Deterministic Design II: General Formulation

  • Yakov Ben-Haim
Part of the Mathematics and Its Applications book series (MAIA, volume 20)


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.


Convex Hull Auxiliary Parameter Thickness Profile Resolution Capability Uranium Hexafluoride 
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  1. [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. [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. [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. [4]
    P. A. M. Dirac, The Principles of Quantum Mechanics, Cambridge Univ. Press, 1958.zbMATHGoogle Scholar
  5. [5]
    Y. Ben‐Haim, Convex Sets and Nondestructive Assay, S. I. A. M. J. Alg. Disc. Methods, accepted for publication.Google Scholar
  6. [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. [7]
    See ref. [7.2] of Chapter 2, pl45.Google Scholar
  8. [8]
    A. Friedman, Foundations of Modern Analysis, Dover 1982.zbMATHGoogle Scholar
  9. [9]
    See section 5.3 of ref. [7.2] of Chapter 2.Google Scholar
  10. [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. [11]
    See refs. [7] and [12] of Chapter 1 andGoogle Scholar
  12. 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
  13. [12]
    See ref. [7] of Chapter 1.Google Scholar
  14. [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
  15. The advantages of employing a high energy‐resolution germanium detector are explored inGoogle Scholar
  16. 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
  17. [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
  18. 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
  19. [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
  20. 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
  21. [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
  22. 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
  23. 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
  24. 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
  25. [18]
    See refs. cited in ref. [16.1] of Chapter 1 and:Google Scholar
  26. J. A. Oyedele, Spatial Effects in Radiation Diagnosis of Two‐Phase Systems, Int. J. Appl. Rad. Isot., 35: 865 – 73 (1984).CrossRefGoogle Scholar
  27. [19]
    T. A. Boster, Source of Error in Foil Thickness Calibration by X‐ray Transmission, J. Appl. Phys., 44: 3778 – 81 (1973).CrossRefGoogle Scholar
  28. [20]
    J. A. Oyedele, The Bias in On‐Line Thickness Calibration by Radiation Transmission, Nucl. Instr. Meth., 217: 507 – 14 (1983).CrossRefGoogle Scholar
  29. [21] 1.
    H. Harmuth, Transmission of Information by Orthogonal Functions, Springer‐Verlag, 1972.zbMATHGoogle Scholar
  30. 2.
    S. Tzafestas and N. Chrysochoides, Nuclear Reactor Control Using Walsh Function Variational Synthesis, Nucl. Sci. Eng., 62: 763 – 70 (1977).Google Scholar
  31. [24]
    Thorough expositions of dynamic programming may be found in many sources, including the following.Google Scholar
  32. 1.
    R. Bellman, Dynamic Programming, Princeton University Press, 1957.zbMATHGoogle Scholar
  33. 2.
    R. Bellman, Introduction to the Mathematical Theory of Control Processes, Vol I, Academic Press, 1967.zbMATHGoogle Scholar
  34. 3.
    R. Bellman, Introduction to Matrix Analysis, McGraw‐Hill, 1970.zbMATHGoogle Scholar
  35. 4.
    R. Bellman, Methods of Nonlinear Analysis, Academic Press, 1973.zbMATHGoogle Scholar
  36. [25]
    M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, 1982.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1985

Authors and Affiliations

  • Yakov Ben-Haim
    • 1
  1. 1.Department of Nuclear EngineeringTechnion-Israel Institute of TechnologyIsrael

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