The Assay of Spatially Random Material pp 85-169 | Cite as
Deterministic Design II: General Formulation
- 101 Downloads
Abstract
The previous Chapter was devoted to developing the conceptual foundations of the deterministic design-analysis. The concept of relative mass resolution was introduced as a deterministic measure of performance. The convexity theorem established a simple analytic relation between the point-source response set and the complete response set. This Theorem leads to the conclusion that the relative mass resolution is precisely equal to the expansion of the complete response set. Furthermore, an efficient computerizable min-max algorithm was established which enables evaluation of the expansion of the complete response set, while requiring explicit knowledge only of the point-source response set. Finally, the concept of relative mass resolution was extended to include the statistical uncertainty of the measurement.
Keywords
Convex Hull Auxiliary Parameter Thickness Profile Resolution Capability Uranium HexafluoridePreview
Unable to display preview. Download preview PDF.
References
- [1]P. Kehler, Accuracy of Two‐Phase Flow Measurement by Pulsed Neutron Activation Techniques, in Multiphase Transport Fundamentals, Reactor Safety Applications, Vol. 5, p.2483, Hemisphere Pub., 1980.Google Scholar
- [2]M. Perez‐Griffo et al, Basic Two‐Phase Flow Measurements Using N‐16 Tagging techniques, NUREG/CR‐0014, Vol. 2, pp. 923, 1980.Google Scholar
- [3]P. B. Barrett, An Examination of the Pulsed‐Neutron Activation Technique for Fluid Flow Measurements, Nucl. Eng. Design, 74: 183 – 92, (1982).CrossRefGoogle Scholar
- [4]P. A. M. Dirac, The Principles of Quantum Mechanics, Cambridge Univ. Press, 1958.zbMATHGoogle Scholar
- [5]Y. Ben‐Haim, Convex Sets and Nondestructive Assay, S. I. A. M. J. Alg. Disc. Methods, accepted for publication.Google Scholar
- [6]For sets in Euclidean space, compactness and closed‐bounded‐ ness are equivalent. Compactness is however a much more general concept, whose properties we shall exploit.Google Scholar
- [7]See ref. [7.2] of Chapter 2, pl45.Google Scholar
- [8]A. Friedman, Foundations of Modern Analysis, Dover 1982.zbMATHGoogle Scholar
- [9]See section 5.3 of ref. [7.2] of Chapter 2.Google Scholar
- [10]M. H. Dickerson, K. T. Foster and R. H. Gudiksen, Experimental and Model Transport and Diffusion Studies in Complex Terrain, 29th Oholo Conf. on Boundary Layer Structure and Modelling, Zichron Ya’acov, Israel, March 1984.Google Scholar
- [11]See refs. [7] and [12] of Chapter 1 andGoogle Scholar
- R. E. Goans and G. G. Warner, Monte Carlo Simulation of Photon Transport in a Heterogeneous Phantom ‐I: Applications to Chest Counting of Pu and Am, Health Physics, 37: 533 – 42 (1979).CrossRefGoogle Scholar
- [12]See ref. [7] of Chapter 1.Google Scholar
- [13]C. D. Berger, R. E. Goans and R. T. Greene, The Whole Body Counting Facility at Oak Ridge National Laboratory: Systems and Procedure Review, ORNL/TM‐7477 (1980).Google Scholar
- The advantages of employing a high energy‐resolution germanium detector are explored inGoogle Scholar
- 2.C. D. Berger and R. E. Goans, A comparison of the Nal‐ Csl Phoswich and a Hyperpure Germanium Detector Array for In‐VivoDetection of the Actinides, Health Physics, 40: 535 – 42 (1981).CrossRefGoogle Scholar
- [14]J. D. Brain and P. A. Valberg, Deposition of Aerosol in The Respiratory Tract, Amer. Rev. Respiratory Disease, 120: 1325 – 73 (1979).Google Scholar
- 2.C. P. Yu and C. K. Diu, Total and Regional Deposition of Inhaled Aerosols in Humans, J. Aerosol Sci., 14: 599 – 609 (1983).CrossRefGoogle Scholar
- [15] 1.J. D. Brain et al, Pulmonary Distribution of Particles Given by Intratracheal Instillation or by Aerosol Inhalation, Environmental Research, 11: 13 – 33 (1976).CrossRefGoogle Scholar
- 2.S. M. Morsy et al, A Detector of Adjustable Response for the Study of Lung Clearance, Health Physics, 32: 243 – 51 (1977).CrossRefGoogle Scholar
- [17] 1.I. S. Boyce, J. F. Cameron and D. Pipes, Proc. Symp. on Nuclear Techniques in the Basic Metal Industries, vol.1, pl55, IAEA, 1973.Google Scholar
- 2.R. Bevan, T. Gozani, and E. Elias, Nuclear Assay of Coal, Electric Power Research Institute report EPRI‐FP‐989, vol. 6, 1979.Google Scholar
- 3.E. Elias, W. Pieters and Z. Yom‐Tov, Accuracy and Performance Analysis of a Nuclear Belt Weigher, Nucl. Instr. Meth., 178: 109 – 115 (1980).CrossRefGoogle Scholar
- 4.J. B. Cummingham et al, Bulk Analysis of Sulfur, Lead, Zinc and Iron in Lead Sinter Feed Using Neutron Inelastic Scatter Gamma‐Rays, Int. J. Appl. Rad. Isot., 35: 635 – 43 (1984).CrossRefGoogle Scholar
- [18]See refs. cited in ref. [16.1] of Chapter 1 and:Google Scholar
- J. A. Oyedele, Spatial Effects in Radiation Diagnosis of Two‐Phase Systems, Int. J. Appl. Rad. Isot., 35: 865 – 73 (1984).CrossRefGoogle Scholar
- [19]T. A. Boster, Source of Error in Foil Thickness Calibration by X‐ray Transmission, J. Appl. Phys., 44: 3778 – 81 (1973).CrossRefGoogle Scholar
- [20]J. A. Oyedele, The Bias in On‐Line Thickness Calibration by Radiation Transmission, Nucl. Instr. Meth., 217: 507 – 14 (1983).CrossRefGoogle Scholar
- [21] 1.H. Harmuth, Transmission of Information by Orthogonal Functions, Springer‐Verlag, 1972.zbMATHGoogle Scholar
- 2.S. Tzafestas and N. Chrysochoides, Nuclear Reactor Control Using Walsh Function Variational Synthesis, Nucl. Sci. Eng., 62: 763 – 70 (1977).Google Scholar
- [24]Thorough expositions of dynamic programming may be found in many sources, including the following.Google Scholar
- 1.R. Bellman, Dynamic Programming, Princeton University Press, 1957.zbMATHGoogle Scholar
- 2.R. Bellman, Introduction to the Mathematical Theory of Control Processes, Vol I, Academic Press, 1967.zbMATHGoogle Scholar
- 3.R. Bellman, Introduction to Matrix Analysis, McGraw‐Hill, 1970.zbMATHGoogle Scholar
- 4.R. Bellman, Methods of Nonlinear Analysis, Academic Press, 1973.zbMATHGoogle Scholar
- [25]M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, 1982.Google Scholar