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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15) and the relation Eqs. (18) and (19), we have a backward time evolution equation for the observable variable y: and for a forward time evolution we obtain Since there remains a difficulty in generalization of the above procedure to a higher-dimensional case, we have examined the systematic derivation of the ARMA model, Eq. 9), via the innovation representation, Eqs. 4). 10), where and is the i,j element of P. Since H=(1. 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.

We can easily understand that eigenvalues of are stable from Eq. 5). From Eq. 3 Independence of Random Forces Suppose that a reactor is assumed to be a nonminimum phase feedback system, then some system zeros in the case of the plane lie inside the unit circle in the complex plane, though all system poles are outside the unit circle in the plane. In this case, we need one other assumption to estimate the open loop transfer functions, such that P is a block diagonal matrix. It has already been shown in control theory [57,58] that the block diagonal matrix of P is a necessary and sufficient condition for identification of open loop transfer functions in a 4-block feedback system, and that the assumption of independence of noise sources is one of sufficient conditions to obtain the block diagonal matrix of P.

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.

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