Linear-graph method

In order to check the robustness of the the linear-graph-method, and in particular to examine a possible concentration dependance of the chemical shifts of the various... 

With the validation of our method, we were able to apply this the linear-graph-method to the full assignment of the C H NMR spectra of the major components in marula. 

Walash et al. [14] described a kinetic spectrophotometric method for determination of several sulfur containing compounds including penicillamine. The method is based on the catalytic effect on the reaction between sodium azide and iodine in aqueous solution, and entails measuring the decrease in the absorbance of iodine at 348 nm by a fixed time method. Regression analysis of the Beer s law plot showed a linear graph over the range of 0.01 0.1 pg/mL for penicillamine with a detection limit of 0.0094 pg/mL. 

Further drawbacks associated with the direct linear plot include the fact that this analysis does not readily lend itself to standard computerized graphing methods (for example, use of GraphPad Prism), although specialized software is available (Henderson, 1993). Of course, one of the major advantages of the direct linear plot is the ability to obtain kinetic constants by eye, without the need for a computer. However, for presentation purposes, the use of graphing software is still desirable. Furthermore, any behavior more complicated than simple, single substrate kinetics - for example, turnover in the presence of an inhibitor, or multisubstrate kinetics - caimot readily be shown on a direct linear plot. This is in contrast with the flexibility afforded by nonhnear regression approaches. 

The philosophy is simple make products with build-in robustness against all kinds of environmental disturbances and fluctuations. The experimental design methods are presented as linear graphs and orthogonal arrays, but are not essentially different from established designs like Factorial and Fractional Factorial designs [12]. The methods of analyzing... 

Table 30.3 shows the values of KJ2 and l/ <, for each test, calculated by the method of least squares. In all but test I the first point, which does not fall on the linear graph, was omitted. Also in Table 30.3 are the values of a and R . Figure... 

In this method, chemical species are symbolized by weighted linear graphs. Two vertices mq and vq of a molecular graph are said to be equivalent with respect to r ... 

Some recently obtained results appear to be pertinent to this discussion. We have perfused proximal and distal tubules with 0.1 M phosphate solutions at an initial pH of 5.5, and recorded the alkalinization of these columns toward the steady state level. This is also an exponential process, and linear graphs relating the log of the difference between acid concentration at time t and steady state concentration with time are obtained. According to the previously given pump-leak model, the slopes of these lines should not be different from acidification lines, since they both depend essentially on the permeability of the epithelium to outflow of H ions from the tubular lumen. In our series, the difference between the mean values of the rate constants obtained in the proximal tubule during alkaline and acid perfusions was small, and of borderline significance, in view of the inherent uncertainties of the method, and we believe still compatible with the pump-leak model. In the distal tubule, however, these differences are quite considerable. 

Any transformation that could be affected for such curves so that they would yield linear graphs would have manifest advantages, because it would afford a sound mathematical basis for computation, which is a desirable consideration for any analytical method. In any type of microbiological assay of vitamin Bu the results should be plotted to test whether a dose-response, a log dose-response, or a log dose-log response curve is sufficiently linear to make possible the use of statistical methods. In the assay of vitamin B12 activity in crude materials, however, the most pertinent problem at present is to relate this activity to certain defined substances rather than to obtain the highest accuracy in measuring the Bu activity. 

The first step of this method is to simulate an EEA model of a noncorroded pipe. The load is then plotted as the ordinate while the strain is plotted as the abscissa in a linear graph. Subsequently, a double-elastic curve (DEC) that has a gradient half of the linear elastic region of the load—strain curve is plotted through the origin. The PACE corresponds to the intersection of the DEC and stress—strain curves. Finally, the DL is determined by dividing the PACE with a margin value, which in this case is 2. The maximum permissible strain limit is defined as the strain value at the intersection of the DEC and DE curves. 

Correlation methods discussed include basic mathematical and numerical techniques, and approaches based on reference substances, empirical equations, nomographs, group contributions, linear solvation energy relationships, molecular connectivity indexes, and graph theory. Chemical data correlation foundations in classical, molecular, and statistical thermodynamics are introduced. 

PVSA-SG film was used for determination of Fe(Phen) + and Zn + as ternary complex Zn +-Phen-bengal rose by spectrophotometric method. The calibration graph was linear in the concentration 5T0 -5T0 mol/lfor Fe(II) and FlO - 5T0 mol/1 for Zn(II). The film can be regenerated and reused. LG-PDMDA-SG film was shown to be perspective modificator of the PG electrode surface and used for voltammetric detection of Mo(VI) at ppb level. 

It was shown that Zn + adsorbed onto SG-PVSA composite film as Zn(Phen) complex. It can be detected spectrophotometrically after treatment with anionic dye Bengal Rose (BR). Ternary complex Zn + - Phen-BR formed on the surface under optimal conditions. SG-PVSA film was used for determination of Zn + by spectrophotometric method. The calibration graph was linear in the concentration range 2,5T0 - STO mol/l. 

Following this procedure urea can be determined with a linear calibration graph from 0.143 p.g-ml To 1.43 p.g-ml and a detection limit of 0.04 p.g-ml based on 3o criterion. Results show precision, as well as a satisfactory analytical recovery. The selectivity of the kinetic method itself is improved due to the great specificity that urease has for urea. There were no significant interferences in urea determination among the various substances tested. Method was applied for the determination of urea in semm. 

Most of the 2D QSAR methods are based on graph theoretic indices, which have been extensively studied by Randic [29] and Kier and Hall [30,31]. Although these structural indices represent different aspects of molecular structures, their physicochemical meaning is unclear. Successful applications of these topological indices combined with multiple linear regression (MLR) analysis are summarized in Ref. 31. On the other hand, parameters derived from various experiments through chemometric methods have also been used in the study of peptide QSAR, where partial least square (PLS) [32] analysis has been employed [33]. 

Once a linear relationship has been shown to have a high probability by the value of the correlation coefficient (r), then the best straight line through the data points has to be estimated. This can often be done by visual inspection of the calibration graph but in many cases it is far better practice to evaluate the best straight line by linear regression (the method of least squares). 

The values used in plotting Figs. 2-1 and 2-2 can be used to illustrate the method for first-order and second-order data. Plots of t/E versus time are shown in Fig. 2-9. The second-order data define a precise straight line, and those for n = 1 are linear to E < 0.4. The latter graph has a slope of 0.6, giving n = 1.2. 

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