Process function similarity

Chemithon secured patents on a somewhat similar oleum-type continuous sulfonation and sulfation process (259,260). So-called dominant bath sulfonation processes function well because they appear to operate ia or near the homogeneous area of the phase diagram (1) and heat removal is readily controllable with relatively small iacremental reaction. 

The multipath dispersion on a thin layer plate is the process most likely to be described by a function similar to that in the van Deemter equation. However, the actual mobile phase velocity is likely to enter that range where the Giddings function (3) applies. In addition, as the solvent composition is continually changing (at least in the vast majority of practical applications) the solute diffusivity is also altered and thus, the mobile phase velocity at which the Giddings function applies will vary. 

This key paper was followed by a flurry of activity in this area, spanning several years." " "" A variety of workers reported attempts to deconvolute the temperature dependence of carbene singlet/triplet equilibria and relative reactivities from the influence of solid matrices. Invariably, in low-temperature solids, H-abstraction reactions were found to predominate over other processes. Somewhat similar results were obtained in studies of the temperature and phase dependency of the selectivity of C-H insertion reactions in alkanes. While, for example, primary versus tertiary C-H abstraction became increasingly selective as the temperature was lowered in solution, the reactions became dramatically less selective in the solid phase as temperatures were lowered further. Similar work of Tomioka and co-workers explored variations of OH (singlet reaction) versus C-H (triplet reaction) carbene insertions with alcohols as a function of temperature and medium. Numerous attempts were made in these reports to explain the results based on increases in triplet carbene population... 

The Wegstein method is a secant method applied to g(x) = x - Fix). In Microsoft Excel, roots are found by using Goal Seek or Solver. Assign one cell to be x, put the equation for/(x) in another cell, and let Goal Seek or Solver find the value of x that makes the equation cell zero. In MATLAB, the process is similar except that a function (m-file) is defined and the command fzeroCf .xO) provides the solution x, starting from the initial guess xO. 

The enthusiasm for using Caco-2 cells and other epithelial cell cultures in studies of drug transport processes has been explained by the ease with which new information can be derived from these fairly simple in vitro models [7]. For instance, drug transport studies in Caco-2 cells grown on permeable supports are easy to perform under controlled conditions. This makes it possible to extract information about specific transport processes that would be difficult to obtain in more complex models such as those based on whole tissues from experimental animals. Much of our knowledge about active and passive transport mechanisms in epithelia has therefore been obtained from Caco-2 cells and other epithelial cell cultures [10-15]. This has been possible since Caco-2 cells are unusually well differentiated. In many respects they are therefore functionally similar to the human small intestinal enterocyte, despite the fact that they originate from a human colorectal carcinoma [16, 17]. 

The procedure has been tested primarily on realistic distillation column models. This choice was deliberate because most industrial processes have similar gain, deadtime, and lag transfer functions. Undoubtedly some pathological transfer functions can be found that the procedure cannot handle. But we are interested in a practical engineering tool, not elegant, rigorous all-inclusive mathematical theorems. 

Shinkai s 38 is also a PET system whose fluorescence is controlled by Na" binding to a coordinatively active spacer which is a calix[4]aiene tetraester in this case. However, the through-space distance between the photoactive termini is expanded by Na complexation, thus reducing the PET efficiency. Kuhn s 39 is not dissimilar in that a PET-type quencher (a nitroaromatic unit) is held away from the lumophore by Ca binding. However a conventional lumophore-spacer-receptor is also contained within 39 as found in 24. At this point it would not be out of place to mention several important studies on the control of PET/EET by ion binding to a coordinatively active spacer between photoactive terminii." " System 36 is structurally related to Verhoewen s 40 since they both contain an aromatic lumophore and an aromatic amine with one or more interposed aliphatic amines. System 40 also displays the functional similarities that PET processes were... 

Apart from liquid phase adsorption on a solid adsorbent such as bauxite, the early processes for sweetening and desulfurization were of a chemical nature. Some are in operation today in substantially their original forms, some have been greatly improved, and new processes performing similar functions have been developed. It is beyond the scope of this paper to cover them all, even in outline, therefore a comparative selection has been made to illustrate the advances achieved. The division, which is on a rather arbitrary basis, is given in Table V. 

At task complete, the Fortran programs in the larger computer process the result and determine the course of the experiment. Getting a piece of information measured on the diffractometer is functionally similar to calling a subroutine which returns after the information is available. An alternative way to achieve the same flexibility is to build up the instrument control minicomputer into a much larger system. 

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