Hawkins’ equation

Skin is a mathematical representation of the degree of damage present. It can be represented, qualitatively, by the Hawkins equation, as follows ... 

Annuli Approximate heat-transfer coefficients for laminar flow in annuh may be predicted by the equation of Chen, Hawkins, and Sol-berg [Tron.s. Am. Soc. Mech. Eng., 68, 99 (1946)] ... 

Hawkins and Loren225 reported simple chiral arylalkyldichloroborane catalysts 352 which were effectively used in the cycloadditions of acrylates lib and 350 to cyclopen-tadiene, affording adducts 351a and 351b, respectively (equation 99). A crystal structure of the molecular complex between methyl crotonate and the catalyst allowed the authors to rationalize the outcome of the reaction. One face of methyl crotonate is blocked by tt-tt donor-acceptor interactions, as becomes clear from the structure of complex 353. The cycloadduct of methyl acrylate and cyclopentadiene (5 equivalents) was obtained with 97% ee, using the same catalyst. Three years later, the authors reported that the cycloadduct was obtained with 99.5% ee in the presence of 10 equivalents of cyclopentadiene226. 

The bottleneck of GB calculations is the determination of the effective Born radii (a), since their magnitude depends not only on the intrinsic atomic (Bondi, or atomic) radii of the atom (p), but also on the geometry of the rest of the molecule, which modulates the average distance of the atom to the solvent. Original formulations of the method used Equation (4.19) for the computation of Born s radii, but all current version rely on an approximate formalism, such as that developed by Hawkins et al. [34], where a pairwise approximation to atomic overlap is used to simplify Equation (4.19) see Equations (4.20)-(4.22). Using this approach Born s radii can be computed very fast, which makes the method suitable for MD calculations ... 

A number of studies have explored ways in which partial vapor pressures may be obtained using TGA data, thereby allowing both prediction of vapor pressure under a range of circumstances and calculation of the constants associated with the approaches described previously. In particular, Price and Hawkins (12) have argued that the rate of mass loss for vaporization and sublimation within a TGA should be a zero-order process, and hence should be constant for any given temperature, subject to the important condition that the available surface area also remains constant. This means that the value of v from Equation 6.4 should be easily calculated from the TGA data. If one performs this experiment for materials with known vapor pressure and temperature relationships (the authors used discs of acetamide, benzoic acid, benzophenone, and phenanthrene), then the constant k for the given set of TGA experimental conditions may be found. Once this parameter is known, the vapor pressure may be assessed for an unknown material in the same manner. 

Hawkins et al. have reported a simple, efficient catalyst for the Diels-Alder reaction based on a chiral alkyldichloroborane (4, Equation 21) [21]. A molecular complex between methyl crotonate and the chiral catalyst has been isolated for the first time. 

Mentz and Wilkins studied the problem of convergence of the NASA method. Bernhard and Hawkins, Tsao and Wiederhold, applied Newton s method to solving the set of non-linear equations (5.48), and Michels and Schneiderman used the NASA method to obtain solutions for real gas systems. 

Dienophiles such as a,P-unsaturated ketones tend to present sterically similar lone pairs for metal coordination. To address this issue, Hawkins and coworkers have recently shown that the previously reported catalyst (7) functions well in catalyzing the cycloadditions of a,p-unsaturated ketones with cyclopentadiene (Equation 4) [14]. 

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