Rationality

In current practice, rationalized units are not used in IR the absorption bands have long been identified in terms of wavelengths, i. e., in micrometers. The general trend now is to express energy by a scale proportional to the frequency the wave number designated by v is defined as (... 

The gradual reduction and ultimate elimination of lead has seen considerable effort by the refiner to maintain the octane numbers at satisfactory levels. In Europe, the conventional unleaded motor fuel, Eurosuper, should have a minimum RON of 95 and a minimum MON of 85. These values were set in 1983 as the result of a technical-economic study called RUFIT (Rational Utilization of Fuels in Private Transport). A compromise was then possible between refining energy expenses and vehicle fuel consumption (Anon., 1983). 

All the analytical results are represented as curves that enable easy and rational utilization. 

Since the discovery of petroleum, the rational utilization of the fractions that compose it has strongly influenced the development of refining processes as well as their arrangement in refining flowsheets. 

RUFIT rational utilization of fuels in private transport... 

Incidentally, a quantity called the rational potential is defined as E for the mercury-water interface (no added electrolyte) so, in general, = E + 0.480 V if a normal calomel reference electrode is used. 

A major contribution to the rational organization of contact angle data was made by Zisman and co-workers. They observed that cos 6 (advancing angle) is usually a monotonic function of 7l for a homologous series of liquids. The proposed function was... 

One may rationalize emulsion type in terms of interfacial tensions. Bancroft [20] and later Clowes [21] proposed that the interfacial film of emulsion-stabilizing surfactant be regarded as duplex in nature, so that an inner and an outer interfacial tension could be discussed. On this basis, the type of emulsion formed (W/O vs. O/W) should be such that the inner surface is the one of higher surface tension. Thus sodium and other alkali metal soaps tend to stabilize O/W emulsions, and the explanation would be that, being more water- than oil-soluble, the film-water interfacial tension should be lower than the film-oil one. Conversely, with the relatively more oil-soluble metal soaps, the reverse should be true, and they should stabilize W/O emulsions, as in fact they do. An alternative statement, known as Bancroft s rule, is that the external phase will be that in which the emulsifying agent is the more soluble [20]. A related approach is discussed in Section XIV-5. 

This simple model is adequate for some properties of rare gas fluids. When it is combined with an accurate description of the electrostatic interactions, it can rationalize the structures of a large variety of van der Waals... 

The simplest extension to the DH equation that does at least allow the qualitative trends at higher concentrations to be examined is to treat the excluded volume rationally. This model, in which the ion of charge z-Cq is given an ionic radius d- is temied the primitive model. If we assume an essentially spherical equation for the u. . 

Subsequently Onsager (1948) reported other exponents, and Yang (1952) completed the derivation. The exponents are rational numbers, but not the classical ones. 

The small uncertainties in the calculated exponents seem to preclude the possibility that the d = 3 exponents are rational numbers (i.e. the ratio of integers). (At an earlier stage this possibility had been suggested, since not only die classical exponents, bnt also tlie rational numbers pre-RG calculations had suggested p = 5/16 and y = 5/4.)... 

In classical kinetics, intemiolecular exchange processes are quite different from the uniniolecular, first-order kinetics associated with intramolecular exchange. However, the NMR of chemical exchange can still be treated as pseudo-first-order kinetics, and all the previous results apply. One way of rationalizing this is as... 

To rationalize the two-centre approximation , the effective potential is written as... 

Equation B3.5.5 is, in turn, equivalent to the minimum condition on the rational fiinction... 

Aq becomes asymptotically a g/ g, i.e., the steepest descent fomuila with a step length 1/a. The augmented Hessian method is closely related to eigenvector (mode) following, discussed in section B3.5.5.2. The main difference between rational fiinction and tmst radius optimizations is that, in the latter, the level shift is applied only if the calculated step exceeds a threshold, while in the fonuer it is imposed smoothly and is automatically reduced to zero as convergence is approached. 

The EF algoritlnn [ ] is based on the work of Cerjan and Miller [ ] and, in particular, Simons and coworkers [70,1Y. It is closely related to the augmented Hessian (rational fiinction) approach[25]. We have seen in section B3.5.2.5 that this is equivalent to addmg a constant level shift (damping factor) to the diagonal elements of the approximate Hessian H. An appropriate level shift effectively makes the Hessian positive definite, suitable for minimization. 

Accordingly, the exterior surface is much more reactive than planar analogues, and is comparable to those of electron deficient polyolefins. This, in turn, rationalizes the high reactivity of the fullerene core towards photolytically and radiolytically generated carbon- and heteroatomic-centred radicals and also other neutral or ionic species [8]. The interior, in contrast, is shown to be practically inert [9]. Despite these surface related effects, the... 

Ericksen J L 1966 Some magnetohydrodynamic effects in liquid crystals Arc/r. Ration. Mech. Analysis23 266-75... 

Leslie F M 1968 Some constitutive equations for liquid crystals Arch. Ration. Mech. Analysis 28 265-83... 

Lattice models are particularly suited for answering the questions posed. We will show that the two physical restrictions are sufficient to rationalize the emergence of very limited (believed to be only of the order of a thousand... 

The proportionality between nonnal and frietion forees is observed for many systems but is not founded in any basie physies. Mueh work in the field of tribology has been devoted to rationalizing the implieation that the frietion eoeffieient does not depend upon the apparent eontaet area between the two solid surfaees. For this reason the field of eontaet meehanies has always been intimately linked to tribology. 

Grabar K C ef a/1996 Kinetio oontrol of interpartiole spaoing in Au oolloid-based surfaoes-rational nanometer soale arohiteoture J. Am. Chem. See. 118 1148... 

Mirkin C A ef a/1996 A DNA-based method for rationally assembling nanopartioles into maorosoopio materials Nature 382 607... 

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