Usefulness rule

Hopgood, F.F., N. Woodcock, N.J. HaUam, and P.D. Picton, Interpreting ultrasonic images using rules, algorithms and neural networks , European Journal of NDT, Vol. 2, No. 4, April 1993, pp. 135-149. 

Practical systems will often have mixtures of surfactants. A useful rule is that the CMC of the mixture. Cm, is given by [196,197]... 

Rule 3. If the new vertex has the worst response, then reject the vertex with the second-worst response, and calculate the new vertex using rule 2. This rule ensures that the simplex does not return to the previous simplex. 

More shortcut design methods and rules of thumb have been developed for fractionation than probably any other unit operation. For example the paper reprinted in Appendix 5 on development of shortcut equipment design methods contains 18 references for fractionation shortcut methods out of 37 total. Both the process and mechanical aspects of fractionation design have useful rules of thumb. Many of the mechanical design rules of thumb become included in checklists of do s and don ts. 

We conclude this subsection with a bravo to Bravo" who provides useful rules of thumb for tower retrofits. These are intended for engineers comparing structured packing to high-performance trays for replacing older conventional trays. 

First, one must estimate air or other gas leakage into the vacuum system. Of course every effort is made to keep it as tight as possible. The author is aware of possible leak points being sealed with polystyrene, which produces an excellent seal. When tests cannot be made, one must use rules of thumb. Many such rough estimating techniques exist. 

The term (l/((Un) is sometimes ealled the equivalent time eonstant Tc for a seeond-order system. Note that In50 (2% toleranee) is 3.9, and ln20 (5% toleranee) is 3.0. Thus the transient period for both first and seeond-order systems is three times the time eonstant to within a 5% toleranee band, or four times the time eonstant to within a 2% toleranee band, a useful rule-of-thumb. 

The two Ziegler-Niehols PID tuning methods provide a useful rule of thumb empirieal approaeh. The eontrol system design teehniques diseussed in Chapters 5 and 6 however will generally yield better design solutions. 

It is rare in praetise to work near to the limit given by Shannon s theorem. A useful rule of thumb is to sample the signal at about ten times higher than the highest frequeney thought to be present. 

Choose N based on seale-up studies or eommonly used rules. 

For example, in the case of dilute solutions, the van t Hoff s equation may be used to piedict the osmotic pressure (jr = CRT) where n is the osmotic pressure of the solution, C is the molar concentration of the solute, ft is the universal gas constant and T is the absolute temperature, Fm dissociating solutes, the concentration is that of the total ions. For example, NaCI dissociates in water into two ions Na" " and Cl . Therefore, the total molar concentration of ions is hvice the molar concentration of NaCI. A useful rule of thumb for predicting osmotic pressure of aqueous solutions is 0,01 psi/ppm of solute (Weber, 1972). 

A useful rule of thumb is that the turbine work in a STIC plant is increased by a factor of about (1 + 25), since the specific heat of the steam is about double that of the specific heat of the dry gas. This is in agreement with the example given above and with the earlier detailed calculations by Fraize and Kinney [3]. (Their work was based on the assumption that the mixture of air and steam in the turbine behaved as a semi-perfect gas, with specific heats being determined simply by mass averaging of the values for the two components.)... 

This is a very useful rule to apply it you start with the Lewis structure. 

FIGURE 11.12 Overextrapolation of data, (a) Nonlinear curve fitting techniques estimate an ordinate maximal asymptote that is nearly 100% beyond the last available data point, (b) The curve fitting procedure estimates a maximal asymptote much closer to the highest available data point. A useful rule is to reject fits that cause an estimated maximal asymptote that is >25% the value of the highest available data point. 

First, we assign oxidation numbers to each element, using rules 1-5. We find... 

This same sensitivity can, however, be misleading. Even minor radical routes to a particular reaction product could give rise to intense polarized n.m.r. signals which could obscure the normal monotonic increase of the signal due to product formed by a non-radical route. This problem can be overcome in some cases by estimation of the spectral enhancement factor. Again, it is not possible to justify a firm, threshold value, but as a useful rule of thumb when enhancements fall below about 100 then the possibility of an important alternative non-radical route to the same product should be carefully investigated. 

Thus, if 5 = 1mm, / = 15.8 Hz. This very simple result is quite useful for approximately evaluating the gravity driven deflections of a stmeture given its natural frequency, or visa versa. Of course this was derived for a specific and very simple system, so it does not perfectly apply to more complex systems. Still it is a very useful rule of thumb. For a mass on the end of a cantilever beam, the above formula is correct. The lowest natural frequency of a massive cantilever beam is about 1.2 x the prediction of the above formula. 

Increase the nonpolar character of the solute by using rules Pb(WS) = 0.5 and J(WS) = 0.7. Keep all the other rules constant. Run each experiment 10 times and collect and average the fi values. Repeat the study using a more nonpolar parameter set for the solute, for example Pb(WS) = 0.8 and J(WS) = 0.25. Other parameters are retained as in Example 4.3. Record the fx values and the average cluster size for water at the end of each run. 

Obtain a thorough history of prescription, nonprescription, natural, and illicit drug product use. Rule out medications or medical disorders that may cause or mimic depressive symptoms. 

EPA. 1992. Chemicals toxic chemical release reporting community right-to-know proposed significant new use rule. U.S. Environmental Protection Agency. Federal Register 57(174) 41020. 

The information to which the rule is applied might be extracted from the knowledge base, it might be provided by the user in response to questions from the ES, or it may be provided by combining the two. An expert system that uses rule-based reasoning is, quite reasonably, known as a rule-based system. This is the most widely used form of expert system in science, and it is on this type of system that this chapter concentrates. 

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