Schwartz formula

Twenty years ago, we extended asymptotic extrapolations to polyatomic molecules by transformation of the Schwartz formulae to a symmetry-independent form based on the total number N of pair natural orbitals (PNOs) [8-10, 14],... 

In clinical practice, glomerular filtration rate (GFR) can be estimated from prediction equations such as the Schwartz formula, which takes into account serum creatinine concentration and the patient s height, gender, and age. The advantage of estimating GFR using the Schwartz equation is rapid determination and the avoidance of a cumbersome 24-hour urine collection." " The following formula is used to estimate GFR ... 

Studies comparing the Schwartz-predicted GFR versus measured GFR noted that the Schwartz formula overestimated GFR in patients with decreasing GFR. The formula may not provide an accurate estimation of GFR in patients with rapidly changing serum creatinine concentrations, as seen in the critical care setting, in infants younger than 1 week of age, and in patients with obesity, malnutrition, or muscle wasting. Factors that interfere with serum creatinine measurement also may cause errors in estimation of GFR. 

Comment The Schwartz formula enables simple and rapid estimation of GFR without urine collection. It is established in pediatric nephrology and widely used for daily routine (see Chap. 21)... 

One exact formulation for the quantum rate is the Miller-Schwartz-Tromp rate formula. In this formulation the quantum rate is given by an integration of the correlation fimction... 

We wish here to obtain the thermodynamic equations defining the liquidus surface of a solid solution, (At BB)2, ). It is assumed that the A and atoms occupy the sites of one sublattice of the structure and the C atoms the sites of a second sublattice. For the specific systems considered here Sb and play the role of C in the general formula above. It is also assumed that the composition variable is confined to values near unity so that the site fractions of atomic point defects is always small compared to unity. This apparently is the case for the solid solutions in the two systems considered. Then it can be shown theoretically (Brebrick, 1979), as well as experimentally for (Hgj CdJ2-yTe)l(s) (Schwartz et al, 1981 Tung et al., 1981b), that the sum of the chemical potentials of A and C and that of and C in the solid are independent of the composition variable y ... 

Fig. 24. Partial pressure of Hg along the three-phase curves for various solid solutions. The labels are the value of x in the formula, Hg, xCd,Te(s). Experimental points from Schwartz el al. (1981) and Tung et al. (1981b, 1982). 

Besides the work with Carr and Schmidt, I had a very pleasant interaction with Ed Cussler over some problems in mass transfer through membranes with barriers [238], through anisotropic membranes [232], and by facilitated diffusion [247]. A severely mathematical problem of diffusion through a slot could be solved by a Schwartz-Christoffel transformation,41 and provided an asymptotic formula that proved useful in the barrier problem [223]. Cussler was delightful to work with because he refused to accept any mathematical solution that could not be unpacked and shown to be physically sensible (cf. [244]). Next to Bosanquet, he is the most intuitive problem solver with whom I have worked. Chapter 19 [232] is reprinted here. 

Proof TjCt us evaluate, first, the difi crcnce between the (7 .+ l)-th and -th iterations. According to formulae (4.74), (4.65), and the Schwartz, inequality... 

Calculated Clearance. The mathematical relationship between plasma creatinine and GFR can be improved by correcting for the confounding variables that make that relationship nordinear. More than 25 different formulas have been derived that estimate GFR using plasma creatinine corrected for some or all of gender, body size, race, and age. These may produce a better estimate of GFR than serum creatinine alone. Indeed the National Kidney Foundation of the United States has recommended that such estimates should be used in preference to serum creatinine, and that either the Cockcroft and Gault or Modification of Diet in Renal Disease (MDRD) formula should be used in adults. The Schwartz and Counahan-Barratt formulas are recommended for use in children. 

A suitable substance or mixture of substances to prevent growth of, or destroy, microorganisms accidentally introduced during use must be added to ophthalmic ointments that are packaged in multiuse containers, regardless of the method of sterilization employed, unless otherwise directed in the individual monograph or unless the formula itself is bacteriostatic in accordance with the USP (771), Ophthalmic Ointments. Schwartz... 

Pierrat A, Gravier E, Saunders C, et al. Predicting GFR in children and adults a comparison of the Cockcroft-Gault, Schwartz, and modification of diet in renal disease formulas. Kidney Int 2003 64 1425-1436. 

Haycock, G.B., Schwartz, G.J. and Wisotsky, D.H. Geometric method for measuring body surface area A height weight formula validated in infants, children and adults. Journal of Pediatrics 1978 93 62-66. 

This result may be viewed as an application of the Schwartz inequality. The problem with this formula is that it suffers from the same numerical troubles that plague the exact FEP perturbation formula the integrand might have significant contributions from configurations that are poorly sampled by the simulation. 

The Landau-Teller formula was generalized in SSH theory (Schwartz, Slawsky, Herzfeld, 1952) and, in particular, by Bilhng (1986). A semi-empirical numerical relation... 

In the above equation, N E) denotes the cumulative reaction probability at total energy E and /3 = 1 / A b T is the inverse temperature. However, the most direct derivation [29,30] starts from the MUler-Schwartz-Tromp formula for the rate constant [31] ... 

Another set of cubic compounds are the elpasolites which have the typical formula Cs2NaRCl6, in which the lanthanide ion is six-coordinated to the chlorine ions. EPR measurements on trivalent ions of Ce, Dy, Yb and Er in Cs2NaYCl6 (Schwartz and Hill 1974, O Connor et al. 1977) have confirmed the presence of cubic symmetry, but for a number of other ions, and for some undiluted compounds, phase transitions have been observed at temperatures of 100 to 160 K. EPR measurements (Bleaney et al. 1982b) on the compounds with Pr, Tb andTm, indicate the presence at low temperatures of cubic symmetry with a small tetragonal distortion. 

Fig. 172. Reflectance spectra R() below 200 cm on a linear scale. Reproduced by permission of the American Physical Society from K. Lee, R. Menon, A. J. Heeger, K. H. Kim, Y. H. Kim, A. Schwartz, M. Dressel, and G. Griiner, Phys. Rev. B, in press.

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