Justifications

Arsenic is an ubiquitous element which occurs in the form of various chemical species in the environment. In biological tissues, the main species identified is arsenobetaine which is considered to be non-toxic and present at more than 90% in fish tissues but does not exceed 50% in mollucs [128], Other species such as arsenocholine, tetramethylarsonium ion, trimethylarsenoxide, dimethyl-arsinic acid and arsenosugars have also been identified [129-132]. 

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There is justification for allowing t to increase beyond 1, and in many particular applications this may be desirable. Here a more conservative approach is used to reduce the chance of unstable iterations. 

The main justification for diesel fuel desulfurization is related to particulate emissions which are subject to very strict rules. Part of the sulfur is transformed first into SO3, then into hydrated sulfuric acid on the filter designed to collect the particulates. Figure 5.21 gives an estimate of the variation of the particulate weights as a function of sulfur content of diesel fuel for heavy vehicles. The effect is greater when the test cycle contains more high temperature operating phases which favor the transformation of SO2 to SO3. This is particularly noticeable in the standard cycle used in Europe (ECE R49). 

As a field matures, bottlenecks may appear in other areas, such as water treatment or gas compression processes, and become factors limiting oil or gas production. These issues can often be addressed both by surface and subsurface options, though the underlying justification remains the same the NPV of a debottlenecking exercise (net cost of action versus the increase in net revenue) must be positive. 

The development and validation of UTDefect has now progressed so far so that the program can be of real help in the development of testing procedures, in parametric and sensitivity studies and in such technical justifications that are used for qualifications of testing procedures. 

In general, the assumption of quasi-stationarity is difficult to justify a priori. There may be several possible choices of intemiediates for which the assumption of quasi-stationary concentrations appears justified. It is possible to check for consistency, for example [A ]qj, [Pg.792]

Hirschfeld T and Chase B 1986 FT-Raman spectroscopy development and justification Appl. Spectrosc. 40 133-9... 

Herman M F and Kluk E 1984 A semiclassical justification for the use of non-spreading wavepackets in dynamics calculations Chem. Phys. 91 27... 

Even cursory inspection of typical (v,[) data shows tliat tire evolution does not follow tire single exponential approach to saturation implied by, for example, (equation C2.14.22) witli initial concentrations Xq Such data are sometimes described as biphasic , and one encounters attempts to fit and inteiyDret tliem witli two exponentials, even tliough tliere does not seem to be any tlieoretical justification for doing so. The basic kinetics of adsorjDtion are described by ... 

In Section IX, we intend to present a geometrical analysis that permits some insight with respect to the phenomenon of sign flips in an M-state system (M > 2). This can be done without the support of a parallel mathematical study [9]. In this section, we intend to supply the mathematical foundation (and justification) for this analysis [10,12], Thus employing the line integral approach, we intend to prove the following statement ... 

Another way to overcome the step-size restriction fc < is to use multiple-time-stepping methods [4] or implicit methods [17, 18, 12, 3). In this paper, we examine the latter possibility. But for large molecular systems, fully implieit methods are very expensive. For that reason, we foeus on the general class of scmi-implicit methods depicted in Fig. 1 [12]. In this scheme. Step 3 of the nth time step ean be combined with Step 1 of the (n - - l)st time step. This then is a staggered two-step splitting method. We refer to [12] for further justification. 

The procedure of Mason and Evans has the electrical analog shown in Figure 2.2, where voltages correspond to pressure gradients and currents to fluxes. As the argument stands there is no real justification for this procedure indeed, it seems improbable that the two mechanisms for diffusive momentum transfer will combine additively, without any interactive modification of their separate values. It is equally difficult to see why the effect of viscous velocity gradients can be accounted for simply by adding... 

These are the flux relations associated with the dusty gas model. As explained above, they would be expected to predict only the diffusive contributions to the flux vectors, so they should be compared with equations (2.25) obtained from simple momentum transfer arguments. Equations (3,16) are then seen to be just the obvious vector generalization of the scalar equations (2.25), so the dusty gas model provides justification for the simple procedure of adding momentum transfer rates. 

Thermal transpiration and thermal diffusion effects have been neglected in developing the dusty gas model, and will be neglected throughout the rest of the text. The physics of these phenomena and the justification for neglecting them are discussed in some detail in Appendix I. 

The nearest thing to a complete justification of equations (11.3)i for pellets of arbitrary shape, is an argument given by W. E. Stewart [74], which does not depend on any particular choice of flux relations. In Chapter 10 it was pointed out that all isothermal flux models must have the general form... 

We have assumed that the order of the subscripts on the atomic orbitals p is immaterial in writing a, p, and S. In the general case, these assumptions are not self-evident, especially for p. The interested reader should consult a good quantum mechanics text (e.g., Hanna, 1981 McQuarrie, 1983 Atkins and Eriedman, 1997) for their justification or critique. 

John von Neuman, one of the greatest mathematicians of the twentieth century, believed that the sciences, in essence, do not try to explain, they hardly even try to interpret they mainly make models. By a model he meant a mathematical construct that, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work. Stephen Hawking also believes that physical theories are just mathematical models we construct and that it is meaningless to ask whether they correspond to reality, just as it is to ask whether they predict observations. 

When standardizing a solution of NaOH against potassium hydrogen phthalate (KHP), a variety of systematic and random errors are possible. Identify, with justification, whether the following are systematic or random sources of error, or if they have no effect. If the error is systematic, then indicate whether the experimentally determined molarity for NaOH will be too high or too low. The standardization reaction is... 

Growth in the radial direction is assumed to occur at a constant velocity. There is ample experimental justification for this in the case of three-dimensional spherical growth. 

For both 1 = 4 and 1 = 8, the polymer is favored over the ring to a far greater degree than for 1 = 6. In the latter case the difference between AH° and T AS° is so small that there is probably no justification for retaining as many figures as shown in the calculated results. 

The arguments given below are concerned with a justification of C °°-regularity of the solution for the crack of zero opening. We shall prove the solution regularity in the neighbourhood of the line x (0,t°), where = (0,0), > 0, i.e. in the vicinity of the crack tip. The solution... 

A convergence justification of the nonlinear terms 5 p rrf )ij to the term 5 p m )ij can be done by monotonicity arguments. The details are omitted here. 

The following step is the justification of the passage to the limit as A —> 0. Let a subsequence, denoted as before, possess the following properties as A —y 0i... 

The first criterion was associated with improved secondary and tertiary petroleum recovery processes. This is the justification for the patent appHcations issued to the Dow (50) and Exxon (51) corporations. The additional costs of production and the increased adsorption of such modified water-soluble polymers are detrimental to the commercial appHcation of such polymers and even the academic studies in this area have decreased in recent years. 

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