Subject maximum-minimum

The problem involved in the application which is the subject of this chapter is the optimisation of a property of a mixture of compounds (a common situation in pharmaceutical practice, where for example tablet formulations have to be optimised). This property has to be optimised with respect to a certain goal (maximum, minimum or target value) and also with respect to the robustness or ruggedness of the mixture property. This means that despite any variation in the response or the independent variables (mixture variables in our case) due to unknown variation the response values have to be as close as possible to a desired value (target value). 

After a single oral dose of 100 mg given to 6 subjects, peak serum concentrations of about 2 xg/ml were attained in 1 hour (F. Nielsen-Kudsk and A. K. Pederson, Acta pharmac. tox., 1979,44, 391-399). Following oral administration of 50 mg three times a day to 10 subjects, maximum steady-state plasma concentrations of 0.4 to 2.6 pg/ml (mean 1.4) were reported trough concentrations were 0.1 to 1.5 ig/ml (mean 0.7). In 10 subjects given 75 mg twice daily, the corresponding maximum and minimum steady-state concentrations were 0.5 to 4 pg/ml (mean 1.7) and 0.1 to 2.6 pg/ml (mean 0.9) (C. Mahony et al., J. din. Pharmac., 1983, 23,123-126). 

Following oral administration of 250 mg of erythromycin four times a day to 16 subjects, maximum and minimum steady-state plasma concentrations of 1.7 and 0.45 pg/ml were reported on the third day, compared to 1.34 and 0.58 pg/ml respectively, following repeated oral administration of erythromycin estolate (A. R. DiSanto et al., J. din. Pharmac., 1980, 20, 437-443X... 

Each is subjected to one of the maximum-minimum stress cycles listed in the following table the frequency is the same for all three tests. 

If there is insufficient data to describe a continuous probability distribution for a variable (as with the area of a field in an earlier example), we may be able to make a subjective estimate of high, medium and low values. If those are chosen using the p85, p50, pi 5 cumulative probabilities described in Section 6.2.2, then the implication is that the three values are equally likely, and therefore each has a probability of occurrence of 1/3. Note that the low and high values are not the minimum and maximum values. 

In so doing, we obtain the condition of maximum probability (or, more properly, minimum probable prediction error) for the entire distribution of events, that is, the most probable distribution. The minimization condition [condition (3-4)] requires that the sum of squares of the differences between p and all of the values xi be simultaneously as small as possible. We cannot change the xi, which are experimental measurements, so the problem becomes one of selecting the value of p that best satisfies condition (3-4). It is reasonable to suppose that p, subject to the minimization condition, will be the arithmetic mean, x = )/ > provided that... 

In practice, industrial crystallization processes are subject to a number of constraints, which tend to limit equipment selection. For example, since particle size and purity tend to be such important variables, equipment and operating conditions that induce minimum particle breakdown or achieve maximum crystal purity are normally desirable. 

The baffle cut determines the fluid velocity between the baffle and the shell wall, and the baffle spacing determines the parallel and cross-flow velocities that affect heat transfer and pressure drop. Often the shell side of an exchanger is subject to low-pressure drop limitations, and the baffle patterns must be arranged to meet these specified conditions and at the same time provide maximum effectiveness for heat transfer. The plate material used for these supports and baffles should not be too thin and is usually minimum thick-... 

With 77 % aqueous acetic acid, the rates were found to be more affected by added perchloric acid than by sodium perchlorate (but only at higher concentrations than those used by Stanley and Shorter207, which accounts for the failure of these workers to observe acid catalysis, but their observation of kinetic orders in hypochlorous acid of less than one remains unaccounted for). The difference in the effect of the added electrolyte increased with concentration, and the rates of the acid-catalysed reaction reached a maximum in ca. 50 % aqueous acetic acid, passed through a minimum at ca. 90 % aqueous acetic acid and rose very rapidly thereafter. The faster chlorination in 50% acid than in water was, therefore, considered consistent with chlorination by AcOHCl+, which is subject to an increasing solvent effect in the direction of less aqueous media (hence the minimum in 90 % acid), and a third factor operates, viz. that in pure acetic acid the bulk source of chlorine ischlorineacetate rather than HOC1 and causes the rapid rise in rate towards the anhydrous medium. The relative rates of the acid-catalysed (acidity > 0.49 M) chlorination of some aromatics in 76 % aqueous acetic acid at 25 °C were found to be toluene, 69 benzene, 1 chlorobenzene, 0.097 benzoic acid, 0.004. Some of these kinetic observations were confirmed in a study of the chlorination of diphenylmethane in the presence of 0.030 M perchloric acid, second-order rate coefficients were obtained at 25 °C as follows209 0.161 (98 vol. % aqueous acetic acid) ca. 0.078 (75 vol. % acid), and, in the latter solvent in the presence of 0.50 M perchloric acid, diphenylmethane was approximately 30 times more reactive than benzene. 

A large thermoplastic sheet, 10 mm thick, at an initial temperature of 20 C (293 K). is to be heated in art oven in order to enable it to be moulded. The oven temperature is maintained at 100°C (373 K), the maximum temperature to which the plastic may be subjected, and it is necessary to ensure that the temperature throughout the whole of the sheet reaches a minimum of 80 °C (353 K). Calculate the minimum length of time for which the sheet must be heated. 

In order to answer these questions, the kinetic and network structure models were used in conjunction with a nonlinear least squares optimization program (SIMPLEX) to determine cure response in "optimized ovens ". Ovens were optimized in two different ways. In the first the bake time was fixed and oven air temperatures were adjusted so that the crosslink densities were as close as possible to the optimum value. In the second, oven air temperatures were varied to minimize the bake time subject to the constraint that all parts of the car be acceptably cured. Air temperatures were optimized for each of the different paints as a function of different sets of minimum and maximum heating rate constants. 

If the penalty weight w is larger than the maximum of the absolute multiplier values for the problem, then minimizing P(x, w) subject to 1 x < u is equivalent to minimizing/in the original problem. Often, such a threshold is known in advance, say from the solution of a closely related problem. If w is too small, PSLP will usually converge to an infeasible local minimum of P, and w can then be increased. Infeasibility in the original NLP is detected if several increases of w fail to yield a... 

For prefilming type of atomizers, minimum droplet sizes are obtained with nozzle designs that spread liquid into thinnest sheet before subjecting its both sides to air-blast action 86] and provide maximum contact between liquid and air. 468 From experimental data obtained over a wide range of process conditions and material properties, it was found 469 that the effect of liquid viscosity on the mean droplet size is independent of that of surface tension and air velocity. Therefore, the mean droplet size can be expressed as a sum of two terms one dominated by surface tension, air velocity and air density, and the other by liquid viscosity, as suggested by Lefebvre 4691... 

The Class A Prescription balance has a sensitivity requirement of 6 mg with no load and with a load of 10 g on each pan. Subject to the physical limitation of the material being weighed, the maximum amount that can be weighed on this balance is 120 g. A Class B prescription balance has a sensitivity requirement of 30 mg. The minimum amounts that can be weighed with an error of not more than 5% on Class A and Class B balances are 120... 

The (3-glucuronidase activity of human blood has been studied by Fishman and co-workers.26 The range in 230 normals was found to be from 41 to 1285 units per 100 ml. of serum. In the diseased subjects studied, the minimum values tended to be higher and the maximum values were up to 2340 units. 

Changes in such physical factors as light, temperature (particularly maximums and minimums), relative humidity, and wind speed in forest communities subject to structural alteration by mortality of susceptible species could change the suitability of some sites for growth, reproduction, and re-establishment of survivor species. We can only speculate on some of the possible secondary effects until more data are gathered. ... 

Unless your instructor has asked you to use a certain number of sources, there is no maximum or minimum number of citations that any research paper should contain. In other words, some topics and papers require a lot of documentation, particularly if the subject matter is controversial or previously undocumented, while other subjects require very little. When in doubt about whether to footnote a particular statement, it is usually better to back up any statement that may need support with a proper footnote or citation. Remove any doubt that may be lingering in the reader s mind about the authenticity of your research. However, if you are writing many footnotes, which may be perfectly legitimate for your paper and subject matter, you may have questions such as, What do I do if I have to cite the same page twice in a row Or, you may find that you have multiple citations that come from the same author and are on the same page. Do you have to have to write out all that material over and over again The answer is no. Once you have provided the full information on any book or source that you have consulted, you do not have to mention all that material again. Footnotes that immediately follow one another and are taken from the... 

---