Rogers equation

The OZ equation was solved using the closure of Rogers and Young [50], Eq. (42), which for the multicomponent system takes the form... 

The latter assumption has been proposed because the droplets are known to have a velocity of approximately 80% vg and a gas-phase residence time on the order of 0.01 sec, according to Russell and Rogers (R5). Equations (17) become... 

Gases that do not react irreversibly with epithelial tissue, such as anesthetic gases, may diffuse into the bloodstream and will ultimately be eliminated from the body. A different and earlier model developed by DuBois and Rogers estimates the rate of uptake of inhaled gas from the tracheobronchial tree in terms of diffusion through the epithelial tissue, rate of blood flow, and solubility of the gas in blood. The rate of uptake from the airway lumen is determined by the equation ... 

The problems surrounding Hamilton s test (vide supra), as well as some misconceptions and misuses encountered in the literature, led Rogers to propose an alternative and more reliable method for determining the absolute structure58. A factor >7 is introduced which multiplies the imaginary component Aff of the anomalous scattering terms of the atomic scattering factors of all atoms (equation 11, which replaces equation 9, see Section 4.2.2,1.1), and which is treated as a variable in the least-squares refinement. 

By the use of the multiple linear regression, Abraham and Rogers [16] determined the parameters of the Abraham linear solvation free energy relationship (LSFER) equation [17,18]... 

As for the reaction occurring as the result of irradiating methyl nitrate Gray and Rogers suggest that this chemical change may be expressed by means of the equation ... 

Fig. 4.45 Structure factors versus wavevector for rfPS-PI diblocks in core-contrast matched decane solutions (Gast 1996 McConnell et al. 1994) (a) dPS,W3PI >o( at cote volume fractions of 0.012 (A), 0.02(+), 0.03( ), 0.04 (A) and 0.05 (o) (b) f/PS Pl at core volume fractions of 0.006 (o), 0.013 ( ) and 0.019 (A). The lines are theoretical fits from the self-consistent field interaction potentials and the Rogers-Young closure to the Ornstein-Zernike equation.

Since the early work of Kissinger (Ref 2) much work has gone into the improvement of the study of the kinetics of decompn. Table 5 lists the data of Rogers (Ref 45), and additional values can be found in Vol 7, K11, Equation (1) suggests that one should be able to vary the size of the shape at will, whereas in our experience the assumption of a size independent decompn rate is not justified. Most expls decomp by an autocatalytic mechanism, particularly at the upper temp limits so that in these cases thermo-analytically obtained kinetic data are not trustworthy... 

Shortly after Trost introduced the idea of atom economy, Roger Sheldon of Delft University of Technology in the Netherlands reported another green metric called E-factor.30 31 E-Factor is the ratio of the mass of the total waste from a process to the mass of the product generated in that same process (Equation 13.5). 

As mentioned above, practical applications of the Klopman relationship (Equation 6.50) often require further simplifications, particularly in cases where the relevant MO properties are known only for one of the two reaction partners. The latter is the typical situation in QSAR investigations that aim to elucidate the impact of molecular reactivity characteristics on the toxic potential of chemical agents. While the Coulomb interaction term can be reduced to calculate net atomic charges (see above), a possible candidate to replace the orbital interaction term of Equation 6.50 by a one-molecule property is Fukui s delocalizability, as was pointed out over 35 years ago (Cammarata, 1968 Cammarata and Rogers, 1971). 

FIG. 18.8 Typical isotherm plots of sorbed concentration versus ambient vapour pressure. (I) Henry s law, S is a constant (II) Langmuir equation (III) Flory-Huggins equation (IV) BET equation, site saturation at point B (from C.F. Rogers, 1985). 

Matsunaga, N. Rogers, D. W. Zavitsas, A. A. Pauling s electronegativity equation and a new corollary accurately predict bond dissociation enthalpies and enhance current understanding of the nature of the chemical bond, J. Org. Chem. 2003, 68, 3158-3172. 

Levey AS, Bosch JP, Breyer Lewis J, Greene T, Rogers N, Roth D. A more accurate method to estimate glomerular filtration rate from serum creatinine A new prediction equation. Ann Intern Med 1999 130 461-70. 

Rogers [34] described four different types of sorption isotherms. For very dilute feed solution sorption isotherm is linear obeying Henry s law (Equation 5.6). It is also called type-I sorption isotherm. 

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