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

By Jeffery Lewins, Martin Becker

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

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2 K. KISHIDA Weights of AR Poles [51] Since an AR model is a linear equation, it is important to examine properties of its eigenvalues and eigenvectors mathematically. If poles of an AR model correspond to eigenvalues, then weights of AR pole become eigenvectors. Since the asymptotic properties of pole location of AR models have been made clear as in Section IV. 1, we will examine properties of weights. In order to proceed analytically, the following properties of an ARMA (d,1) process are assumed to take advantage of the asymptotic pole location rule of AR-type models: (1) All ARMA poles are located inside the convergence circle.

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.

The two state variables of the theory are the total numbers of neutron and precursor, since the thermal, mechanical, and hydraulic effects are negligible in a zero power reactor. There are mainly two kinds of approaches, such as the Kolmogorov and the Langevin formalisms. By means of the first collision probability method, [35] and Bell [36] examined the branching process in the framework of probability distribution of backward Kolmogorov formalism. The forward Kolmogorov formalism was presented by Courant and Wallance [37] to understand neutron population dynamics.

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