What Have We learned

One interesting lesson that we can learn from having solved problem 3 in Sect. 8.6 is that the larger the number of bioreactors ( ) in series (for the same total volume V) was, the lower the output substrate concentration (S) was. But, possibly, of much greater interest was the discovery that the output substrate concentration was not very sensitive to an increasing number of bioreactors (Table 9.1). 

From the table you will notice that the output substrate concentration decreases with the number of bioreactors, but this is barely noticeable. For example, we increased the number of reactors from 1 to 

9 Fundamentals of Mathematical Modeling, Simulation, and Process Control 

8 (700 %), the substrate concentration just decreased from 33.3 to 30.78 g/L (7.6 %). In this case, intuitively, for several practical and operational reasons, we can infer that it is better to have just one bioreactor instead of several bioreactors in series. 

Mathematical models will help us improve our decisions. In this example, we have developed a tool that allows us to further analyze the system and then find the optimum number of bioreactors. With a good model, we will be able to run simulations of different scenarios, improve our understanding and knowledge of the system, and design better control systems, as we will see in Sect. 9.4. Moreover, with an adequate mathematical model, we can drastically reduce the required number of experiments. 

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Similarides Between Potential Ruid Dynamics and Quantum Mechanics Electrons in the Dirac Theory The Nearly Nonrelativistic Limit The Lagrangean-Density Correction Term Topological Phase for Dirac Electrons What Have We Learned About Spinor Phases ... 

H. What Have We Learned About Spinor Phases ... 

What have we learned in this estimate Surely we can say the age of the earth cannot be shorter than 5 X 10s years. That was when the uranium mineral clock was wound—but the clock could be much older. To evaluate this number further, we must look for other types of data. 

Feldmann M, Maini RN (2001) Anti-TNFa therapy of rheumatoid arthritis what have we learned Ann Rev Immunol 19 163-196... 

V. Ponec, Review Forty years in CATALYSIS what have we learned , Journal of Molecular Catalysis A Chemical 133, 221-239 (1998). 

What have we learned about the modus operandi of the Department of Defense that should prove useful as we move through a transition to a new era for support of science and engineering in the universities First, the Department of Defense, despite its mission-oriented character, has had... 

K. Wuthrich, Six years of protein structure determination by NMR spectroscopy What have we learned in Protein Conformation. Ciba Foundation Symposium 161, John Wiley Sons, Chichester, 1991, pp. 136-149. 

Guengerich, F.P (2004) Cytochrome P450 what have we learned and what are the future issues Drug Metabolism Reviews, 36, 159-197. 

John Dupre I guess what I want to point to is not to deny that there is any evolutionary basis for maternal attachment. The question that I put to you after your talk - what do we learn more than the fairly banal empirical observation that people have certainly made before anybody had ever heard of natural selection, that mothers are generally attached to their children This is an empirical fact. It s one certainly that is entirely consistent with and indeed even implied by the theory of evolution by natural selection. So what do we learn, what have we learned, other than that evolutionary. .. ... 

Couse JF, Korack KS (1999b) Estrogen receptor null mice what have we learned and where will they lead us Endocr Rev 20 358... 

Bernatchez, L. and Landry, C. (2003) MHC studies in nonmodel vertebrates what have we learned about natural selection in 15 years J. Evol. Biol. 16, 363-377. 

Now what have we learned about the companies which have submitted these PMNs Here, on Figure 3, I show the number of PMNs submitted per company as a function of the number of companies for the period from July 1, 1979 through the end of 1981. For example, 61 companies each submitted one PMN, 36 companies submitted two each, and so on. There were 25 companies which submitted more than 10 PMNs each and I can add that the three most prolific developers of new chemicals during this 21/2 year period as judged by this yardstick each submitted 60 or more PMNs. With time, this curve is tending to flatten out as more of these companies submit additional PMNs and at a faster rate than new companies enter the PMN area with their first submissions. 

Shall S, de Murcia G (2000) Poly(ADP-ribose) polymerase-1 what have we learned from the deficient mouse model Mutat Res 460 1-15... 

In summary what have we learned in 25 years In some areas, surprisingly little— for example, we cannot say that we really understand the condensed chromatin fiber structure much better than we did in 1978. Although the significance of the great majority of histone variants remains unknown, replacement histones appear now to be involved in major chromosomal functions. There are areas in which we have accrued incredible amounts of detailed information yet still do not quite know what to do with it. Histone acetylation is a prime example. Allfrey et al. [56] could predict its role in a general sense in 1964. We now know a whole rogue s gallery of acetylases and deacetylases plus the specific histone sites for many. Nevertheless, authorities in the field must still write in 2000, The mechanisms by which histone acetylation affects chromatin structure and transcription is not yet clear [58]. 

Samet JM, Utell MJ The risk of nitrogen dioxide What have we learned from epidemiological and clinical studies Toxicol Ind Health 6 247-262, 1990... 

Huang, S.M. and Lesko, L.J. (2004) Drug-drug, drug-dietary supplement, and drug-dtrus fmit and other food interactions what have we learned Journal of Clinical Pharmacology, 44, 559-569. 

Rather than revisiting the various debates, controversies, and survey findings, I summarize the accumulated empirical evidence in this chapter What have we learned to date about the composition, overall size, and impacts of DTCA in the United States More specifically, in assessing the United States experience with DTCA, I consider four sets of empirical issues (1) What is the magnitude of DTCA relative to other forms ofpharmaceutical... 

Kirn D. Clinical research results with dll520 (Onyz-015), a replication-selective adenovirus for the treatment of cancer What have we learned Gene Therapy 2001 8 89-98. 

Hammerschmidt R. (1999). Phytoalexins what have we learned after 60 Years Annual Review of Phytopathology, 37,285-306. 

Cantwell DP. Hyperactive children have grown up what have we learned about what happens to them. Arch Gen Psychiatry 1985 42 1026-1028. 

Wallace, Lance. 1993. A Decade of Studies of Human Exposure What Have We Learned Risk Analysis 13 (April) 135-39. 

Drug Interactions of Grapefruit and Other Citrus—What Have We Learned ... 

Hoffman GA, Harrington A, Fields, HK Pain and the placebo response What have we learned. Perspect Biol Med 2005 48 248.[PMID 15834197]... 

What have we learned so far The first issue has to do with the scope that the modification of standards would imply. The double standard as a criterion is broader than the scope that appeared to guide the initial reflections. It began by targeting AIDS but quickly pervaded all research. It has affected not only standards of treatment, but also the placebo debate. If it had been introduced into ethical codes like the Declaration of Helsinki, it would have implied a "universal policy" regulating all research. 

Ferry C, Socie G. 2003. Busulfan-cyclophosphamide versus total body irradiation-cyclophosphamide as preparative regimen before allogeneic hematopoietic stem cell transplantation for acute myeloid leukemia What have we learned Exp Hematol. 31 1182-1186. 

Rainov NG, Ren H. 2003. Clinical trials with retrovirus mediated gene therapy - What have we learned J Neurooncol. 65 227-236. 

Zinman B. Insulin pump therapy and rapid acting insulin what have we learned Int J Clin Pract Suppl 2001 (123) 47-50. 

Kumar TR. What have we learned about gonadotropin function from gonadotropin subunit and receptor knockout mice Reproduction. 2005 130 293-302. 

Goldenberg DL. Fibromyalgia syndrome a decade later what have we learned Arch Intern Medi 1999 159 777-785. 

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