Calibration matrix representation

The element y is determined by the sensitivity parameter dx/dc, and the sensitivity of the method is numerically determined by the value of y. This example can readily be expanded to consider a multicomponent case, where X, y, and c become matrix representations and a partial sensitivity dx/dc is employed. A mathematical rearrangement of the yij matrix to place the largest y value in each row on the main diagonal results in a useful calibration... 

The approach presented above is referred to as the empirical valence bond (EVB) method (Ref. 6). This approach exploits the simple physical picture of the VB model which allows for a convenient representation of the diagonal matrix elements by classical force fields and convenient incorporation of realistic solvent models in the solute Hamiltonian. A key point about the EVB method is its unique calibration using well-defined experimental information. That is, after evaluating the free-energy surface with the initial parameter a , we can use conveniently the fact that the free energy of the proton transfer reaction is given by... 

Second, progress has been made in the theoretical approach to the analysis of DCEMS measurements. The underlying theory of resonance excitation (-> excitation matrix) in the sample by y-quanta including secondary absorption and emission processes, electron transport (- transport tensor), and detection response (—> response function) have been included in a least-squares fit routine [ 103. 105). Adjustable parameters in this fitting are. on the one hand, the hyperfine interaction and line shape variables, and, on the other hand, the variables that give a parametric representation of the depth profiles. The response parameters are also included to allow energy calibration of the experimental apparatus. 

FIGURE 4 Graphical representation of external calibration, standard addition and internal standard strategies related to obtaining the quantitative information from the C matrix provided by multiset analysis. 

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