Integral methods graphical procedure

A General Integral Method for the Analysis of Kinetic Data—Graphical Procedure. 

Integral Methods for the Analysis of Kinetic Data—Numerical Procedures. While the graphical procedures discussed in the previous section are perhaps the most practical and useful of the simple methods for determining rate constants, a number of simple numerical procedures exist for accomplishing this task. 

Gates and Marlar<<0) devised a graphical procedure to determine the kinetic constants which took into account the data in the Anal stages of the growth-phase of a batch fermentation. As a result, their procedure can be used to estimate values of fim, Ks and the yield coefficient Y. The method involves rewriting equation 5.125, which is the complementary expression to the integrated form of the Monod equation 5.124, but refers to the substrate ... 

An alternate method to determining the number of transfer units is the graphical integration of dy/(y - y). The procedure is basically the same as for absorbers, that is ... 

In practice, even the determination of a fourth-order correlation function requires a large amount of calculation. However, this procedure may be standardized by a graphical method, which performs the integration in Eq. (1.54) by using properties of Hermite polynomials [37], Without going into details, we give the result... 

Cluster analysis is far from an automatic technique each stage of the process requires many decisions and therefore close supervision by the analyst. It is imperative that the procedure be as interactive as possible. Therefore, for this study, a menu-driven interactive statistical package was written for PDP-11 and VAX (VMS and UNIX) series computers, which includes adequate computer graphics capabilities. The graphical output includes a variety of histograms and scatter plots based on the raw data or on the results of principal-components analysis or canonical-variates analysis (14). Hierarchical cluster trees are also available. All of the methods mentioned in this study were included as an integral part of the package. 

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