Download Advances in Nuclear Science and Technology, Volume 23 by Jeffery Lewins, Martin Becker PDF

By Jeffery Lewins, Martin Becker

Quantity 23 makes a speciality of perturbation Monte Carlo, non-linear kinetics, and the move of radioactive fluids in rocks.

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Advances in Nuclear Science and Technology, Volume 23

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3) There are no robust and/or non-robust singular poles. Let a scalar ARMA (d,1) model under these assumptions be expressed by where (j=1, 2, . . , d) are system (ARMA) poles and is an ARMA zero. Weights of poles of the AR model Eq. (6), are defined b y : Though coefficients of the AR model are determined from the fast recursion algorithm, we cannot treat the AR model analytically. 1. That is, from Eq. (18), where the TAR of order m is defined by truncating at the mth power of Furthermore, the TAR-type model can be approximately expressed as, for large m, CONTRACTION OF INFORMATION AND ITS INVERSE PROBLEM where The 35 last polynomial of the TAR model can be written where In this seen that the zero is equivalent to lar poles Then, the transfer function of Eq.

KISHIDA under the controllability and observability conditions of H and G [25]. For simplicity, we assume hereafter that all finite poles and zeros are distinct. Since HG is a nonsingular matrix, system zeros are determined from the characteristic equation (7): From Eq. (8), system zeros in the plane are reciprocal numbers of eigenvalues of It should be noted that all system poles in the plane lie outside the unit circle in the complex plane from the assumption of stability. However, the system zeros distribute in the total plane.

1 are follows: 22 K. KISHIDA Then we have In this way we obtain where and After the interchange of columns, we obtain the system matrix mentioned in Eq. 13). For the 2 dimensional case, we can rewrite Eq. 5) as where and From Eq. (24) , we have and then an ARMA model via Eq. (23) is the same as Eq. (21). The details have been reported in papers [34,39]. Hence, the formalism developed in Section II can be applied to the analysis of power reactors with complicated reactions from the viewpoint of contraction of information.

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