Derivative graph

The coordinates (jc = 86.0, y = 0.071) are plotted in the second derivative graph at the bottom of Figure 11 -6. These calculations are tedious by hand, but trivial with... 

Prepare a second derivative graph to find the end point from the following titration data. 

FIGURE 5.26 pH-rate constant profile for the specific acid-base catalyzed hydrolysis of a water-soluble diaziridinyl benzoquinone derivative. [Graph reconstructed from data by Jain et al., AAPS National Meeting, Paper No. 2268, Indianapolis, IN, Oct. 29, 2000.]... 

For a series of successive derivative graphs L ,. .., Lm, a local synthetic invariant S/(i ) of the vertex i in the n th order line graph is calculated as ... 

The principle of derivative spectrometry consists of calculating, by a mathematical procedure, derivative graphs of the spectra to improve the precision of certain measurements. This procedure is applied when the analyte spectrum does not appear clearly within the spectrum representing the whole mixture in which it is present. This can result when compounds with very similar spectra are mixed together. 

The traces of the successive derived spectral curves are much more uneven than the one of the original spectrum (called zeroth order spectrum). These derivative plots amplify the weak slope variations of the absorbance curve (Figure 9.29). The procedure of obtaining the first derivative graph, dA/dA = (de/dA)/C, can be extended to successive derivatives (nth derivatives). 

The curve of the second derivative matches the points of inflection in the zeroth order spectrum by regions of zero slope which correspond to maxima or minima (Figure 9.30). The fourth derivative reveals even further the weak absorbance variations in the initial spectrum. Numerous analyses would be improved by adopting this principle, knowing that to make a measurement from the derivative spectra is no more difficult than from the absorbance spectrum. The amplitude between the maxima and the minima of the nth derivative graph is proportional to the absorbance value of the solution. The calibration graph is established from a few standard solutions of different concentrations to which the same mathematical treatment has been applied, as to the sample solution. 

Clarke (1974a, b, 1980) gives a detailed analysis of the stability of the steady state using the structure of the Vol pert graph and several derived graphs to check the Routh-Hurwitz criterion. 

Fig. 3. Comparison of the antigenicity of calf ADA and its mPEG derivative. Graph shows the activity of ADA remaining in the supernatant after double antibody precipitation using calf ADA antiserum Unmodified calf ADA (-0—0-), mPEG modified calf ADA (- - ), CS is...

Graphical representation of the atom economy vs. F C for common carbohydrates and their derivatives. Graph and data are reproduced with permission of Springer (Based on DusseHer M, Mascal M, Sels B. In Nicholas KM, editor. Selective catalysis for renewable feedstocks and chemicals, vol. 353. Springer... 

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