Download PDF by D. Ramkrishna (auth.): Advances in Biochemical Engineering, Volume 11

By D. Ramkrishna (auth.)

ISBN-10: 354008990X

ISBN-13: 9783540089902

ISBN-10: 3540356789

ISBN-13: 9783540356783

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Mathematical Methods in Chemical Engineering. New Jersey: Prentice Hall 1973 Powell, E. : J. Gen. Microbiol. 15, 492 (1956) Harris• T. : The The•ry •f Branching Pr•cesses. : Methods of Mathematical Physics. Vol. 1. New York: Interscience 195: Eakman, J. , Fredrickson, A. , Tsuchiya, H. : Chem. Eng. Prog. Symp. Series, No. 69. 62, 37 (1966) Bertalanffy, L. yon: Human Biol. 10, 280 (1938) Bertalanffy, L. yon: Theoretische Biologie. : Math. Biosci. 10, 1 (1971) Hulburt, H. , Katz, S. : Chem. Eng.

Amundson, N. : Mathematical Methods in Chemical Engineering. New Jersey: Prentice Hall 1973 Powell, E. : J. Gen. Microbiol. 15, 492 (1956) Harris• T. : The The•ry •f Branching Pr•cesses. : Methods of Mathematical Physics. Vol. 1. New York: Interscience 195: Eakman, J. , Fredrickson, A. , Tsuchiya, H. : Chem. Eng. Prog. Symp. Series, No. 69. 62, 37 (1966) Bertalanffy, L. yon: Human Biol. 10, 280 (1938) Bertalanffy, L. yon: Theoretische Biologie. : Math. Biosci. 10, 1 (1971) Hulburt, H. , Katz, S.

K=l k=l n "/ikRk(Z,C)] [ k=l ~/jkRk(Z, C)] fl(Z; C; t) (96) Again as before, Eq. (96) reinforces the necessity for calculating higher order product densities if fluctuations about expected values are to be calculated. The expected value of C(t) is obtained from EIC(t)] = f c fc(c, t)dc (97) and for the second moment, the following covariance terms are evaluated. E[CiCj] = f cicj fc(e, t)dc (98) Finally, we consider a function F(C), which is analytic in C and examine its expected value E[F(C)].

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