Pooling equilibrium

While we are mainly interested in the set of contracts that credibly signal the manufacturer s type, it is worth beginning with the possibility that the manufacturer does not signal her type. In other words, the manufacturer chooses an action such that the action does not provide the supplier with additional information regarding the manufacturer s type. That outcome is called a pooling equilibrium because the different manufacturer types behave in the same way, i.e., the different types are pooled into the same set of actions. As a result, Bayes rule does not allow the supplier to refine his beliefs regarding the manufacturer s type. 

Thin adsorbed hexane film. We can apply Eq. (7.21) although the film has no continuous liquid connection with the pool. Equilibrium is estabhshed via the vapor phase. The thickness is... 

Fig. 3. AHoy evaporation from a single rod-fed source under steady-state conditions p° = 10p° AB feed rod, A B molten pool, A qB and vapor and deposit, A B, where p° = the equilibrium vapor pressure of component B B, and p° = the equilibrium vapor pressure of component A A. Part (a) shows...

Sta.bilizers. Cyanuric acid is used to stabilize available chlorine derived from chlorine gas, hypochlorites or chloroisocyanurates against decomposition by sunlight. Cyanuric acid and its chlorinated derivatives form a complex ionic and hydrolytic equilibrium system consisting of ten isocyanurate species. The 12 isocyanurate equilibrium constants have been determined by potentiometric and spectrophotometric techniques (30). Other measurements of two of the equilibrium constants important in swimming-pool water report significantly different and/or less precise results than the above study (41—43). A critical review of these measurements is given in Reference 44. 

Thus, the concentration of H2CO3 is itself buffered by the available pools of CO2. The hydration of CO2 is actually mediated by an enzyme, mrbonie anhydrase, which facilitates the equilibrium by rapidly catalyzing the reaction... 

Under the conditions of temperature and ionic strength prevailing in mammalian body fluids, the equilibrium for this reaction lies far to the left, such that about 500 CO2 molecules are present in solution for every molecule of H2CO3. Because dissolved CO2 and H2CO3 are in equilibrium, the proper expression for H2CO3 availability is [C02(d)] + [H2CO3], the so-called total carbonic acid pool, consisting primarily of C02(d). The overall equilibrium for the bicarbonate buffer system then is... 

To this point, the pathway has generated a pool of pentose phosphates. The AG° for each of the last two reactions is small, and the three pentose-5-phosphates coexist at equilibrium. The pathway has also produced two molecules of N/ DPH for each glucose-6-P converted to pentose-5-phosphate. The next three steps rearrange the five-carbon skeletons of the pentoses to produce three-, four-, six-, and seven-carbon units, which can be used for various metabolic purposes. Why should the cell do this Very often, the cellular need for... 

Several additional points should be made. First, although oxygen esters usually have lower group-transfer potentials than thiol esters, the O—acyl bonds in acylcarnitines have high group-transfer potentials, and the transesterification reactions mediated by the acyl transferases have equilibrium constants close to 1. Second, note that eukaryotic cells maintain separate pools of CoA in the mitochondria and in the cytosol. The cytosolic pool is utilized principally in fatty acid biosynthesis (Chapter 25), and the mitochondrial pool is important in the oxidation of fatty acids and pyruvate, as well as some amino acids. 

The diversity of these subcellular actin structures is remarkable and appears to be determined by the interactions of many actin-binding proteins (ABPs) as well as by changes in the concentrations of intracellular signaling molecules such as Ca and cAMP, by small GTP-binding proteins, and by signals arising from mechanical stress. Approximately 50% of the actin molecules in most animal cells are unpolymerized subunits in the cytosolic pool and exist in a state of dynamic equilibrium with labile F-actin filamentous structures (i.e., new structures are formed while existing structures are renewed) (Hall, 1994). 

Figure 2. The carbon dynamics of a primary forest prior to and following deforestation and slash burning. Arrows represent the relative magnitude of C flux. In the primary forest (represented by the large box at the top of the figure), the C pool is in a dynamic equilibrium with inputs approximately equalling exports. With deforestation and fire, the balance is altered with exports far exceeding imports.

Over the eons, the flow and evaporation of water inside a cavern creates a stunning array of rock sculptures. Stalagmites grow upward from the floor, sometimes joining stalactites to form massive columns. Limestone dams create beautiful pools of water. Limestone draperies fall like curtains from water flowing around overhanging rock. Delicate mineral flowers sprout from the walls. All these features result from the aqueous solubility equilibrium of calcium carbonate. 

For laboratory purposes it is sometimes convenient to recycle the foamate directly to the pool in a manner analogous to an equilibrium still. This eliminates the feed and bottoms streams and makes for a more reliable approach to steady-state operation. However, this recycling may not be advisable for colligend measurements in the presence of slowly dissociating collector micelles. 

A useful analogy for understanding secular equilibrium is visualizing a decay chain as a series of pools of water (Fig. 2). These pools eventually lead to a continuously filling pool representing a stable isotope of lead (either ° Pb, ° Pb or ° Pb). Over the timescale... 

Supercritical fluid extraction can be performed in a static system with the attainment of a steady-state equilibrium or in a continuous leaching mode (dynamic mode) for which equilibrium is unlikely to be obtained (257,260). In most instances the dynamic approach has been preferred, although the selection of the method probably depends just as much on the properties of the matrix as those of the analyte. The potential for saturation of a component with limited solubility in a static solvent pool may hinder complete recovery of the analyte. In a dynamic system, the analyte is continuously exposed to a fresh stream of solvent, increasing the rate of extraction from the matrix. In a static systea... 

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