Schwarz formula

From these and other experimental results Pinner and Schwarz suggested that pilocarpine could be represented by formula (V), and subsequently Jowett confirmed this by the preparation of a series of disubstituted glyoxalines from wopilocarpine by distillation with soda-lime, 1 although he pointed out that the reactions of the alkaloid were... 

Flaxseed oil has been proposed to be a valuable ingredient for ice cream products (Hall and Schwarz, 2002). Flaxseed oil replaced between 10% and 25% of the milk fat in ice cream formulas has been investigated. The 25% flaxseed product exhibited an oil-like mouth feel however, the presence of... 

A similar interpretation may be based upon the results of Schwarz and coworkers580 581>. These authors hydrolyzed higher silicon chlorides and found solid white polymeric compounds in which the original Si-Si framework is retained. An irregular network containing Si-O-Si bond systems is also formed, so that the earlier postulated structural formulas are certainly incorrect. 

The most probable number of faces of polyhedra filling up the space was determined by Schwarz [71] who employed the stereometric formula of Euler and Plateau s laws. For a convex polyhedron the following ratio is valid... 

The proof of Theorem 19 repeats practically all the steps of Theorem 18. For example, according to formulae (4.7), (4.13), and the Schwarz inequality (4.34), we obtain... 

A common form of model selection is to maximize the likelihood that the data arose under the model. For non-Bayesian analysis this is the basis of the likelihood ratio test, where the difference of two -2LL (where LL denotes the log-Ukelihood) for nested models is assumed to be approximately asymptotically chi-squared distributed. A Bayesian approach— see also the Schwarz criterion (36)—is based on computation of the Bayesian information criterion (BIC), which minimizes the KuUback-Leibler KL) information (37). The KL information relates to the ratio of the distribution of the data given the model and parameters to the underlying true distribution of the data. The similarity of the KL information expression (Eq. (5.24)) and Bayes s formula (Eq. (5.1)) is easily seen ... 

K k)/K k ) is due to Schoen (1970), who adapted a result of Schwarz (1890), and the work of Stessmann (1934) shows that the same formula applies to the F-RD minimal surface. Stessmann s analysis was not complete enough to yield the modulus k, but by Schwarz s work it is known that k =(fl2 — 3) where a, a2,a3 are roots (in descending order) to... 

Extracted from graphs and formulas, pages 372, 373, Differential Equations in Engineering Problems, Salvador and Schwarz, published by Prentice-Hall, Inc., 1954. 

Formula CT 06-13-04 SOURCES Zschimmer Schwarz GmbH Co. General Formulati ons... 

Von Bruchhausen and Bersch (21, 22) reinterpreted Gadamer s data in conjunction with the later findings of Kling (28) and of Schwarz (29), who subjected chelidonine to Emde and Hofmann degradations. When its methine is oxidized with permanganate there results a mixture of hydrastic acid (II) and a dimethylaminomethylmethylenedioxybenzoic acid. The latter was erroneously formulated by Schwarz, whose formula indicated... 

Recently, the theory of dielectrophoresis was applied to explain the microscopic physics of the movement of pigments in electrophoretic image displays and to prove the discrepancies between theory and measurement [9], Dielectrophoresis is induced by the interaction of the electric field and the induced dipole and is used to describe the behavior of polarizable particles in a locally nonuniform electric field. For example, the phenomenon of the delay time can be explained by the principle of dielectrophoresis. In electrophoresis, when the backplane voltage is switched, the particles on the electrode have to move instantaneously under a given electric field. However, the particles need a removal time which results in a delay time in the switching process. The time constant to obtain an induced dipole from a particle at rest is derived by Schwarz s formula [10] and used to compute the dielectrophoretic force at its steady-state value. The force and the velocity fields under a nonuniform electric field due to the presence of pigments also help to estimate realistic values for physical properties. 

Conformal mapping (the Schwarz-Christoffel transformation) was employed to calculate conductivity from experimentally measured biofilm resistance. The details of the conformal mapping procedure are presented elsewhere [53, 58], Variables are defined in Figure 7.3a. In the limiting cases a [Pg.231]

Schwarz. Moreover, this half-metallicity leads to an integral magnetic moment of 2 gB/f-u- (f.u. = formula unit), the same as predicted by Hund s rule for the spin moment of Cr (3d ) ion. This agrees with the measured saturation moment of 2... 

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