Schmidt method

Cerkovnikov and Ustricev (1938) starting from tetrahydropyran-4-propionic acid (A R = CHj. CHj. COjH), which was converted by the Curtius-Schmidt method into 4-(2-aminoethyl)-tetrahydropyran (A R = (CH2)2NH2), and this with fuming hydrobromic acid at 100°... 

In the explicit (or Schmidt) method, the partial derivatives are replaced by finite difference as follows15,16 ... 

Determined using the Schmidt method (IS) at ambient temperature. ... 

If the xs are not orthogonal they must first be orthogonalized by the Schmidt method (Magnasco, 2007). Then, we construct the matrices ... 

The shortcomings of the Beckmann rearrangement at nitrogen as a method to synthesize the isomeric benzazepinones discussed above apply also to the Schmidt method. In this case, another side reaction, the formation of tetrazoles, may occur. The acidic medium used for the rearrangement plays a decisive role in directing the course of the reaction. The rearrangement may in some cases be nonstereospecific. 

A sensitive technique used for real time reconstruction of chromatograms from the interferogram is the Gram Schmidt vector orthogonalization method. The Gram Schmidt method relies on the fact that the interferogram contains information on absorbing samples at all optical retardations less than the reciprocal of the width of each band in the spectrum. 

Since only one orbital is involved we may use the simple two-orbital Schmidt method which gives ... 

The researchers extended the Kety-Schmidt method to the use of chemically inert radioactive tracers, krypton-79 and xenon-133, because it was easier to measure their concentrations in blood. Later, oxygen-15 and xenon-133 were used to measure regional blood flow to the brain. Oxygen-15 made it possible to measure the rate of metabolism of oxygen to carbon dioxide. Oxygen-15 is produced in a cyclotron, its use complicated by its short (2.5 min) half-life. 

Streptavidin, a tetrameric protein (Mr 60 kDa) from Streptomyces avidinii with a high affinity to biotin (fC 10 M). Streptavidin is used in various laboratory techniques for detecting biotinylated molecules, and is preferred to avidin due to its more favorable isoelectric point and lack of glycosylation. It belongs to the protein superfamily calycins [N. M. Green, Methods Enzymol. 1990, 184, 51 S. Freitag et al.. Protein Sci. 1997, 6, 1157 A. Skerra, T. G. Schmidt, Methods Enzymol. 2000, 326, 271]. 

O. T. Schmidt, Methods Carbohydr. Chem. 2 (1968) 318. l,2 5,6-Di-0-cyclohexylidene-a-D-glucofuranose... 

The Gram-Schmidt method to orthogonalize a set of vectors is considered obsolete because of its poor stability. Moreover, it requires 0(wy) evaluations. 

First one can build up other effective Hamiltonians based on hierarchized orthogonalization procedures. The Gram-Schmidt procedure is recommended if one starts from the best projected wavefunctions of the bottom of the spectrum. Thus one can obtain a quite reliable effective Hamiltonian with well behaved wavefunctions and good transferability properties (see Section III.D.2). The main drawback of this approach is that the Gram-Schmidt method, which involves triangular matrices, does not lead to simple analytical expressions for perturbation expansions. A partial solution to these limitations is brought about by the new concept of intermediate Hamiltonian,... 

Simplified Schmidt method for a slab. If the value of M = 2, then a great simplification of Eq. (5.4-2) occurs, giving the Schmidt method. 

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