Correlation profile

Many academic and industrial laboratories have shown that the drug permeability measured in Caco-2 cell monolayers can be used to predict the oral absorption of drugs in humans. Various datasets have therefore been used to establish correlations between Caco-2 permeability and the fraction absorbed orally in humans [85, 86, 96]. Taken together, these studies show good predictability, though with a relatively wide variation in the appearance of correlation profiles between different laboratories [86]. These studies emphasize the need to establish correlations and standardization procedures in each laboratory. 

The importance of stratigraphic studies and the identification of sedimentary units at extensively disrupted sites like Hierakonpolis can be illustrated by the excavations at locality II, where there is evidence for habitation (trash mounds and pottery) as well as industry (pottery kilns). This locality ofiered a unique opportunity to study Predynastic ecology because of the excellent state of organic preservation in an area where there was a clustering of multi-functional components (6,14). Four test pits were dug in one area through the site, in the direction NIO °E-SIO °W. The correlation profile is shown in Figure I. The oldest unit identified was Nile silt (Masmas formation). In some areas, this silt was covered by eolian and/or wadi sands, which probably represents a local feature of sand accumulation under arid to semiarid conditions. 

Figure 1. Correlation profile for the four studied sections at locality 11 in Hierakonpolis. Vertical scale...

The parameters of (1.1) have also been presented in the right column of Table 3.3. Another way of determining the shear velocity t/, is the use of the correlation profiles... 

Partial ordering is useful as technique for rank correlation analysis, where a simple and transparent mapping of a correlation profile is possible. The principle described in this chapter is supported by the software named Po Correlation presented by Sorensen et al. (2005) and the content of this chapter is based on that paper. Non-commercial use of the software for research and education is free if reference is given to Sorensen et al., (2005) and can be made available by contacting the first author of this chapter. Two other software products exist for application of Partial... 

Fig. 5.14. Correlation profiles for mineral oil, calcium carbonate, polypropylene and pol)mrethane of a multilayer laminate using mineral oil as a mounting medium. After Martoglio Smith [491]. Reproduced from Vibrational Spectroscopy 24, RA. Martoglio Smith, 47-62 (2000), with permission of Elsevier.

The CONTIN method uses a regularization technique to seek smooth solutions, no matter whether the G(r) distribution is unimodal, multimodal, or broad. So the CONTIN method is appropriate for photocount correlation profile analysis without an a priori assumption on the form of the G(r) distribution. We used the CONTIN method, which was kindly provided by Dr. S.W. Provencher (European Molecular Biology Laboratory), mainly for correlation function profile analysis of unimodal and bimodal G(r) distributions. 

Digital subtraction of equations (1) from (2) produces a correlation image, or shearogram. For normal illumination and viewing, the intensity profile /, of the image is given by... 

A system of interest may be macroscopically homogeneous or inliomogeneous. The inliomogeneity may arise on account of interfaces between coexisting phases in a system or due to the system s finite size and proximity to its external surface. Near the surfaces and interfaces, the system s translational synnnetry is broken this has important consequences. The spatial structure of an inliomogeneous system is its average equilibrium property and has to be incorporated in the overall theoretical stnicture, in order to study spatio-temporal correlations due to themial fluctuations around an inliomogeneous spatial profile. This is also illustrated in section A3.3.2. 

Figure Bl.9.12. The schematic diagram of the relationships between the one-dimensional electron density profile, p(r), correlation fiinction y (r) and interface distribution fiinction gj(r).

Figure Bl.9.13. Time-resolved SAXS profiles diirmg isothennal crystallization (230 °C) of PET (the first 48 scans were collected with 5 seconds scan time, the last 52 scans were collected with 30 seconds scan time) calculated correlation fiinctions j(r) (nonnalized by the invariant 0 and lamellar morphological variables...

The quantitative analysis of the scattering profile in the high q range can be made by using the approach of Debye et aJ as in equation (B 1.9.52). As we assume tiiat the correlation fiinction y(r) has a simple exponential fomi y(r) = exp(-r/a ), where is the correlation length), the scattered intensity can be expressed as... 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

Seam correlations, measurements of rank and geologic history, interpretation of petroleum (qv) formation with coal deposits, prediction of coke properties, and detection of coal oxidation can be deterrnined from petrographic analysis. Constituents of seams can be observed over considerable distances, permitting the correlation of seam profiles in coal basins. Measurements of vitrinite reflectance within a seam permit mapping of variations in thermal and tectonic histories. Figure 2 indicates the relationship of vitrinite reflectance to maximum temperatures and effective heating time in the seam (11,15). 

According to a kinetic study which included (56), (56a) and some oxaziridines derived from aliphatic aldehydes, hydrolysis follows exactly first order kinetics in 4M HCIO4. Proton catalysis was observed, and there is a linear correlation with Hammett s Ho function. Since only protonated molecules are hydrolyzed, basicities of oxaziridines ranging from pii A = +0.13 to -1.81 were found from the acidity rate profile. Hydrolysis rates were 1.49X 10 min for (56) and 43.4x 10 min for (56a) (7UCS(B)778). O-Protonation is assumed to occur, followed by polar C—O bond cleavage. The question of the place of protonation is independent of the predominant IV-protonation observed spectroscopically under equilibrium conditions all protonated species are thermodynamically equivalent. 

Because of the close similarity in shape of the profiles shown in Fig. 16-27 (as well as likely variations in parameters e.g., concentration-dependent surface diffusion coefficient), a contrdling mechanism cannot be rehably determined from transition shape. If rehable correlations are not available and rate parameters cannot be measured in independent experiments, then particle diameters, velocities, and other factors should be varied ana the obsei ved impacl considered in relation to the definitions of the numbers of transfer units. 

The potential of LA-based techniques for depth profiling of coated and multilayer samples have been exemplified in recent publications. The depth profiling of the zinc-coated steels by LIBS has been demonstrated [4.242]. An XeCl excimer laser with 28 ns pulse duration and variable pulse energy was used for ablation. The emission of the laser plume was monitored by use of a Czerny-Turner grating spectrometer with a CCD two-dimensional detector. The dependence of the intensities of the Zn and Fe lines on the number of laser shots applied to the same spot was measured and the depth profile of Zn coating was constructed by using the estimated ablation rate per laser shot. To obtain the true Zn-Fe profile the measured intensities of both analytes were normalized to the sum of the line intensities. The LIBS profile thus obtained correlated very well with the GD-OES profile of the same sample. Both profiles are shown in Fig. 4.40. The ablation rate of approximately 8 nm shot ... 

Geon and Seo [47] also determined the effect of vulcanization time on the adhesion of natural rubber to brass-plated steel. For relatively short times, there was a peak at the end of the copper profile that corresponded well with a peak in the sulfur profile. Similarly, peaks in the zinc and oxygen profiles corresponded well. These results showed that copper sulfide and zinc oxide mostly formed at short times but some evidence for formation of zinc sulfide was also obtained. For long times, the peak in the sulfur profile no longer corresponded with that in the copper profile. Instead, the peak in the sulfur profile corresponded to the peak in the zinc profile. It was concluded that the formation of zinc sulfide increased substantially at long times. An increase in vulcanization time correlated well with a decrease in the force required to pull brass-plated steel wires out of rubber blocks. 

B. Gotzelmann, S. Dietrich. Density profiles and pair correlation functions of hard spheres in narrow slits. Phys Rev E 55 2993-3005, 1997. 

In any relation given above, the knowledge of the total or direct pair correlation functions yields an equation for the density profile. The domain of integration in Eqs. (14)-(16) must include all the points where pQ,(r) 0. In the case of a completely impermeable surface, pQ,(r) = 0 inside the wall... 

A set of equations (15)-(17) represents the background of the so-called second-order or pair theory. If these equations are supplemented by an approximate relation between direct and pair correlation functions the problem becomes complete. Its numerical solution provides not only the density profile but also the pair correlation functions for a nonuniform fluid [55-58]. In the majority of previous studies of inhomogeneous simple fluids, the inhomogeneous Percus-Yevick approximation (PY2) has been used. It reads... 

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