Distribution of dissimilarities

The basic feature of these kinetic equations is the assumption that reaction rate K is a constant, i.e., time-independent parameter due to which all spatial dependencies resulting from real particle motion or interaction are completely ignored. This would be the case if relative spatial distribution of dissimilar reactants remained the same in a course of reaction. We demonstrate below that it is not always the case. 

A graphical display of the distribution of dissimilarity values between all pairs of structures in a file give a clear picture of the homogeneity, or otherwise, of the file, indicating whether or not clear groupings are present. 

The quality of bonding is related direcdy to the size and distribution of solidified melt pockets along the interface, especially for dissimilar metal systems that form intermetaUic compounds. The pockets of solidified melt are brittle and contain localized defects which do not affect the composite properties. Explosion-bonding parameters for dissimilar metal systems normally are chosen to minimize the pockets of melt associated with the interface. 

In the final stage, when the dimethochloride of either Aim thyldesbisneo-strychnidine or that of dimethyldesstrychnidine-D is heated with sodium methoxide in alcohol N (6) is eliminated as trimethylamine and there is formed a mixture of the two desazostrychnidines, a and b, of which the first is amorphous but yields a crystalline methiodide, m.p. 154-5°, and the second is crystalline, m.p. 109-110°, giving a methiodide, m.p. 105-6°. Each yields a hexahydro-derivative, which may be a mixture of stereo-isomerides, and the differenee between the forms a- and h- is probably the result of dissimilar distribution of the three ethylenie linkages thus indi-... 

Dispersion is the minute uniform distribution of one substance throughout a dissimilar substance. Considerations involved in the development of stable dispersions which are discussed here are the dispersion phase, the liquid phase, the interphases, and stabilization. 

Systems with dissimilar media (cases 2 and 3) as a rule are selective because of differences in the chemicaf driving forces, the equilibrium distributions of the components between the two phases are dissimilar. When the selectivity is perfect, some components may exist in only one of the phases and will not transfer to the other. 

DISTRIBUTION OF THE IONS BETWEEN DISSIMILAR BUT MISCIBLE ELECTROLYTES... 

Technical 1,2, 5, 6, 9,10-HBCD is produced industrially by addition of bromine to cis-trans-trans-1,5,9-cyclododecatriene. This process leads theoretically to a mixture of 16 stereoisomers (six pairs of enantiomers and four mesoforms) and the product usually is a mixture of the three diastereoisomers a-, p- and y-isomer [14]. Normally, the y-isomer is the most dominant in the commercial mixtures (ranging between 75 and 89%), followed by a- and then p-isomer (10-13% and 1-12%, respectively) [15]. The dissimilarities in the structure of a-, p- and y-isomer might raise differences in polarity, dipole moment and in solubility in water. For example, the solubility of a-, p- and y-HBCD in water was 48.8,14.7, and 2.1 pg/L, respectively. Therefore, these different properties may explain the differences observed in their environmental behavior [16]. Covaci et al. [17] and Morris et al. [18] found that in sediments, the distribution of HBCD isomers was the same of... 

The U.S. government is quite dissimilar to knowledge-intensive industries, such as the vaccine industry. One difference is between the occupational distributions of employment in the U.S. government and the pharmaceutical industry. In 2001 office and administrative support occupations accounted for 41% of U.S. government employment, but only 12% of pharmaceutical industry employment. The number of employees in production occupations accounted for 35% of pharmaceutical industry employment but only 2% of U.S. government employment. 

Since diversity is a collective property, its precise quantification requires a mathematical description of the distribution of the molecular collection in a chemical space. When a set of molecules are considered to be more diverse than another, the molecules in this set cover more chemical space and/or the molecules distribute more evenly in chemical space. Historically, diversity analysis is closely linked to compound selection and combinatorial library design. In reality, library design is also a selection process, selecting compounds from a virtual library before synthesis. There are three main categories of selection procedures for building a diverse set of compounds cluster-based selection, partition-based selection, and dissimilarity-based selection. 

Due to the existence of two quite different distinctive distances (scale factors) - lo and l - the recombination kinetics also reveals two stages called monomolecular and bimolecular respectively. The defects survived in their geminate pairs go away, separate and start to mix and recombine with dissimilar components from other pairs. It is clear that the problem of kinetics of the monomolecular process is reduced to the time development of the probability w(f) to find any single geminate pair AB as a function of the initial spatial distribution of the pair components f(r), recombination law cr(r) and interaction Uab (r). The smaller the initial concentration of defects, n(0) —> 0, as lo —> oo, the more correct is the separation of the kinetics into two substages, whereas the treatment of the case of semi-mixed geminate pairs is a very difficult problem discussed below. 

As no —> 0, the predominant term here is of the order of n0. Therefore, the shortcoming of equation (4.1.23) arises due to the incorrect use of the superposition approximation in a situation of very particular (strongly correlated) particle distribution. Strictly speaking, the correct treatment of the recombination process with arbitrary initial distribution requires the usage of the complete set of correlation functions. At the joint correlation level, such description yields reasonable results only for the particle distribution close to a random equation (4.1.12). For the infinitely diluted system the correlation function (4.1.10) of dissimilar closely spaced particles reveals... 

For the static tunnelling luminescence decay and correlated defect distribution the joint density of dissimilar defects is governed by equations (4.1.40) to (4.1.42). 

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