Seidel function

Three different methods that are commonly used to present graphically emulsion calibrations will be described. These include the H and D curve, the percentage transmittance curve, and the Seidel function curve. 

FIGURE 8-9. A photographic emulsion calibration curve using the Seidel function plotted versus relative intensity on a log—log scale. 

A third method of preparing an emulsion calibration curve is to plot the Seidel function, log[( o/ ) — 1] against log intensity, where Jq is the galvanometer deflection through the clear plate and d is the deflection through the spectral line. If the galvanometer is adjusted to read 100 through the clear... 

Included as parts of the calculating board are a movable vertical scale with a percentage T scale presented logarithmically. A Seidel function scale... 

Fig. 37B.3. Ilford Q-2 photoplate calibration curves established using intensity ratios for isotopes recorded on the same exposure. Several curves are depicted, utilising data from several exposures. From this information an average value of tan 6 ( gamma ) is computed. Note that the reciprocal of the Seidel function is plotted on the vertical axis, (Reproduced, with permission, from Geo-chim Cosmochim. Acta, 35 (1971) 1190, Pergamon Press.)...

Solubility of nitric oxide in water as a function of temperature (Seidell, 1919). 

A Jacobi or Gauss-Seidel iteration on (6) will provide us with the coordinates of the steady state, or it will cycle indefinitely, depending on the slope of the functions. On the other hand, determining the trajectory by numerical integration of equation (5) will lead to a stable steady state or to a limit cycle depending on the slope of the functions. There is thus an obvious formal similarity between the two situations. However, the steepness corresponding to the transition from a punctual to a cyclic attractor is much smaller in the first case (in which the cyclic attractor is an iteration artifact) as in the second case (in which the cyclic attractor is close to the real trajectory). 

The situation is rather similar if one applies iterative methods to the Boolean description. As noticed by, for example, Robert39 and by Goles,40 Boolean iterations in parallel and in series correspond, respectively, to the Jacobi and Gauss-Seidel iterations used in the quantitative description. In the first case (Jacobi), from an initial Boolean state (ot0 Jo yo.. . . ) one computest the values of the functions a, b, c,. . . which are reintroduced, respectively, as ot,Pi-y,.. . , and so on in the second case (Gauss-Seidel), the new value of each variable is reintroduced in a defined (but arbitrary) order. 

The optimization can be carried out by several methods of linear and nonlinear regression. The mathematical methods must be chosen with criteria to fit the calculation of the applied objective functions. The most widely applied methods of nonlinear regression can be separated into two categories methods with or without using partial derivatives of the objective function to the model parameters. The most widely employed nonderivative methods are zero order, such as the methods of direct search and the Simplex (Himmelblau, 1972). The most widely used derivative methods are first order, such as the method of indirect search, Gauss-Seidel or Newton, gradient method, and the Marquardt method. 

Becker CFW, Hunter CL, Seidel R, Kent SBH, Goody RS, Engelhard M. Total chemical synthesis of a functional interacting protein pair the protooncogene H-Ras and the Ras-binding domain of its effector c-Rafl. Proc. Natl. Acad. Sci. U.S.A. 2003 100(9) 5075-5080. 

FIGURE 4.8. Si02 etch rate as a function of KOH concentration. After Seidel et al. (Reproduced by permission of The Electrochemical Society, Inc.)... 

Furstner, A., Seidel, G. Ring-closing metathesis of functionalized acetylene derivatives a new entry into cycloalkynes. Angew. Chem., Int. Ed. Engl. 1998, 37, 1734-1736. 

Fig. 25 Normalized <100> silicon etch rates as a function of dopant concentration for boron, phosphorus, germanium, and carbon in KOH and EDP solutions (after Seidel et al. [33] and Lehmann et al. [79]).

The rate or velocity of coke formation is, first of all, a function of the feedstock characteristics. Seidel [1] reported about the tendencies of different components of heavy vacuum residues to coke formation. The following sequence shows a descending tendency to coke formation during thermal treatment ... 

The solubility of many inorganics in aqueous solution is available in the book by Linke and Seidell (1958). This reference also contains the solubilities of electrolytes in the presence of other species. As an example. Figure 1.7 shows the solubility of NaCl as a function of NaOH concentration. As a general rule, the solubility of most inorganics in water is available as a function of temperature. What is more difficult to find is the effect of other species on the solubility. If several other sf)ecies are present the... 

On the ritual function of the tripod in relation to political power see Seidel, Imperial Treasures and Taoist Sacraments, 296-302. On the date and the hrst recipient of the commentary to the Nine Elixirs see below, pp. 61-62 and Appendix C. 

In principle, correlation at even shorter time-scales is possible by including the micro times of both modules in the calculation of the correlation function. The problem with this approach is that the micro time scales of the modules may be slightly different, and the macro time transitions may be shifted due to different transit times in the detectors, cables and TCSPC modules. Correcting all these effects is extremely difficult, yet not impossible. Suitable calibration and correlation algorithms were developed by S. Felekyan, R. Ktihuemuth, V. Kudryavtsev, C. Sandhagen, and C.A.M. Seidel, Universitat Dortmund. 

Snawder JE, Roe AL, Benson RW, Roberts DW (1994) Loss of CYP2E1 and CYP1A2 activity as a function of acetaminophen dose relation to toxicity. Biochem Biophys Res Cmiunun 203 532-539 Steinberg P, Schlemper B, Molitor E, Platt KL, Seidel A, Oesch F (1990) Rat liver endothelial and Kupffer cell-mediated mutagenicity of polycyclic aromatic hydrocarbons and afiatoxin Bl. Environ Health Perspect 88 71-76... 

---