Sample computation programs

The sum expressed by equation (21) lends itself to a digital calculation and can be employed in an appropriate computer program to calculate actual peak profiles. In doing so, however, as (v) is measured in plate volumes and sample volumes are usually given in milliliters, they must be converted to plate volumes to be used with equation (21). To demonstrate the effect of a finite charge and the use of equation (21), the peak profiles resulting from a sample dispersed over the twenty-one consecutive plates of a column are shown in Figure 16. 

The sum expressed by equation (25) also lends itself to a digital solution and can be employed in an appropriate computer program to calculate actual peak profiles for different volumes of pure mobile phase that have been injected onto an equilibrated column. The values of (Xg) were calculated for a column having 500 theoretical plates and for sample volumes of 20, 50, 100 and 200 plate volumes, respectively. The curves relating solute concentration (Xe) to plate volumes of mobile phase passed through the column are shown in Figure 17. 

P.K. Hopke, D.J. Alpert and B.A. Roscoe, FANTASIA — A program for target transformation factor analysis to apportion sources in environmental samples. Comput. Chem., 7 (1983) 149-155. 

Ph.D., performed the computer programming and statistical analysis. Candace Young and Frieda Fisher helped with data management. William Bax, Joseph Wade, Charles Bennett, Gertie King, Dennis Miles, Jimmie Pickett, Frank Porter, Deborah Richardson, and Alice Roberts collected urine samples. 

From these noisy structure factor amplitudes squared, a sample of 2532 noisy structure factor amplitudes F Noisy up to 0.463 A, and the associated standard deviations cr(/F Noisy), have been computed using the computer program BAYES [55]. A number... 

Various methods, such as influence sampling, can be used to reduce the number of calculations needed. See also Lapeyre, B., Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press (2003), and Liu, J. S., Monte Carlo Strategies in Scientific Computing, Springer (2001). Some computer programs are available that perform simple Monte Carlo calculations using Microsoft Excel. 

Chloride can also be estimated by potentiometric titration using standard silver nitrate [27]. The results are recorded directly and evaluated by means of a computer program based on the Gran extrapolation method. The determinations have a precision of 0.02% and since many samples can be titrated simultaneously, the time for a single determination can be reduced to less than 5 min. 

Figure 6.2 shows a frequency plot for a much larger sample of data (1000 data points) which was simulated from the data set shown in Table 6.1, using a computer program. 

The results from VIRS analyses are amenable to several methods of interpretation. In the simplest sense, the spectra can be used as empirical measurements on given rock types or formations, without specific reference to the causative minerals. We have found that superficially identical rock types with different geological contexts can in some cases be effectively characterized and discriminated. The comparison of measured spectra with reference spectra from minerals is the main tool used for identification, and is very effective in cases where samples are monomineralic or dominated by a single infrared active species. The size of the area analyzed is 1 cm in diameter. Computer programs with variable levels of automation can speed the process of identification, but... 

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