Indirect transformations

The correctness of this statement is to be inferred from the exact agreement between the values of the mechanical equivalent of heat obtained by different methods. Thus, in Joule s second series of experiments, mechanical work is directly converted into heat in the first and third series, it is indirectly transformed through the medium of electro-magnetic energy in the fourth series, the energy of an electric current is converted into heat the identity of the values of J so obtained implies a complete conversion of the initial forms of energy into heat energy. 

Indirect transformations leading to changes in the microenvironment (pH, depletion of Oj to lower Eh, addition of CO )... 

In physics and chemistry there are two different forms of spatial symmetry operators the direct and the indirect. In the direct transformation, a rotation by jr/3 radians, e.g., causes all vectors to be rotated around the rotation axis by this angle with respect to the coordinate axes. The indirect transformation, on the other hand, involves rotating the coordinate axes to arrive at new components for the same vector in a new coordinate system. The latter procedure is not appropriate in dealing with the electronic factors of Born-Oppenheimer wave functions, since we do not want to have to express the nuclear positions in a new coordinate system for each operation. 

Svergun, D. I. (1992). Determination of the regularization parameter in indirect-transform methods using perceptual criteria. J. Appl. Crystallogr. 25, 495—503. 

The DNA Funhouse. The Main Powerhouse connects indirectly with the DNA Funhouse in that Main Powerhouse ingredients may indirectly become part of purine and pyrimidine nucleotides. Conversely, nucleic acid breakdown may contribute molecules that indirectly transform into Main Powerhouse molecules. 

The solute, which is in rather low concentration is indirectly transformed by the numerous reactive species of the water radiolysis, so the yield of solute transformation is much higher than in the pure solid state. 

Irradiation-induced features with a diameter of 1 nm and a volume fraction of 1.2% for a dose of 0.06 dpa and of 2 nm and volume fraction of 4.3% for both doses of 0.6 and 1.5 dpa and the A-ratio of two have been found by SANS for the neutron-irradiated Fe-12.5at%Cr alloy (Bergner et al. 2009, Ulbricht et al. 2010). These featnres were related to pure Cr precipitates in a-Fe as well as to a -particles dispersed in the a-Fe matrix. A decrease in the scattering cross-section of SANS with decreasing scattering vector, Q, was fonnd, as is typical for the interference effects in concentrated alloys. The size distribution of the a -particles was obtained by the indirect transformation method applied to the fitted measured nuclear scattering cross-sections. The range of the g-values was restricted to values greater than 1 nm" in the fit, where interference effect can be excluded. 

O. Glatter, Determination of particle-size distribution functions from small-angle scattering data by means of the indirect transformation method ,/. App/. Crystallogr., 1980,13,7-11. 

The protection of carboxylic acids as their phenacyl esters has been described regeneration is effected with great facility at room temperature by zinc in glacial or dilute aqueous acetic acid. Of notable applicability is the formation of y-hydroxyesters from y-lactones, an otherwise indirect transformation an example is the obtention of the ester (13) from the sodium salt of santonin (12). This protection can be extended to phenols. 

A model-free approach to analyze the complete SAXS of a dilute system of particles is Clatter s indirect transformation method. The isotropic form of the forward Fourier transform corresponding to the Fourier back transform [5] can be written as... 

The indirect transformation technique models the r -multiplied autocorrelation function r (y(r)) , = r y(r) = p r) as a superposition of equidistant B-splines (up to a cutoff maximum particle size that needs to be given in advance) that are Fourier transformed, subjected to any applicable collimation effects (the method was originally developed for a Kratky slit collimation), and then least-squares fitted to the experimental intensity distribution, so that p r] can be computed using the fit coefficients and the untransformed B-splines. The shape of p(r) is known for many standard particles including solid spheres, core-shell hollow spheres, and rods. 

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