The Final Result

During the methods optimisation work, approximately 1100 samples were run on three instruments in 21 working days. Diu-ing that time, no problems with plugging of the variable restrictors were encountered. The summary of the recoveries and precisions is presented in Table 3 the recommended SFE conditions are summarised in Table 4. 

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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. 

The information received is begin processed in SC EDC according to the above-described algorithm, and the final result indicates on LCI. 

If the surface is to be in mechanical equilibrium, the two work terms as given must be equal, and on equating them and substituting in the expressions for dx and dy, the final result obtained is... 

On applying Stirling s approximation, replacing V/N by kT/P, and using Eq. XVII-20 and setting P = 1 atm, the final result, known as the Sackur-Tetrode equation, is... 

The last identity follows from the orthogonality property of eigenfunctions and the assumption of nomralization. The right-hand side in the final result is simply equal to the sum over all eigenvalues of the operator (possible results of the measurement) multiplied by the respective probabilities. Hence, an important corollary to the fiftli postulate is established ... 

At the critical pohit (and anywhere in the two-phase region because of the horizontal tie-line) the compressibility is infinite. However the compressibility of each conjugate phase can be obtained as a series expansion by evaluating the derivative (as a fiuictioii of p. ) for a particular value of T, and then substituting the values of p. for the ends of the coexistence curve. The final result is... 

Reverting this series and simplifying yields the final result in powers of t... 

The final result that we wish to present in this connection is an example of the Green-Kubo time-correlation expressions for transport coefficients. These expressions relate the transport coefficients of a fluid, such as... 

These quartic equations are solved in an iterative maimer and, as such, are susceptible to convergence difficulties. In any such iterative process, it is important to start with an approximation reasonably close to the final result. In CC theory, this is often achieved by neglecting all of tlie temis tliat are nonlinear in the t amplitudes (because the ts are assumed to be less than unity in magnitude) and ignoring factors that couple different doubly-excited CSFs (i.e. the sum over i, f, m and n ). This gives t amplitudes that are equal to the... 

A major achievement [71, 82, 83, 84, 85, 86, 87 and 88] was the development of a simple quantum ( flux-flux ) expression for the cumulative reaction probability, N E), with the final result... 

The second integral in Eq. (155) seemed to be singular when n + / + q = 0. However, in this case, (i must be zero, and consequently this term will never contribute to the final result for being suppressed by the prefactor. With the definition in Eq. (132), we can write... 

The initial step is to identify which database, from a few thousands worldwide (about 10 000 in 2002), provides the requested information. The next step is to determine which subsection of the topic is of interest, and to identify typical search terms or keywords (synonyms, homonyms, different languages, or abbreviations) (Table 5-1). During the search in a database, this strategy is then executed (money is charged for spending time on some chemical databases). The resulting hits may be further refined by combining keywords or database fields, respectively, with Boolean operators (Table 5-2). The final results should be saved in electronic or printed form. 

The summation on the right hand side of this can be simplified by recalling that > J =0, with the final result that... 

The underlying theory of r-RESPA is somewhat involved, but the final result and const quent implementation is actually rather straightforward, being very closely related to th velocity Verlet integration scheme. For our four-way decomposition the algorithm woul... 

C,H5N,NHC,Hs+HC1 = C,H 5N C1+H,NC,H5- C H5N NC H NH +HC1 gen atom of the aniline molecule, giving aminoazobenzene. Since this reaction is irreversible, whilst the former is freely reversible, the final result is the complete conversion of the diazoaminobenzene into the aminoazobenzene. (The intermediate formation of the benzenediazonium chloride can be demonstrated by adding dimethylaniline, with which the diazonium chloride couples preferentially, giving dimethylaminoazobenzene, C6HsN NC6HiN(CH3)i.)... 

Input and output subroutines to read and echo print data, allocate and initiahze working arrays, and output the final results generally in a form that a post processor can use for graphical representations. 

The calculated result as we have found it by this dissection of the G2 method agrees with the final result of the G2 script... 

When an alkyl halide is treated with sodium, the main product is the paraffin hydrocarbon. The final result may be represented by the equation ... 

An equivalent result may be obtained by treating excess of sodium acetate with phosphorus oxychloride acetyl chloride is an intermediate product and the final result is ... 

As a first step in applying these rules, one must examine > and > and determine by how many (if any) spin-orbitals > and > differ. In so doing, one may have to reorder the spin-orbitals in one of the determinants to aehieve maximal eoineidenee with those in the other determinant it is essential to keep traek of the number of permutations ( Np) that one makes in aehieving maximal eoineidenee. The results of the Slater-Condon rules given below are then multiplied by (-l) p to obtain the matrix elements between the original > and >. The final result does not depend on whether one ehooses to permute ... 

This is the final result of the first-order time-dependent perturbation theory treatment of light-indueed transitions between states i and f. 

So, the final result is the order golden rule expression ... 

Once the molecules are aligned, a molecular field is computed on a grid of points in space around the molecule. This field must provide a description of how each molecule will tend to bind in the active site. Field descriptors typically consist of a sum of one or more spatial properties, such as steric factors, van der Waals parameters, or the electrostatic potential. The choice of grid points will also affect the quality of the final results. 

The choice of the NDO method depends on several factors including your previous experience and preferences. If you want to compare the results to other studies, you must use the same semi-empirical method. Since some methods can converge much more quickly than others, you might want to use a fast method to obtain an approximation of the final answer, and then a more accurate method for the final result. 

Parallel processing requires that each transputer be able to communicate efficiently with others (up to four immediate neighbors with current transputers) if the final result is not to be garbled. 

The index m drops out of the last summation we compensate for this by multiplying the final result by n - 1 in recognition of the fact that the summation adds up n - 1 identical terms. Accordingly, the desired result is obtained ... 

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