Inverse theoretical background

In what follows the theoretical background of the most common physical properties and their measuring tools are described. Examples for the wet bulk density and porosity can be found in Section 2.2. For the acoustic and elastic parameters first the main aspects of Biot-Stoll s viscoelastic model which computes P- and S-wave velocities and attenuations for given sediment parameters (Biot 1956a, b, Stoll 1974, 1977, 1989) are summarized. Subsequently, analysis methods are described to derive these parameters from transmission seismograms recorded on sediment cores, to compute additional properties like elastic moduli and to derive the permeability as a related parameter by an inversion scheme (Sect. 2.4). 

CHEMICAL AND THEORETICAL BACKGROUND Box 13.6 Normal spinel and inverse spinel lattices... 

In this section we present the results of a recent paper (Ben-Naim and Santos 2009) where we directly recalculated the KBIs for two component mixtures of particles interacting via square-well potential. The theoretical background is lengthy and will not be presented here. Instead, we show a sample of results for mixtures of square-well particles. It is shown that the results are in quantitative agreement with those obtained from the inversion of the Kirkwood-Buff theory of solution. We also... 

For points 1-7, species O is consumed at the electrode and a reduction current is observed, whereas for points 8-10, O is regenerated by oxidation of R and an oxidation current is observed. Note that the change of sign in the current is directly related to the inversion of the concentration gradient for O at the electrode surface the gradient is positive for points 1-7 and negative for points 8-10. For additional theoretical background readers should consult Chapters 6 in reference (1), 6 in reference (2), 6 in reference (3) and 10 in reference (15). 

During the past 40 to 50 years, inverse gas chromatography (IGC) has developed into a widespread, popular, and fruitful technique for the physico-chemical characterization of various materials, as well for providing descriptions of the interactions between components in various systems. Indeed, during the past 20 year several reviews detailing the theoretical background of IGC, as well as its parameters, the interpretation of experimental data and applications have been produced [1-8]. 

I would like to emphasize, at the end of this section, that practical uniqueness has nothing in common with theoretical uniqueness. The requirement that the observations should be a function of the same or greater number of parameters than the model provides a qualitative background for the uniqueness only. Theoretically, even in this situation, the inverse problem could have several equivalent solutions. However, this requirement serves as a useful practical guide to ways of obtaining a unique solution for a practical problem. 

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