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Download e-book for iPad: Advances in Nuclear Science and Technology, Volume 23 by Jeffery Lewins, Martin Becker

By Jeffery Lewins, Martin Becker

ISBN-10: 0306451840

ISBN-13: 9780306451843

ISBN-10: 0306478102

ISBN-13: 9780306478109

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

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Extra resources for Advances in Nuclear Science and Technology, Volume 23

Sample text

Poles of the AR model are roots of in the Let the number of time-series data be assumed to be so large that the statistical error of the correlation function is negligible. However, there still remains a bias between the ARMA model (4) and a fitted AR model (6). From the viewpoint of system identification or diagnosis, it is important to know dynamic properties of the fitted AR model, of which the coefficients are determined from the normal equation, owing to the minimum prediction error. Coefficients of the AR model are related recursively by nonlinear transformations [40,41], and we cannot know the properties of AR poles analytically.

11), we have If we put components as From Eq. (13) we have Eq. D. (5), Eq. (15) can be transformed 30 K. KISHIDA into where with The degree of the polynomial is d, and that of varies with the order of the TAR model. On some closed domain in the plane it can be evaluated that is finite and that the absolute value of decreases to zero as Using the difference on the TAR model order dependence between and we can determine the number of roots of in a suitable closed domain. By using the Rouché Theorem, the asymptotic nature of pole location of TAR model can be stated in three following Theorems: Theorem 1: For any real number there exists some positive integer such that if the TAR model of order m has poles in the region of And poles of the TAR model converge to system poles as m becomes large.

Since roots of inside C" are and there are m roots of inside C". Therefore there exist in poles of in the circular region between C and C". In the case where there are also m+1 roots of inside C" for There are m-1 roots of inside C". In the outer region of C" there is a single real root of since the number of total roots is m. This pole of the TAR model outside the convergence circle is called a "non-robust singular" pole. Therefore there exist poles of in the circular region between C and C", and a single real pole in the outer region of C".

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


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