INDEX spatial arrangements

Because each member of a pair of enantiomeric molecules differs from the other only in the spatial arrangement of the ligands attached to the chiral center, their physical properties, that is, melting point, boiling point, refractive index, solubility, etc., are identical. The major difference between the isomers of an enantiomeric pair was first observed by Biot in 1815 when he noted that one form of tartaric acid rotated plane-polarized light, whereas another form did not (1). 

Automated assembly systems are used mainly for the production of series and mass-produced articles. In the field of indexing machines, a distinction is made between rotary indexing turntables and rectilinear transfer machines. The essential difference between the two systems is the spatial arrangement of the individual workstations. 

We now go on to discuss a polymer system of A4 chains in the volume V. Each chain is marked by its index m, X, being the length of the mth chain. The vector rm( m) characterises the spatial arrangement of the mth chain, where A, is the length measured along the chain from its beginning to the point with the mark Tm (0 < A, < Xm). 

The science of geometric crystallography was concerned with the outward spatial arrangement of crystal planes and the geometric shape of crystals. Workers of that day arrived at three fundamental laws (a) the law of constancy of interfacial angles, (b) the law of rationality of indexes, and (c) the law of symmetry (14). 

Here B is an optical constant, or is the total polarizability of the particle, and n is the number of components in each particle. The indexes i and j refer to components of the same particle. If the assumption of independent particles was not made, then the indexes could refer to components of any two particles, and the autocorrelation expression could not be written as a simple sum of contributions from individual particles. The spatial vector r(r) refers to the center of mass of the particle. R(r). In the case of a nonspherical particle (arbitrary shape), Eq. (I0) would describe the coupled motion of the center of mass and the relative arrangement of the components of the particle. For spherical particles, translational and rotational motion arc uncoupled and we have a simplified expression for the electric field time correlation function ... 

The method of Kotrly and Vytras has been used to obtain the optimum concentrations of the indicators for the titration arrangement used. They pointed out that the spatial transition curve of a color change can be divided into small segments related to a suitable variable, usually pH or the concentration of free perchloric acid, Chcio4j in acetic acid medium. The ratio ApH/AE or APCHCIO4/AE was taken as an index of color change perceptibility. 

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