Resorts

If the material in two process alternatives is both flammable and highly toxic, then they can be compared on both bases separately. If the assessments of the relative flammability and toxicity are in conflict, then we can only resort to a safety index. 

When water is produced along with oil, the separation of water from oil invariably leaves some water in the oil. The current oil-in-water emission limit into the sea is commonly 40 ppm. Oily water disposal occurs on processing platforms, some drilling platforms, and at oil terminals. The quality of water disposed from terminals remains an area of scrutiny, especially since the terminals are often near to local habitation and leisure resorts. If the engineer can find a means of reducing the produced water at source (e.g. water shut-off or reinjection of produced water into reservoirs) then the surface handling problem is much reduced. 

This short-cut method could be repeated to include another variable, and could therefore be an alternative to the previous two methods introduced. This method can always be used as a last resort, but beware that the range of uncertainty narrows each time the process is repeated because the tails of the Input variables are always neglected. This can lead to a false impression of the range of uncertainty in the final result. 

Many phenomena in solid-state physics can be understood by resort to energy band calculations. Conductivity trends, photoemission spectra, and optical properties can all be understood by examining the quantum states or energy bands of solids. In addition, electronic structure methods can be used to extract a wide variety of properties such as structural energies, mechanical properties and thennodynamic properties. 

As data of the binary diflfiision coefficient Dam(P> tne not available in many cases, one has to resort to taking the solvent self-diflfiision coefficient Dy p,T) which requires rescaling in the low-pressure regime according to... 

There is no general, simple solution to this set of coupled differential equations, and thus one will usually have to resort to numerical teclmiques [42, 43] (see also chapter A3.4). 

Even when well defined model systems are used, colloids are ratlier complex, when compared witli pure molecular compounds, for instance. As a result, one often has to resort to a wide range of characterization teclmiques to obtain a sufficiently comprehensive description of a sample being studied. This section lists some of tire most common teclmiques used for studying colloidal suspensions. Some of tliese teclmiques are discussed in detail elsewhere in tliis volume and will only be mentioned in passing. A few teclmiques tliat are relevant more specifically for colloids are introduced very briefly here, and a few advanced teclmiques are highlighted. 

Development of laser technology over the last decade or so has permitted spectroscopy to probe short-time events. Instead of having to resort to the study of reactants and products and their energetics and shuctures, one is now able to follow reactants as they travel toward products. Fast pulsed lasers provide snapshots of entire molecular processes [5] demanding similar capabilities of the theory. Thus, explicitly time-dependent methods become suitable theoretical tools. 

Our first approach took resort in simple resonance theory [36, 37]. For each conjugated nr-system aU resonance structures were generated, such as those shown in Figure 7-5. 

The thermodynamic properties that we have considered so far, such as the internal energy, the pressure and the heat capacity are collectively known as the mechanical properties and can be routinely obtained from a Monte Carlo or molecular dynamics simulation. Other thermodynamic properties are difficult to determine accurately without resorting to special techniques. These are the so-called entropic or thermal properties the free energy, the chemical potential and the entropy itself. The difference between the mechanical emd thermal properties is that the mechanical properties are related to the derivative of the partition function whereas the thermal properties are directly related to the partition function itself. To illustrate the difference between these two classes of properties, let us consider the internal energy, U, and the Fielmholtz free energy, A. These are related to the partition function by ... 

Though you can in principle add a carbonyl group anywhere in a target molecule, remember it means extra steps in the synthesis so use it only as a last resort. 

Obtain the transition structure from the entire potential energy surface. It is questionable that there will be any case where this is the only option, but it should work as a desperate last resort. 

As a last resort, compute the entire potential energy surface and then obtain a reaction coordinate from it. 

At the equivalence point, the moles of Fe + initially present and the moles of Ce + added are equal. Because the equilibrium constant for reaction 9.16 is large, the concentrations of Fe and Ce + are exceedingly small and difficult to calculate without resorting to a complex equilibrium problem. Consequently, we cannot calculate the potential at the equivalence point, E q, using just the Nernst equation for the analyte s half-reaction or the titrant s half-reaction. We can, however, calculate... 

Once a mass spectrum from an eluting component has been acquired, the next step is to try to identify the component either through the skill of the mass spectroscopist or by resorting to a library search. Most modem GC/MS systems with an attached data station include a large library of spectra from known compounds (e.g., the NIST library). There may be as many as 50,000 to 60,000 stored spectra covering most of the known simple volatile compounds likely to be met in analytical work. Using special search routines under the control of the computer, one can examine... 

The generalizations demonstrated in the preceding example can be proved without resorting to numbers, but we have looked at enough algebra in this chapter already without adding these manipulations as well ... 

Although we have been able to see on inspection which vibrational fundamentals of water and acetylene are infrared active, in general this is not the case. It is also not the case for vibrational overtone and combination tone transitions. To be able to obtain selection mles for all infrared vibrational transitions in any polyatomic molecule we must resort to symmetry arguments. 

Internal development is usuaHy recommended if the company has a unique process or product for an evolving market or a unique, less expensive process for an existing product, licensing is resorted to when entry is desked and no suitable acquisitions can be found but a Hcensor of a suitable process exists. 

Aerosolized steroids clearly play an important role in the present-day management of asthma (87). They are reasonably safe and work best when taken prophylacticaHy. Patient compliance, however, remains a significant problem. In part this problem is typical of any aerosolized agent. But in the case of steroids, the problem is exacerbated because a patient needs to take the steroids (especially prednisone) are the antiasthmatic agents of last resort and are widely used to treat status asthmaticus. An agent that could mimic the actions of steroids but which would work faster and/or without side effects might be the ideal antiasthmatic agent. 

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