Data Subtraction

As was discussed in section 3.7, a floating baseline can often be purged out of a DTA/DSC trace by subtracting a second run. The process of subtraction is complicated by the fact that the x-axis values of the two data sets may not line up. Extrapolation from nearby points is necessary so that abscissa values from the two data sets may be properly subtracted. The following is a Basic program which reads two data sets into memory, subtracts the second from the first using extrapolation, and then stores the subtracted data set  

INPUT Enter output filename , outfilel OPEN filell FOR INPUT AS 1 OPEN file2 FOR INPUT AS 2 OPEN outfile FOR OUTPUT AS 3 

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Translation of the cell left and right permits the achievement of each of the three objectives listed above, using appropriate data subtraction procedures to remove contributions from gas phase species If present during measurements. 

To calculate the range, find the difference between the largest and the smallest values in the set of data. Subtract the smallest value from the largest value in the set. 

Row centring of the data (subtraction of the mean activity of a compound in all tests). 

Standardized test protocols and routines must be also further developed to make data subtracted from the fuel cell more reliable and comparable. Specific long-term test protocols should be also developed to investigate durability of individual fuel cell components and interactions among themselves. Besides, each fuel cell application may require its own adapted testing protocols. 

The three curves are brought up on the screen, isothermals matched, data subtracted and referenced against the standard. Most software packages will do this automatically, and if the... 

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].

The two main ways of data pre-processing are mean-centering and scaling. Mean-centering is a procedure by which one computes the means for each column (variable), and then subtracts them from each element of the column. One can do the same with the rows (i.e., for each object). ScaUng is a a slightly more sophisticated procedure. Let us consider unit-variance scaling. First we calculate the standard deviation of each column, and then we divide each element of the column by the deviation. 

Two methods are commonly used to correct for the residual current. One method is to extrapolate the total measured current when the analyte s faradaic current is zero. This is the method shown in the voltammograms included in this chapter. The advantage of this method is that it does not require any additional data. On the other hand, extrapolation assumes that changes in the residual current with potential are predictable, which often is not the case. A second, and more rigorous, approach is to obtain a voltammogram for an appropriate blank. The blank s residual current is then subtracted from the total current obtained with the sample. 

Subtracting y —y) from y — T) gives (T — y) which is that portion of the deviation of any data point from the mean which is explained by the correlation. The coefficient of determination, y, a statistical parameter which varies from 0.0 to 1.0, is defined as ... 

The small value of the entropy change reflects the fact that only liquids are involved in tlris reaction. The heat balance in canying out tlris reaction may be calculted, according to Hess s law, by calculating tire heat change at room temperarnre, and subtracting tire heat required to raise the products to the hnal teirrperamre. The data for tlris reaction are as follows ... 

To determine the required amount of planned blowdown, subtract windage losses from B. Use Table 1 for windage losses in liew of manufacturer s or other test data. 

EXAFS data are multiplied by ( = 1, 2, or 3) to compensate for amplitude attenuation as a function of k, and are normalized to the magnitude of the edge jump. Normalized, background-subtracted EXAFS data, versus k (such as... 

Figures Background-subtracted, normalized, and ili -weighted Mo K-edge EXAFS, versus k (A ), for molybdenum metal foil obtained from the primary experimental data of Figure 2 with Eq = 20,025 eV.

A further critical point are the intensities correlated to spectra of the pure elements. Calculated and experimentally determined values can diverge considerably, and the best data sets for 7 measured on pure reference samples still show a scatter of up to 10%. The use of an internal standard or a simultaneously measured external standard seems to be the most successful way to reducing the inaccuracy below 10%. (Eor a more detailed discussion of background subtraction and quantification see, e.g., Seah [2.9].)... 

Take the nth set of data, from this extract the (m +1) data pair and from this take the second number, subtract from this the second number from the mth data point of the same data set divide this by the difference between the first number from the (m +1) pair from the nth set and the first number in the mth data pair of the nth set. Do this for all the n datasets and all the m pairs in each set. 

FIG. 34 (a) Log-log plot of i ads(0 ane for an adsorbed layer containing 64 chains (cf) = 0.25), where at time / = 0 the adsorption energy strength e is reduced from e = -4.0 to values between e = -1.2 and e = -0.2, as indicated in the figure. Straight lines show a power law Fads(t) oc over some intermediate range of times. The inset shows that the (effective) exponent a can be fitted to a linear decrease with e. (b) The same data but with the equilibrium part ads(l l) subtracted [23]. 

Table 27 contains data for some uni-univalent solutes for which both the entropy of solution at 25°C and the viscosity //-coefficient in aqueous solution at 18 or 25° are known. In column 3 from the entropy of solution 16.0 e.u. have been subtracted for the cratic term. 

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