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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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3. 34 IV. 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.

Suppose that and then we can use the system size expansion method mentioned in the previous section. In this way, Eq. (9) becomes a 2-dimensional Langevin equation, with where k is the effective multiplication factor, reactivity, and is the generating time. is the To realize the essence of the contraction in noise sources, let us suppose that the observable variable is the neutron number and the precursor number is a hidden variable. Namely, the observation matrix is H=(1 0). In the discrete time representation we have The time evolution equation of observable variable y in Eqs.

Here we will review it briefly, though a similar theory was already reported by Desai [28] and Aoki [29]. From Eq. (5) we have a relation among P, new matrix where is a and a stable solution of an algebraic equation, If we define a new matrix, then we can obtain three matrices corresponding to H and Q from correlation functions. As in a similar algorithm in deterministic control theory (Ho and Kalman, [30]), we define a Hankel matrix and its associate matrices, and , by arranging equivalent correlation functions, as CONTRACTION OF INFORMATION AND ITS INVERSE PROBLEM where 13 and Output signals in a steady-operated plant are time series data with zero mean, E{y(n)}=0.

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