Read e-book online Advances in Biochemical Engineering, Volume 11 PDF

By D. Ramkrishna (auth.)

ISBN-10: 354008990X

ISBN-13: 9783540089902

ISBN-10: 3540356789

ISBN-13: 9783540356783

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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. Sci. : Chem. Eng. Sci. : The Method of Weighted Residuals. , Fredrickson, A. , Tsuchiya, H. : Bull. Math. Biophys. 3~ 521 (1970) Statistical Models of Cell Populations 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.

The explicit time-dependence in this function would be clear from the following expression for F(a, t) based on the total probability theorem. f~(a, t) f2(a, t) P(a, t) = Pl(a) fl--~-fft)+ P2(a) 2 fl(a, t) (130) In Eq. (130) the coefficient of Fl(a) is the probability that a cell of age a is a singlet, while the coefficient of F2(a) is the probability that the said cell is one of a doublet. In general, these probabilities are clearly time-dependent. Eq. (129) may now be written as a fl(a, t) + 0 fl(a, t) = -P(a, t) fl(a, t) 0-i- (131) which is the same as Von Foerster's equation (Eq.

19. 20. 21. 22. 23. 24. 25. Athreya, K. , Ney, P. : Branching Processes. New York: Springer 1972 Tsuchiya, H. , Fredrickson, A. : Advan. Chem. Eng. 6, 125 (1966) Fredrickson, A. , Tsuchiya, H. : Math. Biosci. 1, 327 (1967) Bharucha-Reid, A. : Elements of the Theory of Markov Processes and their Applications. : Vectors, Tensors and the Basic Equations of Fluid Mechanics. New Jersey: PrenticeHall 1962, pp. 85 Hulburt, H. , Katz, S. : Chem. Eng. Sci. : The Kinetics of Cellular Proliferation (F. ).

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