Schmidt decomposition

Analogous to the Schmidt decomposition, it can be proved that every 1 ) can be represented in an appropriately chosen basis in in a form of Slater decomposition [45],... 

In a simple two-particle interpretation, the spin of a given particle depends on that of the second spin (entangled state) or is independent of the second particle s spin (nonentangled or separable state). In the Schmidt decomposition, the two-particle wave function can be written as... 

Schmidt, H. 1971. Protective Measures and Experiences m Acetylene Decomposition m Piping and Equipment. IChemE Symposium Series No. 34, pp. 165ff. Institution of Chemical Engineers, Rugby, England. 

Balzer, A., Gleixner, G., Grupe, G., Schmidt, H.-L., Schramm, S., Turban-Just, S. (1997). In vitro decomposition of bone collagen by soil bacteria the implications for stable isotope analysis in archaeometry. Archaeometry 39 (2), 415-429. 

Onken, U., Schmidt, E. and Weissenrieder, T. (1996) Enzymatic H202 decomposition in a three phase suspension, Ciba Geigy. International Conference on Biotechnology for Industrial Production of fine Chemicals, 93rd event of the EFB, Zermatt, Switzerland, 29.09.1996. 

At low pressures the rate of decomposition of ammonia on a hot platinum wire is proportional to the partial pressure of ammonia and inversely proportional to the partial pressure of hydrogen. Some total pressure data were obtained at 1348 C (Schwab Schmidt, 2 physik Chem B 3 344, 1929). Check the proposed rate relations. 

Rajagopal, S., Schmidt, M., Anderson, S., and Moffat, K. 2004. Methodology for analysis of experimental time-resolved crystallographic data by singular value decomposition. Acta Cry St. D 60 860-71. 

Schmidt, M., Rajagopal, S., Ren, Z., and Moffat, K. 2003. Application of singular value decomposition to the analysis of time-resolved macromolecular x-ray data. Biophys. J. 84 2112-29. 

The explosive decomposition of tetryl, like that of other explosives, depends on the method of initiation, density etc. Haid and Schmidt [45] give the following equation for the decomposition of tetryl, at a density of 1.56 ... 

The following equation of decomposition, using a 1000 g sample of PETN, has been established by A. Schmidt [27] ... 

It has been found by Haid and Schmidt [28] that the equation of decomposition is practically independent on the loading density. The proportion of gaseous products resulting from the explosive decomposition of PETN under the influence of different stimuli, shown in Table 33, was determined by Bowden and Yoffe [29],... 

Several authors noticed that the addition of chromium salts to ammonium nitrate increases the rate of its decomposition Audrieth and M. T. Schmidt [25], Blinov [26], J. Taylor and Sillitto [5], J. Taylor and Whetstone [27], A. J. B. Robertson [12], Shidlovskii [28], Shirai and Ishibashi [29]. 

A practical example of this reaction is given in Table 23-6 together with examples of related reactions known as the Curtins and Schmidt rearrangements. The latter two probably also involve rearrangement of an acyl nitrene, this time formed by decomposition of an acyl azide ... 

In a later study by the Schmidt group (27), electron microscopy was used to characterize morphological changes in microspheres (<0.6 cm in diameter) of Pt, Rh, Pd, and Pt-Rh alloy in a number of reaction environments the reactions were ammonia oxidation, ammonia decomposition, and propane oxidation. No other experimental techniques, such as weight-loss measurements, were employed. After prolonged exposure to reaction mixtures of ammonia and air at temperatures less than 727°C, the surfaces of the spheres were reconstructed to favor specific crystal planes. The structure of the facets was found to be a function of the reaction mixture, temperature, and metal (Fig. 13). In the same reaction mixtures, as well as in pure ammonia at higher temperatures... 

This reaction works well for simple alkenes and cycloalkenes. Attempts to add hydrazoic acid to di-arylalkenes in the presence of sulfuric acid, however, leads to considerable decomposition due to Schmidt rearrangement.260... 

Table 6.3 provides a summary of the different microscopic techniques that have been applied to hydrate studies and the type of information that can be obtained from these tools. The following discussion provides a brief overview of the application of diffraction and spectroscopy to study hydrate structure and dynamics, and formation/decomposition kinetics. For information on the principles and theory of these techniques, the reader is referred to the following texts on x-ray diffraction (Hammond, 2001), neutron scattering (Higgins and Benoit, 1996), NMR spectroscopy (Abragam, 1961 Schmidt-Rohr and Spiess, 1994), and Raman spectroscopy (Lewis and Edwards, 2001). 

Figure 19. Decomposition products of desflurane in a rebreathing circuit during anesthesia (Schmidt et al., 2000).

One of the advantages of GFAAS is the direct analysis of solid samples without prior decomposition, this technique has been reviewed by Bendicho and de Loos-Vollebregt (1991). The solid samples can be introduced directly or as a slurry. Calibration can be with aqueous standards, synthetic solids, standard additions or with SRMs. SRMs have been used for calibration for solid sampling of plant material (Schmidt and Falk, 1987). Examples of the use of solid samples with ETAAS are shown in Table 9-4. In many cases a matrix modifier is used with the sample, this allows the matrix to be volatilised at the pyrolysis stage without analyte loss, particularly important with volatile analytes such as Cd and Pb. (Ure, 1990). 

---