Limits of applicability

Since derivations and literature references are typically not given in detail (often not at all) it is difficult for users to recognize errors or assess the validity of some statements when applied to a particular situation. It would be helpful for the user to appreciate limitations of applicability and to consider risk tolerance when adopting a specific practice based on minimum safe practices given in codes. 

Corollary 2.—The vapour pressure of the solution is equal to that of the pure solvent when c = c. Since, by Henry s law, c/c depends only on temperature, and since distillation of liquid cannot alter its composition in this case, the solution will distil unchanged at a constant temperature exactly like a pure substance. This holds only within the limits of applicability of Henry s law. 

The structure of cluster compounds of transition metals and the limits of applicability of the electron counting rules forpolyhedral molecules. Y. L. Slovokhotov and Y. T. Struchkov, Russ. Chem. Rev. (Engl. Transl), 1985, 54, 323 (150). 

Which are the limits of applicability of NEMCA in terms of temperature, reaction type, materials etc. Why does NEMCA disappear at high temperatures ... 

The examples given above have been illustrative both for successful applications and for the limits of applicability of present-day brute force MD to complex chemical and biochemical systems. 

See discussion concerning the limits of applicability for this treatment. 

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

Relation of effectiveness and limitation of application to residue load... 

The term detection capability (detection power) represents a generic term of the performance of analytical methods at the lower limit of applicability. Mostly it is used descriptively (detection capability of a method is high , good or sufficient ) or for giving order of magnitudes (detection capability is in the ppm-range or ppb-range ). 

The transit method requires that the central star, the planet and the observer are connected by a line of sight. The dark planet passes across the light source and thus diminishes its light intensity to some extent. Observation is only possible when observer, star and planet are in a favourable position, i.e., the planet lies between the star and the observer. In spite of this requirement, the method permits the discovery of planets of about the size of the Earth information is also available on the size, mass and density of the planet as well as on its orbit. Because of its limits of applicability, this method is not often used. In the case of the star OGLE-TR-56, it was possible to detect an extrasolar planet, the orbit of which is very close to its sun only a twentieth of the distance of Mercury away from it. The temperature of the planet was determined to be around 1,900 K its diameter is about 1.3 times larger than that of Jupiter, its density about 500 kg/m3 (Brown, 2003 Konacki, 2003). 

You are cautioned not to extrapolate equations (30) or (31) beyond their stated limits of applicability. 

One problem for this equation is the rather narrow limits of applicability. These limits are ... 

Limits of application Products which decompose spontaneously Toxic products and products which decompose spontaneously Products which decompose spontaneously, metal dust hazard... 

Proper installation is dependent on the existing explosion protection measures and on the corresponding isolation system to be used. This guarantees operability. In addition the application and installation remarks of the manufacturer as well as the limits of application in accordance with the Type-Examination Certificate are to be obeyed in every detail. In Table 23-15 the most frequently used isolation systems for explosion protection measures are summarized. 

Finally, it must be pointed out that all explosion protection devices or systems used in practice may be used only when their pressure rating, flameproof, and functional testing have been proved by competent bodies and their test results including the limits of application are documented in a type test certificate. 

Figure 23. Plot of normalised flux J s / J versus to illustrate one limit of application...

One of the most important contributions of research in this field will be the development of criteria to define the limits of applicability of existing models, rather than creating a single supermodel that will incorporate all effects. 

The acquisition of substance data and the introduction of harmonised instra-ments for evaluation, conununication, documentation and limitation of application risks in the European market can only function at an extra-corporate level. In so doing, the following should be observed, if such solutions are in line with practice, their development catmot be left solely up to official bodies. If the costs are to be minimised, the companies have to develop standards jointly, which can however also entail the exchange of information that is relevant to a potential competitor. Thus, companies have to demonstrate courage, if efficient system solutions are to be developed at an extra-corporate level. 

Most drop situations in extraction are far above the upper limit of application of the preceding equations. A drop moving through a liquid at a velocity such that the viscous forces could be termed negligible can not exist. It will break up into two or more smaller droplets (HIO, K5). Most real situations involve both viscous and inertial terms, and the Navier-Stokes equations can not then be solved. 

Much remains to be learned, however, regarding the limits of applicability of the fluorescence probe technique to aggregates in non-polar media. A number of obvious experiments are conspicuous by their absence from the published literature. For example, 1-pyrene carboxaldehyde is a well known probe which has been used to measure the microscopic polarity of sodium dodecyl sulfate micelles in aqueous medium (5) there is, however, no account of its use in non-polar media. 

Because it was considered that the intrinsic inexactness of the computer s input information led to uncertainties of at least 5% in ruby s predictions of P, we originally felt that differences of about the same magnitude between arbitrary N, M, and Q and ruby s values could be tolerated in the present study. For this reason the analyses of Tables IV and V led us to set Po= 1.4 g/cc as a tentative lower limit of applicability of the present calculational method. The results below show this restriction to be unnecessary. 

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