.2 Relative Error Criterion.- 5.3 Minimum Variance Criterion.- 5.4 Probabilistic Expansion.- 5.5 Notes.- 6 Adaptive Assay.- 6.1 Motivation.- 6.2 SequentialAnalysis.- 6.3 Adaptive Barrel Assay.- 6.4 Adaptive Assay of a Pulmonary Aerosol.- 6.5 Adaptive Assay of a Uranium Deposit.- 6.6 Notes.- 7 Some Directions For Research.- 7.1 Overview.- 7.2 Nonlinearity in Mass.- 7.3 Non-Convex Response Sets.- 7.4 Asymptotic Designs.- 7.5 Malfunction Isolation.- 7.6 Adaptive Assay: Advanced Concepts.- 7.7 Notes.- Author Index.
