Data reduction procedure

The data-reduction procedure just desciiDed provides parameters in the correlating equation for g that make the 8g residuals scatter about zero. This is usually accomphshed by finding the parameters that minimize the sum of squares of the residuals. Once these parameters are found, they can be used for the calculation of derived values of both the pressure P and the vapor composition y. Equation (4-282) is solved for yjP and written for species 1 and for species 2. Adding the two equations gives... 

Quantitative analysis procedures using infrared spectrometry utilize Beer s law. Thus only sampling cells with a constant pathlength can be used. Once the percent transmittance or absorbance measurements are made, the data reduction procedures are identical with those outlined in Chapter 7 (preparation of standard curve, etc.). 

There are a number of ways by which the data of an elementary EEC experiment (such as NP or PP) can be reduced to a single point of the Mex(x) curve. Since these data-reduction procedures depend upon the signal detection technique, we shall postpone their discussion. It is useful, however, to provide a few comments on how the Mex(x) curves should be evaluated once we have a set of experimental points where y Me (x) and... 

Data Reduction Procedures. Details of the data analysis for the SEC/Viscometer system have been described previously.(16) The data reduction scheme is summarized in Figure 1 and briefly will be reviewed here. The intrinsic viscosity [n](V) of the effluent at a given retention volume V is determined from the DRI and continuous viscosity detector responses according to the following equation... 

An important caution is that any data reduction procedure that begins with extraction of principal components is based on the assumption that the data set consists of a small number of constituents that contribute to the measured spectrum at any point in proportion to their composition at that point. These methods cannot be used if that assumption is not correct. For example, mechanical loading of bone tissue causes wave number and intensity shifts in both mineral and matrix bands. While the shifts are not always linear with Appl. load, they do vary continuously. 

The determination of units of measurements in which analytical results will be reported is part of the data reduction procedure. Table 4.1 shows the commonly used units of measurements for various organic and inorganic analyses. 

The experimental and data reduction procedures are essentially the same as for the static cell experiments. The gas temperature is obtained using a fine wire, radiation-corrected thermocouple. The cold mixing layer at each flame boundary is accounted for by using an effective pathlength (8.0 - 8.2 cm, depending on the fuel-air equivalence ratio) which differs slightly from the actual burner length of 8.6 cm. Fuel-air equivalence ratios of... 

All these calculations will be achievable with PCs of the early- to mid-1990s. An example of an advanced NMR data reduction procedure is shown in Figure 10.1. The contrast enhancement achievable with maximum likelihood reconstruction can be put to good use in structure elucidation of biomolecules such as small nucleic acids and proteins. 

A non-resonance, direct-force method for dynamic shear properties measurements is described, and the results of tests on two commercially available damping polymers are presented. Novel aspects of this method include the means for supporting the sample and for measuring the imposed force and the resultant shear deformation. Addressed in this article are the test configuration, the principle of operation, the data reduction procedure, some typical measured properties, consistency checks on the data, and a brief description of an initial application of the data. 

The temperature scale at the top of the reduced temperature nomograph shows increasing temperature from right to left. Labeling of the temperature lines is done in a uniform temperature increment. The temperature increment is identified at the top of the nomogram. The nomograph presentation and data reduction procedure have been described in earlier publications (6.71. 

Data Reduction Procedure. The nomograph lends itself readily to reduction of viscoelastic data and is particularly convenient for computerized procedures. If one selects the proper position for Tq and the interval At between Tq and Ti, T2, etc., then the grid of lines can be used to place the test data in position. 

In practice the computerized data reduction procedure consists of the series of steps listed in Table I. For both multimodal resonant frequency data and constant frequency dynamic taken at several different frequencies, the correct value of the reference temperature (Tq) is that which reduces the scatter of the modulus and loss tangent data to fit a smooth curve. The initially assumed value of T0 is taken as the temperature corresponding to the loss tangent maximum or Tg. If this value of T0 does not give satisfactory superposition, the assumed value of T0 is adjusted to a slightly higher value and the procedure is repeated until a satisfactory superposition is achieved. Previous... 

In this chapter the experimental ECD and NIMS procedures for studying the reactions of thermal electrons with molecules and negative ions are described. Gas phase electron affinities and rate constants for thermal electron attachment, electron detachment, anion dissociation, and bond dissociation energies are obtained from ECD and NIMS data. Techniques to test the validity of specific equipment and to identify problems are included. Examples of the data reduction procedure and a method to include other estimates of quantities and their uncertainties in a nonlinear least-squares analysis will be given. The nonlinear least-squares procedure for a simple two-parameter two-variable case is presented in the appendix. 

Haber cycle Ea at 0.9 0.1 eV is the least precise [19, 32], The ECD values have no greater uncertainties since a data reduction procedure cannot degrade quality. 

The electron affinity of the acetate radical was determined from the -EDEA obtained from ECD data for ethyl acetate, benzyl acetate, and acetic anhydride. At the same time data were obtained for ethyl trifluoroacetate and ethyl trichlor-acetate, but were not analyzed or reported. These data are revisited with two states and new bond dissociation energies. This gives another example of how CURES-EC can be used to support experimental results [1, 69]. Figure 10.10 is a typical ECD plot of In KTia versus 1,000/7 for these compounds. In Table 10.11 the kinetic and thermodynamic parameters obtained from the data are shown. The values of I) E (acetate) available in the literature were used in the data reduction procedure, and the rate constant and Qan values are obtained from the ECD data. The, 41 values are close to the DeBroglie, 41. The Qan values are less than 1.0. The E values are less than 0.15 eV. The Ea are thus typical of the ECD, although in the lower range of Ea measured in the ECD for ethyl acetate, benzyl acetate, and acetic... 

As we have to cope with a broad data-matrix, that is to say more attributes than objects, data reduction procedures on the attributes side seem to be appropriate. 

We also discussed graphical and numerical data reduction procedures. The most important numerical data reduction procedure is the least squares, or regression, method, which finds the best member of a family of functions to represent a set of data. We discussed the propagation of errors through this procedure and presented a version of the procedure in which different data points are given different weights, or importances, in the procedure. 

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