Curve subtraction

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). 

The second mode is to run the experiment at a fixed magnetic field and sweep the second boxcar gate over time to collect kinetic information. There are two problems with this approach. Eirst, the experiment must be repeated several times with a slow scan rate in order to get satisfactory S/N. To extract the EPR kinetic curve, the experiment is repeated off resonance and the two curves subtracted. Kinetics are more easily obtained using a high-bandwidth transient digitizer instead of a boxcar, and many researchers perform TREPR in this fashion." ° It is important to note here two... 

Spittler and Willig and co-workers measured the temperature dependence of k for a cyanine dye adsorbed onto silver bromide octahedral crystals [196]. Nonexponential experimental decays were observed and a curve subtraction technique... 

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 CALCULATIONS programs permit a wide variety of calculations to be performed on TG data. Programs for curve subtraction and derivative calculations are available. 

TPR experiments were conducted with an Altimira temperature-programmed system following procedures described previously [8]. Catalyst powder samples (100 to 300 mg) were heated from room temperature to 1073 K at a rate of 15o/min in a flowing stream (40 cc/min) of 8% H2 in Ar. Prior to reduction, samples were given a standard in situ preoxidation at 773 K for 1 h. TPR traces reported here are baseline corrected (using a smooth curve subtraction procedure) and nonnalized to an equivalent sample size. 

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. 

Fig. 37 a, b. Estimation of blend composition by TREE curve subtraction, (a) Known component TREE curves, (b) Using computer search technique [14] (see text)... 

General (DTA, DSC, TG, TMA, DMA) Variation of signal amplitude Signal and temperature calibration Accumulation and storage of data Baseline smoothing" Display and calculation of transition temperatures Display of multiple curx es Curve subtraction Derivative TA curve Baseline correction"... 

Figure 19. Left Pyrometrically determined cooling curves for levitated AYx liquids showing crystallization temperatures where Debye-Scherrer features first appeared in the WAXS pattern (dashed arrows). For AY15 and AY20 the crystallization exotherm is anticipated by a prepeak (solid arrow) that is associated with the LLPT identified by the polyamorphic rotor action. Right Curves for AY15 and AY20 with the cooling curves subtracted differentiating the LLTP exotherm from exotherm due to crystallization.

Instrumental effects such as buoyancy and gas flow. These effects can be reduced or eliminated by performing blank curve subtraction. 

Buoyancy effects caused by the density of the surrounding gas decreasing on heating. Typically this results in an apparent mass gain of50-200 jxg. Since buoyancy effects are reproducible, the curves can be corrected by performing automatic blank curve subtraction. This also applies to buoyancy effects due to gas switching, a technique often used in TCA. 

Figure C2.18.5. Si(2p) spectmm of Si(l 11) reacted with 5 x 10 Torr of XeF2, using photon energy of 130 eV. The top panel shows the raw data and the fitted background. The bottom panel shows the spectmm after background has been subtracted and fitted into five components bulk Si and the four fluorosilyl peaks. The solid curve is the sum of the individual dashed component curves. Reproduced from [40].

Note that subtracting an amount log a from the coordinate values along the abscissa is equivalent to dividing each of the t s by the appropriate a-p value. This means that times are represented by the reduced variable t/a in which t is expressed as a multiple or fraction of a-p which is called the shift factor. The temperature at which the master curve is constructed is an arbitrary choice, although the glass transition temperature is widely used. When some value other than Tg is used as a reference temperature, we shall designate it by the symbol To. 

The same procedure maybe used at other pump flows to permit plotting the series of balance-point curves as has been done in Fig. 29-61. From such curves, one can establish the maximum lean pump at any total tower outflow, and combining this with the semilean-pump performance curve results in Fig. 29-55. Bypass flow plotted in Fig. 29-55 is obtained by adding simultaneous lean- and semilean-pump flows and subtracting the recovery pump-turbine flow required to make the balance point at that lean-pump flow. 

Ideally, straight-line isotherm plots are obtained. However there may occasionally be departures from linearity. A curve as shown in Figure 30 (A) may be obtained if a non-adsorbable impurity is present in the liquid being treated. For such simations subtracting Cj from Q and re-plotting the isotherm will usually yield a straight line. 

The nsb for this example was shown to be 15.2 0.2pM/mg protein. This value is subtracted from the total binding numbers or the total binding fit to displacement curves. Total binding with a representation of nsb is used in this example and is shown in Figure 12.2a. 

Figure 5. (a) The ( A, SO,) anion symmetric streching mode of polypropylene glycol)- LiCF,SO, for 0 M ratios of 2000 1 and 6 1. Solid symbols represent experimental data after subtraction of the spectrum corre-ponding to the pure polymer. Solid curves represent a three-component fit. Broken curves represent the individual fitted components, (b) Relative Raman intensities of the fitted profiles for the ( Aj, SO,) anion mode for this system, plotted against square root of the salt concentration, solvated ions ion pairs , triple ions, (c) The molar conductivity of the same system at 293 K. Adapted from A. Ferry, P. Jacobsson, L. M. Torell, Electrnchim. Acta 1995, 40, 2369 and F. M. Gray, Solid State Ionics 1990, 40/41, 637. 

Fig. 8-la. The effect of a nonlinear background on the analysis for silver. Simple subtraction of adjacent background gave inversion observable on curve 1 near ordinate axis. Allowance for variation of background with wavelength gave the more reliable curve 2. (We are indebted to the Eastman Kodak Co. for the films and the results plotted as abscissas.)... 

Fig. 12. Interface width a as a function of annealing time x during initial stages of interdiffusion of PS(D)/PS(H) [95]. Data points are obtained by a fit with error function profiles of neutron reflectivity curves as shown in Fig. 11. Different symbols correspond to different samples. The interface width a0 prior to annealing is also indicated (T) and is subtracted quadratically from the data (a = [

To determine die diffusion current, it is necessary to subtract the residual current. This can be achieved by extrapolating the residual current prior to the wave or by recording die response of the deaerated supporting electrolyte (blank) solution. Addition of a standard or a calibration curve are often used for quantitation. Polarograms to be compared for this purpose must be recorded in the same way. 

The data at short times afford a rate constant that can be evaluated by subtracting the extrapolated curve from long times. This gives a quantity A, defined by... 

Fig. 3.15, The CARS spectrum rotational width versus methane density for various values of parameter y (1) y = 0, (2) y = 0.3, (3) y = 0.5, (4) y = 0.7, (5) y = 0.75, (6) y = 0.9, (7) y = 0.95, (8) y = 1. Curves (4) and (6) are obtained by subtraction of the dephasing contribution from the line width calculated taking account of vibrational broadening. The other dependences are found assuming purely rotational broadening (vibrational relaxation neglected).

Figure 1.30. A histogram of raw weights from Figure 1.29 and the distribution of residuals that resulted after subtraction of a shifted box-car average are superimposed. The CP-curve, plotted with the (NPS) option in HISTO, is for the raw weights the corresponding curve for the residuals would be about twice as steep. The asymmetry of the raw-weight distribution is evident both in the histogram and the lack of linearity of the CP-curve it is due to many subpopulations of product being lumped into one batch. Every time a mechanic makes an adjustment on a knife, a new subpopulation is created. The residuals appear to be normally distributed, however.

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