Exclude

We use Equation (2) primarily with five parameters, or with four parameters, excluding C. When data were sparse or of poor precision, a linear two-parameter fit (C = = 0) was... 

The battery limit is a geographic boundary which deflnes the manufacturing area of the process. This includes process equipment and buildings or structures to house it but excludes boilerhouse facilities, pollution control, site infrastructure, etc. 

Trends in refining costs for a capacity of8 10>> t/an. Excluding fuel consumption. 

Well completions are usually tailored to individual wells, and many variations exist. The following diagrams show a completion with a gravel pack, designed to exclude sand production downhole, and a dual completion, designed to allow controlled production from two separate reservoirs. 

It is possible to expect that the endurance at the fixed loading allows to exclude the component AEl, because the development of prevailing defect is continuing, and numerous initiation of stable micro-cracks outside the zone are excepted. 

The first of them to determine the LMA quantitatively and the second - the LF qualitatively Of course, limit of sensitivity of the LF channel depends on the rope type and on its state very close because the LF are detected by signal pulses exceeding over a noise level. The level is less for new ropes (especially for the locked coil ropes) than for multi-strand ropes used (especially for the ropes corroded). Even if a skilled and experienced operator interprets a record, this cannot exclude possible errors completely because of the evaluation subjectivity. Moreover it takes a lot of time for the interpretation. Some of flaw detector producers understand the problem and are intended to develop new instruments using data processing by a computer [6]. 

But for some liquids exists the third stage of liquid s penetration inside conical capillary, which was established in [5]. During this stage a channel is filling both from its entrance and from its closed top. Two liquid columns arise and are growing towards each other till the complete channel s filling (fig. 2). The most intriguing pattern can be observed when we exclude direct liquid s access to channel s entrance. It corresponds to the cases... 

Certain types of equipment are specifically excluded from the scope of the directive. It is self-evident that equipment which is already regulated at Union level with respect to the pressure risk by other directives had to be excluded. That is the case with simple pressure vessels, transportable pressure equipment, aerosols and motor vehicles. Other equipment, such as carbonated drink containers or radiators and piping for hot water systems are excluded from the scope because of the limited risk involved. Also excluded are products which are subject to a minor pressure risk which are covered by the directives on machinery, lifts, low voltage, medical devices, gas appliances and on explosive atmospheres. A further and last group of exclusions refers to equipment which presents a significant pressure risk, but for which neither the free circulation aspect nor the safety aspect necessitated their inclusion. 

We attempt to delineate between surface physical chemistry and surface chemical physics and solid-state physics of surfaces. We exclude these last two subjects, which are largely wave mechanical in nature and can be highly mathematical they properly form a discipline of their own. 

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

Classic nucleation theory must be modified for nucleation near a critical point. Observed supercooling and superheating far exceeds that predicted by conventional theory and McGraw and Reiss [36] pointed out that if a usually neglected excluded volume term is retained the free energy of the critical nucleus increases considerably. As noted by Derjaguin [37], a similar problem occurs in the theory of cavitation. In binary systems the composition of the nuclei will differ from that of the bulk... 

The Donnan effect acts to exclude like-charged substrate ions from a charged surface region, and this exclusion, as well as the concentration of oppositely charged ions, can be expressed in terms of a Donnan potential pD. Thus for a film of positively charged surfactant ions S one can write... 

If the adiabatic work is independent of the path, it is the integral of an exact differential and suffices to define a change in a function of the state of the system, the energy U. (Some themiodynamicists call this the internal energy , so as to exclude any kinetic energy of the motion of the system as a whole.)... 

However, the possibility that might not go to zero could not be excluded before the development of the quantum theory of the heat capacity of solids. When Debye (1912) showed that, at sufficiently low... 

Because it is necessary to exclude some substances, including some crystals, from the Nemst heat theorem, Lewis and Gibson (1920) introduced the concept of a perfect crystal and proposed the following modification as a definitive statement of the third law of themiodynamics (exact wording due to Lewis and Randall (1923)) ... 

Flere b corresponds to the repulsive part of the potential, which is equivalent to the excluded volume due to the finite atomic size, and a/v corresponds to the attractive part of the potential. The van der Waals equation... 

The nth virial coefficient = < is independent of the temperature. It is tempting to assume that the pressure of hard spheres in tln-ee dimensions is given by a similar expression, with d replaced by the excluded volume b, but this is clearly an approximation as shown by our previous discussion of the virial series for hard spheres. This is the excluded volume correction used in van der Waals equation, which is discussed next. Other ID models have been solved exactly in [14, 15 and 16]. ... 

The major deficiency of the equation as written is that there is no excluded volume, a deficiency DFl could rectify for the central ion, but not for all ions around the central ion. This deficiency has been addressed within the DFl framework by Outhwaite [9]. 

We have seen that the DFI theory in the limiting case neglects excluded volume effects in fact the excluded volume of the centra ion can be introduced into the theory as explained after A2.4.48. If the radius of the ions is taken as a for all ions, we have, in first order. 

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. . 

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