IF-THEN

In a more favourable case, the wavefiinction ]i might indeed correspond to an eigenfiinction of one of the operators. If = //, then a measurement of A necessarily yields and this is an unambiguous result. Wliat can be said about the measurement of B in this case It has already been said that the eigenfiinctions of two commuting operators are identical, but here the pertinent issue concerns eigenfunctions of two operators that do not conmuite. Suppose / is an eigenfiinction of A. Then, it must be true that... 

Fuzzy Logic Control The apphcation of fuzzy logic to process control requires the concepts of Fuzzy rules and fuzzy inference. A fuzzy rule, also known as a fuzzy IF-THEN statement, has the form ... 

One can readily appreciate the usefulness of pK value in purification procedures, e.g. as when purifying acetic acid. If acetic acid is placed in aqueous solution and the pH adjusted to 7.76 [AcOH]/[AcO ] with a ratio of 0.1/99.9], and extracted with say diethyl ether, neutral impurities will be extracted into diethyl ether leaving almost all the acetic acid in the form of AcO in the aqueous solution. If then the pH of the solution is adjusted to 1.67 where the acid is almost all in the form AcOH, almost all of it will be extracted into diethyl ether. 

If the pattern does not fit into an immediately identifiable pattern, the process worker may then consciously apply more explicit "if-then" rules to link the various symptoms with likely causes. Three alternative outcomes are possible from this process. If the diagnosis and the required actions are very closely linked (because this situation arises frequently) then a branch to the Execute Actions box will occur. If the required action is less obvious, then the branch to the Select/Formulate Actions box will be likely, where specific action rules of the form "if situation is X then do Y" will be applied. A third possibility is that the operating team are unable or imwilling to respond immediately to the situation because they are uncertain about its implications for safety and/or production. They will then move to the Implications of plant state box. 

IF(e) THEN—Block if, where e is a logical expression, followed by a sequence of statements and completed by an ENDIF statement. The block may include sub-blocks introduced by one or more ELSEIF statements and/or one ELSE statement and all sub-blocks may contain nested IF-THEN-ELSE blocks within them. For example,... 

Let us next consider a non-uniform field, where the intensity X is a function of position. The expression (7) applies to unit volume if then (7) is multiplied by dv, the expression will give the amount of free energy lost in an clement of volume dv, where the field has an intensity X. The total loss of free energy will be obtained by integrating over the whole volume of the homogeneous dielectric ... 

P(t) favors longer periods of contact than occur between two II20 molecules in pure water. Furthermore, a small ion allows in (39) a closer approach than a larger ion. If then we consider water molecules in contact with Na+ in aqueous solution, we may expect to find that p(r) favors longer duration of contact than in the case of K+, Rb+, or Cs+. 

If, then, values of w/(A0 — A ) obtained from experiment are plotted against the molarity of the water n, a straight line should be obtained, of which the slope is (X+ — X +) and the intercept — r. The results1 in methyl and ethyl alcohol are shown in Fig. 62. It will be seen that from the intercept the value r = 0.25 is obtained in methyl, and r = 0.06 in ethyl. In each solvent the mobility of the (HaO)+ ion is found to be not very different from that of the Na+ ion. 

For comparison, consider now the same ions in methanol solution. Each ionic field will contain more electrostatic energy than the corresponding ionic field in aqueous solution. Suppose that again we raise a proton from the occupied level of a (NIIi) ion to the vacant level of a (CH3COO)- ion. In this process the amount of electrostatic energy released will be greater than in water. If then the value of, / is roughly the same as before, the total amount of work required to transfer the proton will be smaller than in water. Hence, in the chart of the proton levels in methanol, we expect that the interval between these two proton levels will be narrower than in Fig. 36. 

If then we construct a tentative diagram for the proton levels in formic acid solution, the gap between the vacant level of (JICOO)- and the occupied level of HjO will be a little wider than in Fig. 36. This has been shown in Fig. 65. 

The important thing about such a spectrophotometric curve is that it describes a physical property of the material that is fundamentally related to its color. If, then, the color-determining component can be extracted from the product under test, a... 

The expert s use of stracture properly relations can be expressed in if. .. then. .. clauses (Fig. 9.2) as rules to cormect properties to stractures. In such relations stmctures are assigned to a smaller scale compared to properties. Examples are If you have particles with a small diameter (scale = 10 m), then the cormection is less strong (scale = 10 m) , and If I observe a high value of shrinkage (scale = 10 ), then it may have resulted in a low porosity (scale = 10 " m) . Ten stmcture - property relations were identified, but only one stractureHStractme relation was found If I keep defects [stracture] small then I must start with particles... 

Stmcture-property relations usually have a qualitative character (words, causal relations) and can be expressed as if-then clauses by this is an existing property, then it is caused by this type of stmcture or Hf this is the existing stracture, then probably this property can be expected . Stmcture-property relations at the same scale (horizontally) were not found all relations were links between two different (meso-) levels. Stmcture-property relations are different for the different tasks, and even within the same domain (e.g. ceramics) may well be different when the type of requirements is different (e.g. unbreakable versus resistant to certain chemicals). The relations will be specific for specific stmctures and specific properties, e.g. the strength of a jacket, a set of mats, one mat, a cluster of fibres, or one fibre. 

It is advantageous to attach the micropipet to a sampler diluter. In this manner, the sample is aspirated by means of a plunger. The technician is not required to adjust the volume nor to make a judgement, because this is being done by a plunger, and accuracy is a function of the sampler diluter. If then one wipes off the tip and then ejects a diluting fluid, one could then proceed to measure out very small samples limited only on the nature of the tip. This can be seen in the sequence of events in Figure 7. 

With somewhat greater generality we may let a represent the actual branching probability determined by the extent of condensation irrespective of whether or not the critical point has been exceeded, while a is the lowest root of Eq. (20) for the same value of If then a = and according to Eqs. (44) and (45) Ws = l and Wg O. If a>acj then a>a and In the trifunctional case, for example,... 

The most popular representation scheme in expert systems is the mle-based scheme. In a rule-based system the knowledge consists of a number of variables, also called attributes, to which a number of possible values are assigned. The rules are the functions that relate the different attributes with each other. A mle base consists of a number of If... Then... mles. The IF part contains the conditions that must be satisfied for the actions or conclusions in the THEN part to be valid. As an example, suppose we want to express in a mle that a compound is unstable in an alkaline solution if it contains an ester function. In a semi-formal way the mle can be written ... 

Rules seemingly have the same format as IF.. THEN.. statements in any other conventional computer language. The major difference is that the latter statements are constructed to be executed sequentially and always in the same order, whereas expert system rules are meant as little independent pieces of knowledge. It is the task of the inference engine to recognize the applicable rules. This may be different in different situations. There is no preset order in which the rules must be executed. Clarity of the rule base is an essential characteristic because it must be possible to control and follow the system on reasoning errors. The structuring of rules into rule sets favours comprehensibility and allows a more efficient consultation of the system. Because of the natural resemblance to real expertise, rule-based expert systems are the most popular. Many of the earlier developed systems are pure rule-based systems. 

Program 1.5 Example of Simple Conditional Logic IF-THEN/ELSE... 

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