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By C. R. Weisbin (auth.), Jeffery Lewins, Martin Becker (eds.)

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Otherwise, this approximation has seemed adequate up to now for the propagation of uncertainties inherent in nuclear data in analysis of fast reactor cores (12) (and probably in thermal reactor shields) and marginally adequate for fast reactor shields (13) and thermal reactor cores (14). Unless a few-group approximation is employed, the symmetric nuclear data uncertainty matrix is very large, especially if one keeps separate the contributions of the various nuclides and partial cross-sections. Traditionally, the data vector is built up of segments for each material, further subdivided by reaction type and then energy.

In such analyses the linear uncertainty quantities like oa often are called disturbances or errors; they correspond not to mistakes but to the differences of unsure sign and magnitude that are represented by the density function. c. The uncertainty Matrix for Discrete Quantities. The concept of covariance is readily extended to the components 19 UNCERTAINTY IN NUCLEAR DATA y. ). ) The elements of the variance-covariance or uncertainty matrix V:: (Vij) are just V. 1J (6) E ( oy. oy. ) , = 1 J and the other definitions of the above subsections are carried forward.

1J '=)' and the solution is a weighted averL, age of the observations: (16a) 35 UNCERTAINTY IN NUCLEAR DATA 2- where w = 1 (W 1l + w2 ). tru~ value and = w + (l-w) ' The we1ght matr1x affects the value of y only through the combination of components w. Note that theenumerical values of the observations y. are precisely identified as the expected values of the aensity functions of the corresponding experiment~l results, and the is the evaluated value to represent the position of the e~aluated density function.

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