Theoretical Data

Fig. 4.4. The experimentally determined relative phases of harmonics and the corresponding excursion time T as a function of harmonic order (squares). The error bars are about the sizes of the symbols for the experimental data. Theoretically obtained curve are also shown by the gray curve...

The solubility of substances in SCFs has been described by many different approaches [41-43]. Based on experimental data, theoretical treatment allows for modeling the solubility in SCCO2 [44,45]. Other approaches are based on equations of state (EOS) or on statistic models [46,47]. 

Figure 18. Saturation of SHG efficiency in the waveguide (ppKTP and appKTP) experiments (point data). Theoretical predictions incorporating the effects of two-photon absorption for the SH wave and group velocity mismatch are also shown for the ppKTP (dashed line) and appKTP waveguides (solid line).

Another analytical dilemma is the problem of in vitro and in vivo conditions. Alkaloids should be studied in their physiological conditions in organisms. This is not possible in many cases. In vitro experiments give compromised data. Theoretical conclusions and hypotheses in analysis, although they are in many cases indicators of a new breakthrough, also have some problems and some risks. 

This is a controversial area with regard to humans where there is currently little hard data. Theoretically it is possible for a foreign compound to cause mutations in male germ cells, which result in malformations or the development of abnormal offspring. This is similar to the situation in which inherited mutations or chromosomal aberrations lead to the birth of abnormal offspring, such as occur in Down syndrome, for example, where an extra chromosome occurs (Trisomy 21). 

IfemlU. Axial distribution of pressure and porosity of an ignition-plug day measured in a CP cell, (a) Normalized pressure distribution as a"oma m d distance [( ) experimental filtration data theoretical curves (x) AP = 98kN m-2 ( ) AP = 294 kN m-2 (A)... 

Illustration of influence of irreversible faradaic process on (G/o>) data, bias 0.65 V ((X) experimental data (----------) theoretical curve for equiva-... 

Fig. 5.3. SH rotational anisotropy from clean Ag(lll) in UHV at 3xl(T10 torr under p-polarized excitation at 1064 nm. The open circles represent the p-polarized (a) and s-polarized (b) SH data. Theoretical fits using Eqs. (3-11) and (3-13) are indicated with the solid line. From Ref. 124.

Liang, Y. and Kvalheim, O.M., Resolution of two-way data theoretical background and practical problem-solving, Part 1 Theoretical background and methodology, Fresenius J. Anal. Chem., 370, 694-704, 2001. 

Figure 2.9 Changes in the slope angles of the experimental plots shown in Figure 2.8 (ig(aexp)) and theoretically from Equation (2.2) (tg acaic)) as a function of the number of middle phosphate groups in PolyP molecules (nc) (o) experimental data ( ) theoretical data obtained from Equation (2.2) (Krupyanko et al., 1998).

The purposes of studying. in detail the reactions of these metals with gases were as follows (1) to compare the rates of these reactions with those of other metals and to interpret the rate data theoretically, (2) to obtain basic information on the processes involved in the reduction, refining, and working of columbium and tantalum, and (3) to understand the reactions which tantalum and columbium may undergo as components of high-temperature alloys. 

In order to discriminate between subsequent relaxation processes, it is necessary to calculate the orientational relaxation as a fimction of the location of a segment along the chain and to compare the results of such predictions to experimental data. Theoretical expressions are given elsewhere [29] and reference should be made for further details. In this work, the more elaborate treatment of the chsiin fluctuation process has been used and equations used in the calculation of orientation have been extracted from reference [13]. The... 

To determine the average droplet size from the scattering data, theoretical curves of the ratio of I 0,d)/I 4°,d) were calculated as a function of 0 for a range of appropriate droplet diameters. 

As explained in Section III,A,4, a perfect knowledge of mass-transfer data theoretically necessitates simultaneous measurements of mass-... 

Figure 2. Method of Referencing Unpublished Data, Theoretical Organic Chemistry/ Part II, Raman Spectra, Page 81...

Figure 4. Two-body isotropic scattering spectrum for CF4 gas at 294.5 K. The full circles ( ) indicate our experimental data with error bars triangles (A) are just estimated data. Theoretical curves are provided for several contributions using a = 2.93 A3, A = 1 A4, E = 1.5 A5 DID...

FIG. 5 Solution resistance vs distance curves for Ag/AgCl micropipette electrode over (a) Pt and (b) Teflon targets. Solution, 0.1 M KC1 applied voltage 50 mV between the two Ag/AgCl electrodes micropipette diameter, 20 gm (RG = 10). (+ + +) Experimental data ( ) theoretical curves. (From Ref. 77.)... 

Dissolution measurements in the absence of supporting electrolyte were made on both electrochemically grown films and pressed pellets of AgCl, with similar results (7). Approach curves for tips characterized by a = 5, 12.5, and 25 /xm, constructed by plotting the normalized long-time currents, from chronoamperometric measurements, as a function of normalized tip-substrate distance are shown in Figure 34a and b. The curves cover different values of L since, in each case, measurements were made over a range of distances up to 2 /xm from the substrate surface. For comparison with the experimental data, theoretical approach curves are also shown for second-... 

The values of a in the KC1 column enclosed in brackets are obtained from Harned s data (Journ Amer Chem Soc, 38, 1989 (1916)) The values of a in the case of KCI should be compared with the values calculated from the freezing point data by Lewis and Lmhart, quoted later, the values obtained from the freezing point are somewhat higher than those obtained from e m f data Theoretically, they should be identical, except in so far as temperature may exert a small effect The e m f data refer to 2 50 C, the freezing point data to 0° C approximately ]... 

Despite its trial and error nature, such a method is easily implemented on a spreadsheet. We make two columns, one containing the experimental data, the other the theoretical curve as calculated with assumed parameter values. In a third column we calculate the squares of the residuals (i.e., the differences between the two), and we add all these squares to form the sum of squares, SRR. This sum of the residuals squared, SRR, will be our data-fitting criterion. We now adjust the various assumed parameters that define the theoretical curve, in such a direction that SRR decreases. We keep doing this for the various parameters until SRR has reached a minimum. Presumably, this minimum yields the best-fitting parameter values. Incidentally, the third column is not needed when we use the command =SUMXMY2[experimental data, theoretical data). 

This is a controversial area with regard to humans where there is currently little hard data. Theoretically it is possible for a foreign compound to cause mutations in male germ cells which result in... 

Thus, two main conclusions can be drawn from these experiments (i) The QCM does only report on cells that are specifically anchored to the resonator surface. The method is blind to cells that just settle to the surface and attach only loosely, (ii) When specific cell-substrate interactions are omitted, the cells stay away from the surface by more than 100 nm, according to our RICM data. Theoretical considerations have previously indicated that cells may approach the surface as closely as 5-10 nm just by non-specific attraction [21]. This is, however, not confirmed by our optical measurements. 

Historical. About a century ago, experimentalists and theoreticians independently popularized the use of various forms of polynomial expressions for the mathematical description of physical behavior, e.g., the volumetric behavior of a gas. The early use was based solely on convenience, especially for interpolation of data. Theoretical significance was later established for many cases. For the volumetric behavior of a gas, each term of an infinite series expansion in density was given specific significance in terms of intermolecular forces. 

Na(3 i/) + CO. Extensive experimental data have been reported for the quenching of excited Na atoms by various gases, most of it dealing with the overall quenching cross-sections. In order to understand the mechanism by which the electronic energy is released in the course of a collision, it would be extremely helpful to have detailed microscopic data. Theoretical developments have reached the stage where detailed dynamical properties can now be predicted or correlated. By means of CO laser absorption, the vibrational population distribution of the excited CO produced in the reaction Na(3 / ,/2,3/2) + CO(u = 0)- Na(3, S) + CO(u) has been measured and compared with some theoretical models. ... 

ENDOR measured at fields 1 mT above the peak of the g = 2.0 extremum (see Sect. 4.1) ENDOR data , Theoretical values ... 

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