Nuclear Power Generation, Volume Volume J, Third Edition by P.B. Myerscough

By P.B. Myerscough

Nuclear energy new release has gone through significant enlargement and advancements in
recent years; this 3rd variation comprises a lot revised fabric in providing
the cutting-edge of nuclear strength station designs at present in operation
throughout the area. the amount covers nuclear physics and uncomplicated expertise,
nuclear station layout, nuclear station operation, and nuclear protection. each one
chapter is self sustaining yet with the required technical overlap to supply a
complete paintings at the secure and financial layout and operation of nuclear strength

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This section extends the definition to the case of general probability distributions. Intuitively speaking, the relative entropy is defined to measure how close two probability distributions are. I t will be shown that the discrete entropy and the continuous entropy studied in the preceding sections can be expressed as a relative entropy. M RELATIVE ENTROPY Let l i and v be probability measures on a measurable space ( X , B ( X ) ) . , h -< c, i f /i(A) = 0 for every ,4 e B ( X ) such that i/{A) = 0.

5. 8), then H((*\v)< l i m H(p ;u ). 13) is n true. Proof. A t first, we assume that H(fi;v) < co. Then, for any e > 0, there is a partition A = {A\, —, -<4 } such that m H (p\v)> A H{p\v)-e. 9) for the definition of H&(ti; v). By the assumption, for each A i: l i m ft (Ai) n = p{Ai), l i m f„(Ai) n—-co we have = TJ—-co Therefore, i f n is large enough, then |Jf (/i;i/)i/„)| a < e, and This means that lim H& -,v„)>H((ii»)-2e. 13). Next, we assume that H(/i\ v) = oo. 14), we have S a O ; V) > M.

Y\Z) be finite. Then there exist the Radon-Nikodym derivatives , Consequently jixYZ > dpxz . 16) that I(X, (K, 2 ) ) = log a{x, z) diixvzix, / y, z) JXxYxZ + - / \ogff(x,y,z)dp z{x,y,z) XY JX-YxZ I(X,Z) + I(X,Y\Z). 9) is proved by using (1,6) repeatedly. ,Y ). ,y„)) = /{(ji£- ,^ ),(y ,? 5) and the assumption, we see that I(X , l and I(%S,%lXuYi') = i(Xl>%% n 2 %\Yi) Y 1*, 2 ,Yi). 10). U +I(X Y ). 6). 6) is fundamental. 9) are referred to as chain rules for mutual information. 17) of the conditional mutual information.

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