The Expansion Phase

Assuming a binary intended relation and its corresponding predicate r/2, we suppose there is a specification EP r), whose example set is defined as follows  

Example 12-1 The firstPlateaulS problem is used all along this (and the following) chapter for illustration purposes. We assume that EP(firstPlateau) is as follows  

In order to keep this chapter self-sufficient, we here repeat the chosen synthesis strategy (see Section 7.3.2), where synthesis is seen as a sequence of/steps  

We also repeat Schema 8-3, that is version 3 of the divide-and-conquer schema  

Instantiating some predicate-variable(s) of a schema is a synthesis step. The synthesis mechanism is expressed as the following sequence of/= 7 steps (see Example 8-8)  

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Figure 5.3 gives an example of a combustion diagram recorded during knocking conditions. This is manifested by intense pressure oscillations which continue during a part of the expansion phase. 

III. The expansion phase begins when the input valve is closed and the exhaust valve is opened slowly so that cooling occurs at the cold end. 

Fig. 6.4 shows the IT-A curves obtained for microbubble-surfactant monolayers on a variety of aqueous subphases. In order to compare Il-A measurements for monolayers which would contain essentially only glycopeptide-acyl lipid complexes, the data plotted in Fig. 6.4 include only Il-A measurements made during the expansion phase (following an initial compression to at least 23 dyne/cm). Judging from the fact that subphases of either distilled water, 0.1 M HC1 (pH 1.1), 0.1 M NaOH (pH 12.3), or 0.1 M NaF... 

Cavitation bubbles do not enclose a void. During the expansion phase of cavitation bubble generation, vapour from the surrounding liquid will permeate the interface. This produces... 

These main sequence models at the H-limit can certainly not be related to LBVs, but perhaps rather to B[e] stars the material of stars at the Q-limit which has excess angular momentum can not remain on the star but it is also not clear whether it can be pushed to infinity some of it may form a ring or disk close to the star. However, as the mass loss rate at the H-limit depends on the evolutionary speed of the star in the HR diagram, one can expect values of the order 10 5 M0 yr-1 x th/tkh for the expansion phase after core H-exhaustion, when the star hits the fl-limit again due to the helium opacity peak. Here, th is the H-burning time scale and tkh the thermal time scale of the star, such that values of Mq of the order of 10 3 — 10 2 M0 yr-1 can be expected, which is the order of magnitude observed for LBVs. 

Liquids irradiated with ultrasound can produce bubbles. These bubbles oscillate and grow a little more during the expansion phase of the sound wave than they shrink during the compression phase. Under the proper conditions these bubbles can undergo cavitation, violent bubble collapse or implosion, leading to droplets particle size reduction. The use of ultrasonication in emulsification is more efficient than rotor-stator systems. 

Eventually, the poleward advancing aurora reaches the highest latitude. This is the maximum epoch of the auroral substorm. The period between the sudden brightening of the auroral curtain in the midnight sector and the maximum epoch is called the expansive phase. A typical duration of this phase is 30-60 min. As the auroral curtain begins to recede toward lower latitudes and the bulge begins to contract, the recovery phase sets in. This phase typically lasts for about 2 hr thus, a typical substorm lasts for about 3 hr. 

In the expansion phase, the expanding steam-water-melt mixture converts thermal energy into work on the... 

The expansion phase of synthesis comprises the first four steps of this mechanism. In Section 12.1 to Section 12.4, we give complete descriptions of each of these steps we state their objectives, describe the used methods, analyze their correctness and progression behaviors, and illustrate them on the firstPlateaul2 and compress/2 problems. 

Note that the expansion phase of synthesis may be likened to trace generation, while the reduction phase of synthesis may be likened to trace generalization. 

This ends the specification acquisition. Synthesis now starts with the expansion phase... 

In Chapter 12, we give full detail about the expansion phase of synthesis, that is the first four steps of the mechanism. These steps are rather straightforward, and do not require any sophisticated methods. 

The semiconductor equipment industry periodically goes through wide swings in demand. These swings, ranging from 50% drops to 100% increases on the upturn can severely test any supply chain. This case describes the problems encountered by a component supplier in this industry trying to keep up with the expansion phase of one of these cycles. 

Equation (3.11.32) will now be used to transform (3.11.23) into a integral equation for p(x,t) in the expansion phase only. The result is... 

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