Limitations and approximations

When mixed with air, LPG can form a flammable mixture. The flammable range at ambient temperature and pressure extends between approximately 2 per cent of the vapor in air at its lower limit and approximately 10 per cent of the vapor in air at its upper limit. Outside this range, any mixture is either too weak or too rich to propagate flame. However, over-rich mixtures resulting from accidental releases can become hazardous when diluted with air. At pressures greater than atmospheric, the upper limit of flammability is increased but the increase with pressure is not linear. 

The dynamical diffraction theory is very accurate and highly practical, but no theoiy provides a perfect description of the complexity of real specimens. What are the limitations and approximations, and how serious are they ... 

Ceiling Limits and Approximate Safety Factors Recommended by NIOSH for Several Airborne Chemicals... 

The premise behind correlation scaling is particularly simple. Because of basis-set limitations and approximations in the correlation treatment, one is very rarely able to compute the full... 

The results of the theoretical analysis outlined above provide a deep and intuitively satisfying view of the electron transfer process and provide a quantitative basis for accounting for the magnitudes of electron transfer rate constants. Before applying the results to the experimental data in Table 1, it is necessary to remind ourselves of the limitations and approximations upon which the theory was based and to consider how comparisons between theory and experiment are to be made. 

The purpose of this chapter is to present several of the most common models used to describe metal and metalloid ion adsorption by soil components. Empirical models used in soil chemistry are described and their limitations discussed. Common chemical models used to describe metal adsorption on soil minerals are described and their advantages over empirical approaches discussed. Methods for obtaining model parameters are provided. Methods for establishing adsorption mechanisms and surface speciation are addressed. Limitations and approximations in the application of chemical models to natural systems are presented. 

In a recent paper Bricogne [263] has shown a complete equivalence between the maximum entropy formulation and traditional direct methods. He has developed a theory capable of unifying and simplifying the whole of direct methods while avoiding the limitations and approximations inherent in the traditional approaches. Thus, maximum entropy should become general for both small and large structures. 

Of critical importance here are the particular characteristics of the molecule that govern its absorption, transportation, breakdown, and, where appropriate, excretion together, they help answer a critical question how much of the active substance is where, and when This seems a simple question, but to answer it empirically using the techniques of analytical chemistry generally requires high expenditures, and results available during optimization are thus limited and approximate. 

The limitations and approximations given above are presumed to be the reasons why lEC 61508 will not allow the PFDavg value to be used as the measure of SIL if the demand rate is high. If the demand rate D is high and if the test interval cannot be short then DTi becomes large. 

Bearing in mind the limitations and approximations made for Dupre s rule (O 4.50) and Young s equation (O 4.29), finally consider the common treatment of contact angle data which makes use of the combination of the two equations ... 

The application of the theory shown above to computation of photodetachment cross sections of lanthanide negative ion Ce is summarized below. After that, the limitations and approximations in the calculation will be discussed. The work combined with experiment has identified bound-to-bound transitions in Ce for the first time [5]. 

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