Aries

Book D L 1987 NRL Piasma Formu/ary (Washington, DC Naval Research Laboratory)... 

However, th ese alternative methods can be on ly applied to certain elements. For example, the projected CXDO/IXDOi may be used only for molecular system s with atom ic n iiin bers less than or ct nal to IS (Ari. Elements beyond IS are not available in the projected CXDO/IXD(f initial guess. 

The dBASEIV (ordBASEIIT) form of th e parameter sets come in ld( /filcs analogous to the Tt,v( files. Th ese dbf files are bin ary files, so yon can t read them directly. They arenot retpiired for the product and are provided only as an option. In most situations where there is no exten sive use of database operation s on parameter sets, the text form is probably more convenient to use. Many spreadsheet programs, including Microsoft Excel, are also capable of reading files. 

The literature of surface diffusion is now quite extensive. A review of the basic ideas, with reference to many of the earlier papers, is given by Dacey [44], and a good selection of references including more recent work can be found in Aris [45]... 

At the limit of Knudsen diffusion control it is not reasonable to expect that any of the proposed approximation methods will perform well since, as we know, percentage variations in pressure are quite large. Nevertheless it is interesting to examine their results, which are shown in Figure 11 4 At this limit it is easy to check algebraically that equations (11.54) and (11.55) become the same, while (11.60) differs from the other two. Correspondingly the values of the effectiveness factor calculated using the approximation of Kehoe and Aris coincide with the results of Apecetche et al., and with the exact solution, ile Hite and Jackson s effectiveness factors differ substantially. 

Equations (1.6) and (1.7) are used to formulate explicit relationships between the extra stress components and the velocity gradients. Using these relationships the extra stress, t, can be eliminated from the governing equations. This is the basis for the derivation of the well-known Navier-Stokes equations which represent the Newtonian flow (Aris, 1989). 

Aris, R., 1989. Vectors, Tensors and the Basic Equations of Fluid Mechanics, Dover Publications, New York. 

The oxidation of 2- and 5-sulfides is usually performed in acetic acid and 30% hydrogen peroxide (213, 229, 263, 345-350) Or with m-chloroperbenzoic acid (341). Ary] (8, 272. 349, 351-353) and alkyl sulfones (129, 203, 214, 270, 274, 275) are thus obtained in good yields. Other oxidative reagents such as KMn04 (7, 273) or CrO (7) in acetic add have also been used. 

Scheme 99) (416). The 4-acetyloxy-5-ary]thiazo]e or 4-methoxy-5-arylthiazole, which are models of the protomer (174b) do not give cycloaddition products under the same experimental conditions. This rules out the possibility of a Diels-Alder reaction involving the protomer (174b) (416). 

Other 2-alkyi or 2-ary]-A -selenazolines have been prepared in the same way starting from suitably substituted N-acy)ethano)amines (58. 59). 

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