TREATMENT OF RESULTS

At all but the simplest level, treatment of the results from a time-domain experiment involves some mathematical procedure such as non-linear least squares analysis. Least squares analysis is generally carried out by some modification of the Newton-Raphson method, that proposed by Marquardt currently being popular [21, 22]. There is a fundamental difficulty in that the normal equations that must be solved as part of the procedure are often ill-conditioned. This means that rather than having a single well-defined solution, there is a group of solutions all of which are equally valid. This is particularly troublesome where there are exponential components whose time constants differ by less than a factor of about three. It is easy to demonstrate that the behaviour is multi-exponential, but much more difficult to extract reliable parameters. The fitting procedure is also dependent on the model used and it is often quite difficult to determine the number of exponentials needed to adequately represent the data. Various procedures have been suggested to overcome these difficulties, but none has yet received wide acceptance in solid-state NMR [23-26]. 

The first stage in deciding how to treat the results from a ruggedness test is to select a range of parameters to measure which will provide both qualitative and quantitative information on the method s performance. The second stage is to decide how best to evaluate the main effects, standard errors and interaction effects provided by the selected experimental design. For this discussion we will consider only the application of HPLC, normally one of the most complex analytical methods to evaluate. 

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The standard enthalpy of formation of monomeric HF is a hypothetical state that must be related to that of the real associated liquid, gas, or aqueous solution met in calorimetiy. Considerable difficulty has been encountered in allowing for the heat of association, which varies with temperature and pressure. For example, the presence of traces of water can affect the polymerization by entering into the hydrogen bonding (30) the treatment of results will depend on the association model adopted. The magnitude of corrections for gas imperfections has... 

A detailed treatment of results obtained with systems of the kind discussed in Examples 5 and 6 may require the use of equations of this type. 

The setup and treatment of results of such a robustness test are discussed in this chapter. All steps of the test are considered. Finally, a literature review and critique of applications of robustness testing of CE methods has been provided. 

There are two aspects to a report of an interlaboratory study. First the nature, organization, and treatment of results of the trial must be specified,... 

A least-squares treatment of results pertaining to compounds where no steric effect is expected to operate (8 points) as well as one based on all the data in Fig. 1 show very minor differences in the slope (0.004) and intercept (0.070), suggesting that steric factors are unimportant. The line [Eq. (15)], given in Fig. 1 using the result for pyridine as a rate standard, is that based on all the data. There is remarkably little scatter... 

The treatment of results will be described for L-dopa. The procedure for D-dopa is identical. Prepare a table of L-dopa concentration per assay (mmo-lar) vs. A/i/min. Convert all AA/mm units to /xmoles/min as described in part B. Prepare a Michaehs-Menten curve (/xmoles/min vs. [S]) as in Figure E5.1 and a Lineweaver-Burk plot (l//xmole/min vs. 1/[S]) as in Figure E5.2. Alternatively, you may wish to use the direct linear plot. Estimate Ku and Vmax from each graph. The intercept on the rate axis of the Lineweaver-Burk plot is equal to 1/V-. For example, if the line intersects the axis at 0.02,... 

The determination of accurate pK values for the first ionization of isophthalic and of terephthalic acid is very difficult, because the second ionization overlaps with the first. Elaborate treatment of results is required. 

Thermodynamic models analyzed above are applicable to the treatment of results of measurement of characteristics of microporous materials, especially active carbons prepared by pyrolysis of organic materials. 

Oxidative cleavage of the double bond in 168 (Scheme 33, Section 14.10.6.3) by ozonolysis was unsuccessful, while its dihydroxylation and treatment of resulting diol with lead(iv) acetate gave diketone 169 <1999T7471>. Ozonolysis of isopropyl 1,3,4,5,6,7-hexahydro-l-methylisobenzofuran-l-carboxylate 131 (Scheme 23, Section 14.10.5.6.3) proceeded smoothly and led to the corresponding oxonine carboxylate 132 <20020L3059>. 

The characteristics of disperse systems (see Section 1.1.2) are determined by geometrical parameters, i.e. linear dimensions, projection areas, surfaces, volumes, and, sometimes, angular dimensions. In addition, other physical characteristics, which do not directly represent particle size, may be used for the determination of these parameters. In such cases, a mathematical conversion into the desired geometrical dimension takes place. The term particle size analysis defines the experimental determination of particle characteristics and the statistical treatment of results. 

The microbial strains studied were Salmonella thyphimurium (two exercises). Listeria monocytogenes (two exercises) and later Bacillus cereus. Staphylococcus aureus, and Clostridium perfrengens for food microbiology, and Escherichia coli. Enterococcus faecium, Enterobacter cloacae and Staphylococcus warneri for water microbiology. The results were discussed in meetings with all participants. Several standard operating procedures common for several methods were developed, tested and amended, e.g. measurement of pH of culture media, measurement of temperature in incubators, statistical treatment of results, etc. 

We carried out a short and efficient synthesis of trans-tetrahydroactinidiolide (155) from drim-8-en-7-one (27) [105]. On exhaustive ozonolysis of drim-8-en-7-one (27) and subsequent treatment of resulting products with hydrogen peroxide, the keto acid (157) was obtained in a quantitative yield. 

However, proposed by the authors [62] treatment of results does not allow to obtain the common dependence of on the indicated above factors, that reduces pred-... 

Gas adsorption is by far the most common technique used to gain information about the porous structure from the adsorption/desorption isotherms. As adsorbent, nitrogen is the most commonly used. The treatment of results here is based on a cylindrical pore model. 

Partington and Shilling s Specific Heat of Gases reviews the methods and results of heat capacity measurements made in the first quarter of this century. Masi, in an article published in 1954, covered the period from 1925 to 1952 and compared experimental and calculated values of heat capacities for many simple gases. He also briefly described ten possible methods of measuring heat capacities. In the last ten years Rowlinson devoted a chapter of his book, The Perfect Gas , to the measurement of heat capacities, and a detailed account of measurements and treatment of results in vapour-flow calorimetry was written by McCullough and Waddington in Experimental Thermodynamics , Volume I. ... 

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