Definitions for

Standards also give definitions for the characteristics of a material or product, or they provide the means and methods to implement quality tests for them. The difference lies in their method of preparation, therefore, in their legal status. A standard is the result of a consensus between all parties concerned. These parties represent the manufacturers of the product or material, the consumers who are the industries or user services or, ultimately, consumer associations, as well as, finally, governments. 

There are no definitions for categorising reservoir fluids, but the following table indicates typical GOR, API and gas and oil gravities for the five main types. The compositions show that the dry gases contain mostly paraffins, with the fraction of longer chain components increasing as the GOR and API gravity of the fluids decrease. 

The appropriate quantum mechanical operator fomi of the phase has been the subject of numerous efforts. At present, one can only speak of the best approximate operator, and this also is the subject of debate. A personal historical account by Nieto of various operator definitions for the phase (and of its probability distribution) is in [27] and in companion articles, for example, [130-132] and others, that have appeared in Volume 48 of Physica Scripta T (1993), which is devoted to this subject. (For an introduction to the unitarity requirements placed on a phase operator, one can refer to [133]). In 1927, Dirac proposed a quantum mechanical operator tf), defined in terms of the creation and destruction operators [134], but London [135] showed that this is not Hermitean. (A further source is [136].) Another candidate, e is not unitary. 

A saddle point approximation to the above integral provides the definition for optimal trajectories. The computations of most probable trajectories were discussed at length [1]. We consider the optimization of a discrete version of the action. 

Table 2-4. Some basic definitions for graph theory. Graph theory term...

This eommutation relation is easily verified in the eoordinate representation leaving x untouehed (x = x ) and using the above definition for p. In the momentum representation... 

Streitwieser pointed out that the eorrelation whieh exists between relative rates of reaetion in deuterodeprotonation, nitration, and ehlorination, and equilibrium eonstants for protonation in hydrofluorie aeid amongst polynuelear hydroearbons (ef. 6.2.3) constitutes a relationship of the Hammett type. The standard reaetion is here the protonation equilibrium (for whieh p is unity by definition). For eon-venience he seleeted the i-position of naphthalene, rather than a position in benzene as the referenee position (for whieh o is zero by definition), and by this means was able to evaluate /) -values for the substitutions mentioned, and cr -values for positions in a number of hydroearbons. The p -values (for protonation equilibria, i for deuterodeprotonation, 0-47 for nitration, 0-26 and for ehlorination, 0-64) are taken to indieate how elosely the transition states of these reaetions resemble a cr-eomplex. 

Significance tests, however, also are subject to type 2 errors in which the null hypothesis is falsely retained. Consider, for example, the situation shown in Figure 4.12b, where S is exactly equal to (Sa)dl. In this case the probability of a type 2 error is 50% since half of the signals arising from the sample s population fall below the detection limit. Thus, there is only a 50 50 probability that an analyte at the lUPAC detection limit will be detected. As defined, the lUPAC definition for the detection limit only indicates the smallest signal for which we can say, at a significance level of a, that an analyte is present in the sample. Failing to detect the analyte, however, does not imply that it is not present. 

The phenomenological definition for the change in entropy associated with the isothermal, reversible absorption of an element of heat dq is... 

The Textile Eiber Product Identification Act (TEPIA) requires that the fiber content of textile articles be labeled (16). The Eederal Trade Commission estabhshed and periodically refines the generic fiber definitions. The current definition for a polyester fiber is "A manufactured fiber ia which the fiber-forming substance is any long-chain synthetic polymer composed of at least 85% by weight of an ester of a substituted aromatic carboxyUc acid, including but not restricted to terephthalate units, and para substituted hydroxyben2oate units."... 

The FDA appHes the Federal Food, Dmg and Cosmetic Act (3) to the spice iadustry and its products. The FDA has estabUshed a definition for spice which is somewhat general. It states, however, that vegetables such as onions, gadic, and celery are regarded as foods, not spices, even if dried. 

The Fair Packaging and Labeling Act, which uses the same definitions for dmgs and cosmetics as the Food, Dmg and Cosmetic Act, only has jurisdiction over retail products sold to the consumer for use at home. This condition exempts free samples and professional use products not sold to a consumer for personal use. 

Inorganic membranes (29,36) are generaUy more stable than their polymeric counterparts. Mechanical property data have not been definitive for good comparisons. IndustriaUy, tube bundle and honeycomb constmctions predominate with surface areas 20 to 200 m. Cross-flow is generaUy the preferred mode of operation. Packing densities are greater than 1000 /m. Porous ceramics, sintered metal, and metal oxides on porous carbon support... 

In applying the definition of rehabihty, the concept of adequate performance must be estabhshed clearly. Products usually do not fail suddenly, but degrade over time. Gasket leaks on equipment, for example, may start as a slow weep and increase in volume over time. The point at which this undesirable occurrence is called a failure must be clear before rehabihty can be measured objectively. Changing the failure definition for a product changes its rehabihty level, although the product itself has not changed. 

Standards and definitions for whole milk powder, partiy skimmed milk powder, and skimmed milk powder have been set by WHO. This standard apphes exclusively to dried milk products as defined, having a fat content of not mote than 40 mol %. 

Equation 54 implies that U is a function of S and P, a choice of variables that is not always convenient. Alternative fundamental property relations may be formulated in which other pairs of variables appear. They are found systematically through Legendre transformations (1,2), which lead to the following definitions for the enthalpy, H, Hehnholt2 energy,, and Gibbs energy, G ... 

Scotch. In 1988, the Scotch Association Council approved a new, tighter definition for Scotch whisky which is as follows "Scotch whisky is a potable spidt—... 

The cell is the basis of all electrolysis. The anode admits current into the electrolyte and the cathode serves as a means of exit for the electrical current. The electrical flow provides a definition for electrolysis the flow of current from the anode through the electrolyte and out of the cell through the cathode with ensuing decomposition of the electrolyte, with products being formed at the electrodes. 

Chemurgy is defined as that branch of appHed chemistry devoted to industrial utilization of organic raw materials, especially from farm products. A more modem and general definition for chemurgy is the use of renewable resources particularly biomass, usually plant or microbial material, for materials and energy (see Fuels frombiomass Fuels fromwaste). 

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