Excellence, description

The terms Po, Pa, Pt, Pat, Paa, and Pt,t, are adjustable parameters whose values are determined by using linear regression to fit the data to the equation. Such equations are empirical models of the response surface because they have no basis in a theoretical understanding of the relationship between the response and its factors. An empirical model may provide an excellent description of the response surface over a wide range of factor levels. It is more common, however, to find that an empirical model only applies to the range of factor levels for which data have been collected. 

D. M. Litde, Catalytic Reforming, Perm Well Books, Tulsa, OHa., 1985. Refs. 38, 41, 42, and 56 contain excellent descriptions of benzene manufacturing processes. 

Solution Process. With the exception of fibrous triacetate, practically all cellulose acetate is manufactured by a solution process using sulfuric acid catalyst with acetic anhydride in an acetic acid solvent. An excellent description of this process is given (85). In the process (Fig. 8), cellulose (ca 400 kg) is treated with ca 1200 kg acetic anhydride in 1600 kg acetic acid solvent and 28—40 kg sulfuric acid (7—10% based on cellulose) as catalyst. During the exothermic reaction, the temperature is controlled at 40—45°C to minimize cellulose degradation. After the reaction solution becomes clear and fiber-free and the desired viscosity has been achieved, sufficient aqueous acetic acid (60—70% acid) is added to destroy the excess anhydride and provide 10—15% free water for hydrolysis. At this point, the sulfuric acid catalyst may be partially neutralized with calcium, magnesium, or sodium salts for better control of product molecular weight. 

An excellent description of the engineering side of both topics is pro ided by Kessler and Klein [in Ho and Sirl ar (eds,), op, cit, pp, 163-216], A cornprehensi e treatment of diffusion appears in on... 

Parts I and II. John Wiley and Sons, New York, 1987. An excellent description of the fundamental concepts, instrumentation, use, and applications of ICP-OES. 

Figure 6 shows the changes which occur in the diffraction patterns of the heated MCMB samples, and the excellent description of these patterns by the structure refinement program. The structural parameters, P, P, a, doo2> Lc the carbon samples are listed in Table 1 [6]. 

The coupling of supercritical fluid extraction (SEE) with gas chromatography (SEE-GC) provides an excellent example of the application of multidimensional chromatography principles to a sample preparation method. In SEE, the analytical matrix is packed into an extraction vessel and a supercritical fluid, usually carbon dioxide, is passed through it. The analyte matrix may be viewed as the stationary phase, while the supercritical fluid can be viewed as the mobile phase. In order to obtain an effective extraction, the solubility of the analyte in the supercritical fluid mobile phase must be considered, along with its affinity to the matrix stationary phase. The effluent from the extraction is then collected and transferred to a gas chromatograph. In his comprehensive text, Taylor provides an excellent description of the principles and applications of SEE (44), while Pawliszyn presents a description of the supercritical fluid as the mobile phase in his development of a kinetic model for the extraction process (45). 

While MOVB can yield reasonable energetic results and an excellent description of the overall potential energy surface on diabatic states and the adiabatic ground... 

Figure 25 presents the homopolymer data in a scaled form. The splitting into Q-dependent plateau levels is much more pronounced than for PI, a phenomenon resulting from a faster relaxation rate and somewhat stronger constraints. Again, the Ronca model represents an excellent description of the experimental data reproducing the line shape, i.e. the relatively sharp crossover and the... 

An excellent description of the discovery of neurotransmitters is provided by Valenstein (2005). Only the essentials of neurotransmitter metabolism are covered here for more detailed information the reader is directed to textbooks of neurochemistry, e.g. Siegel et al. (1994). For a more advanced coverage of the topics discussed here as well as information on the electrical properties of the neurons involved, the interested reader is directed to Steriade McCarley (2005). 

Excellent descriptions of BBNS theory are given in the classic text ... 

Quantum mechanics is intrinsically probabilistic, but classical theory - as shown above by the existence of the delta-function limit for the classical distribution function - is not. Since Newton s equations provide an excellent description of observed classical systems, including chaotic systems, it is crucial to establish how such a localized description can arise quantum mechanically. We will call this the strong form of... 

As is well known, in the case of the hydrogen atom interacting with a monochromatic field, one-dimensional model provides an excellent description of the experimental chaotization thresholds for real three-dimensional hydrogen atom (Jensen, 1984). 

Although these reaction models give excellent descriptions of the system under particular conditions and are therefore quite satisfactory to account for free molybdenum(VI) in studies of complex formation, for example (73, 84, 88), some uncertainties still prevail. There is often little to choose between alternative models because the addition of a new species to a model, or the replacement of a particular species by one or two others, can have only a marginal improvement of the fit as has been shown by the authors themselves (61, 85, 86, 90) or by others in subsequent recalculations (81, 87, 90, 91). 

As with the other forms of degradation, an excellent description is given in [1],... 

Figure 7 shows the predicted vapor-phase mole fractions of HC1 at 25°C as a function of the liquid-phase molality of HC1 for a constant NaCl molality of 3. Also included are predicted vapor-phase mole fractions of HC1 when the interaction parameter A23 is taken as zero. There are unfortunately no experimental vapor-liquid equilibrium data available for the HC1-NaCl-FLO system however, considering the excellent description of the liquid-phase activity coefficients and the low total pressures, it is expected that predicted mole fractions would be within 2-3% of the experimental values. 

The eigenvalue problem (3.20) can be solved and provides an excellent description of the problem particularly so in the case in which the mass, m2, of the atom in the middle is much larger than that of the two atoms at the end. 

An excellent description of the cellular detonation front, its relation to chemical rates and their effect on the dynamic parameters, has been given by Lee [6], With permission, from the Annual Review of Fluid Mechanics, Volume 16, 1984 by Annual Reviews Inc., this description is reproduced almost verbatim here. 

Performing numerical simulations of the extrusion process requires that the shear viscosity be available as a function of shear rate and temperature over the operating conditions of the process. Many models have been developed, and the best model for a particular application will depend on the rheological response of the resin and the operating conditions of the process. In other words, the model must provide an acceptable viscosity for the shear rates and temperatures of the process. The simple models presented here include the power law. Cross, and Carreau models. An excellent description of a broad range of models was presented previously by Tadmor and Gogos [4]. 

With this approach an excellent description of all PDMS spectra was reached (see Fig. 5.10). 

It is assumed that the reader is familiar with such common chromatographic concepts as efficiency, selectivity, capacity factors, and theoretical plates, and how these parameters affect and effect chromatographic resolution. Excellent descriptions of these general chromatographic principles have been published. Other reviews on various aspects of carbohydrate separations will be cited in the appropriate Sections. 

It has been demonstrated in several benchmark calculations that the CR-CCSD(T) (completely renormalized CCSD(T)) and CR-CCSD(TQ) (completely renormalized CCSD(TQ)) methods provide an excellent description of entire PESs involving single and double bond dissociation (P, 13, 15, 17-19, 21, 111), highly-excited vibrational term values near dissociation 17, 18, 21, 111), and... 

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