Curve subtraction method

This indicated that the two ethylenic linkages in the side chain of pyrethrolone were in conjugation. Similar results were obtained18 by the curve subtraction method with the absorption curves of the semicarbazones of pyrethrolone and tetrahydropyrethrolone. Woodward and Singh19 proposed the structure of patulin as XIX, with the C=C—C=C—C=0 unit, only because of the fact that it absorbs at 276 m/x (e 17,000). 

The known addition method has an advantage in greater rapidity and somewhat improved precision compared with calibration with two standards. It is claimed that it requires about half the time necessary for two-standard calibration [17] and that the relative error is about 2% [22]. A disadvantage is the necessity of determining the value for most systems. The method should be used only for concentrations corresponding to the linear part of the calibration curve. To eliminate the effect of a change in the ionic strength, it has been recommended [19] that a mixture of a standard with the test solution be added to the sample. The known subtraction method is much less used in practice. 

Calculation. The 25 g soil was shaken with 50 ml calcium chloride extractant, and 25 ml of this extract was diluted to 50 ml. There is therefore a x4 dilution factor. Calculate the concentration of SO -S in the blank and samples by comparison with the standard curve. Subtract the blank value from the sample values and multiply by 4 to give the pg SO -S g (= mg SO -S kg- ) air-dry soil. Include any extra dilution factors, and, if required, convert to oven-dry soil using the appropriate factor, as in Method 5.2, Calculation (2). 

Computerized method provides convenient and accurate determination of the ionization constant in aqueous solution and of the apparent ionization constant in the presence of octanol. From these parameters, partition coefficients and apparent partition coefficients are easily calculated and agree with data reported using the shaker technique or HPLC. The curve-fitting method has been applied to the differential titration technique in which the solvent curve is subtracted from the solution curve before calculations are begun. This method has been applied to the potentiometric titration of aqueous solutions of the salts of bases with very low solubility in water. 

Individual membrane proteins can be solubilized by the use of detergents, and the protein-detergent complex can be studied. This method requires monodisperse complexes (i.e the bound micelles should be of similar size and mass) and these are not difficult to prepare. Since the protein-detergent complex exists in equilibrium with free detergent micelles, the buffer background samples should contain detergent also at the equilibrium concentration so that the buffer curve subtraction will lead to the protein-detergent curve only. 

Oxygen is also present in both solutions in the same concentrations, and consequently its waves are subtracted and cause no interference. To obtain curves without disturbances as in ordinary polarography, not only the drop-time, but also the outflow velocity of mercury from both capillaries, as well as the potential of both reference electrodes must be identical. Because these conditions are not very easily obtainable with the subtractive method it has not found many applications so far. 

Now a very useful feature of the excess acidity method comes into play likely nucleophiles or bases can be tested by subtracting their log activities or concentrations from the left-hand side of equations (59) and (60), and the species reacting with SH+ is uniquely identified when linearity of the result against X is achieved.145,161 For instance, subtraction of twice the water activity is required to attain linearity in ester hydrolysis processes such as equation (42), as shown in Fig. 11 for methyl benzoate41 and ethyl benzoate.210 The water activities given in Table 3 were used. The parameters of the lines in Fig. 11, obtained by curve-fitting, are methyl benzoate, slope 0.921 + 0.010, intercept... 

Morton and Stubbs method (and the method using derivative curves, cf. 11.18) allows an efficient baseline correction if it is assumed that absorption varies linearly in the measurement range. Thus, in the situation represented in Fig. 11,24a, it is essential for quantification to correct absorbance A2 at the maximum X2 by subtracting the values indicated as x and y ... 

Figure 19-9 (a) Spectrophotometric titration of 30.0 mL of EDTA in acetate buffer with CuS04 in the same buffer. Upper curve [EDTA] = [Cu2 ] = 5.00 mM. Lower curve [EDTA] = [Cu2 ] = 2.50 mM. The absorbance has not been corrected in any way. (b) Transformation of data into mole fraction format. The absorbance of free CuS04 at the same formal concentration has been subtracted from each point in panel a. EDTA is transparent at this wavelength. [From L D. Hill and P MacCarthy, Novel Approach to Job s Method Chem. Ed. 1986,63, 162.]... 

Once the background is subtracted, the component of the spectrum due to the annihilation of ortho-positronium is usually visible (see Figure 6.5(a), curve (ii) and the fitted line (iv)). The analysis of the spectrum can now proceed, and a number of different methods have been applied to derive annihilation rates and the amplitudes of the various components. One method, introduced by Orth, Falk and Jones (1968), applies a maximum-likelihood technique to fit a double exponential function to the free-positron and ortho-positronium components (where applicable). Alternatively, the fits to the components can be made individually, if their decay rates are sufficiently well separated, by fitting to the longest component (usually ortho-positronium) first and then subtracting this from the... 

According to the DFA method, the time series y t) is first integrated and then divided into boxes of equal length, At. In each box, a least squares line (or polynomial curve of order /, DFA-/) is then fitted, in order to detrend the integrated time series by subtracting the locally fitted trend in each box. The root-mean-square (rms) fluctuation Fd(At) of this integrated and detrended time series is calculated over all timescales (box sizes). 

The radial concentration scans obtained from the UV spectrophotometer of the analytical ultracentrifuge can be either converted to a radial derivative of the concentrations at a given instant of time (dc/dr)t or to the time derivative of the concentrations at fixed radial position (dc/dt)r (Stafford, 1992). The dcf dt method, as the name implies, uses the temporal derivative which results in elimination of time independent (random) sources of noise in the data, thereby greatly increasing the precision of sedimentation boundary analysis (Stafford, 1992). Numerically, this process is implemented by subtracting pairs of radial concentration scans obtained at uniformly and closely spaced time intervals c2 — G)/( 2 — h)]. The values are then plotted as a function of radius to obtain (dc/dt) f versus r curves (Stafford, 1994). It can be shown that the apparent sedimentation coefficient s ... 

Equation (21.34) can only be used to fit data for which Kohs is small, 5T.02, under the initial conditions of the experiment ([Mg2+] = 0). We use a melting experiment under the buffer conditions of the isothermal titration to establish a value for Kohs at the titration temperature. If a significant fraction of the RNA is folded in the absence of Mg2+, baseline (s) are subtracted by an appropriate method and the data are normalized to the appropriate range of 9, 9 = Kohs/(1 + Kohs) for the initial zero Mg2+ concentration point and 1.0 for the maximum value of 9. The following equation works well for fitting these curves ... 

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