Coordination INDEX

Coordinate Indexing and Boolean Logic. Three methods of indexing have been prominent in the chemical Hterature in recent times. The first, articulated indexing, has been used in printed Chemicaly hstracts subject indexes from their earliest days until well into the 1990s. A number of important concepts are identified as permissible index entries, including specific compounds, material types, reactions, and processes. One or more modifying statements foUow each basic index entry. Thus, eg. 

The shear-stress convention is a bit more complicated to explain. In a differential control volume, the shear stresses act as a couple that produces a torque on the volume. The sign of the torques defines the positive directions of the shear stresses. Assume a right-handed coordinate system, here defined by (z, r, 9). The shear-stress sign convention is related to ordering of the coordinate indexes as follows a positive shear xzr produces a torque in the direction, a positive xrg produces a torque in the z direction, and a positive x z produces a torque in the r direction. Note also, for example, that a positive xrz produces a torque in the negative 6 direction. 

Note that, from now on, we omit the coordinate index (x, y). If we now apply the logarithm to both sides, the product of irradiance and reflectance is split into a sum. 

The final step in multiple-base classifications is coordinate indexing, which amounts to making each indexing t6rm a base of its own. The idea is old one of its modem forms is Uniterm indexing (13). 

Mines, Patricia, Uniterm System of Coordinate Indexing, in Advances in Docu-... 

Gamble, D. F., Coordinate Index of Organic Compounds, Abstracts of Papers, 127th Meeting, ACS, April 1955, p. 7G. 

Figure 1 Schematic view of the coordination sites in the hammerhead ribozyme active site. Upper left The coordination pattern of Mg2 in the C-site coordinated to G10.1 N7 and k9 Ow. Upper right The coordination pattern of Mg2 in the B-site bridging A9 02p and Cl.LO of the scissile phosphate. Lower Coordination sites for Na in the hammerhead ribozyme active site found in the RT-Na and dRT-Na simulations. Red numbers next to the coordination sites are the scores used to calculate the coordination index (see text). M, involves direct binding to A9 02P and C.1 02P and indirect binding to G10.1 N 7 through a water molecule. M2 involves direct binding to CT7 02- and C.l 02p M3 involves direct binding to CI7 02 and is positioned toward the outside of the active site. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this book.)...

Based on the idea to model the morphology-functionality relationship in organisms, the functional coordination index is defined in terms of the —> molecular surface area SA, the molecular weight MW, and the standard enthalpy of formation Hjas [Torrens, 2003a]... 

Below a Matlab script implementing the tensor-product QMOM for a simple bivariate case described in this section is reported. The required inputs are the number of nodes for the first (Nl) and for the second (N2) internal coordinates. Since in the formulation described above the moments used for the calculation of the quadrature approximation are defined by the method itself, no exponent matrix is needed. The moments used are passed though a matrix variable m, whose elements are defined by two indices. The first one indicates the order of the moments with respect to the first internal coordinates (index 1 for moment 0, index 2 for moment order 1, etc.), whereas the second one is for the order of the moments with respect to the second internal coordinate. The final matrix is very similar to that reported in Table 3.8. The script returns the quadrature approximation in the usual form the weights are stored in the weight vector w of size N = Mi M2, whereas the nodes are stored in a matrix with two rows (corresponding to the first and second internal coordinate) and M = M1M2 columns (corresponding to the different nodes). 

More precisely, ey is an (r,+l)-dimensionalunit vector with coordinates indexed from 0 up to r,- and such that... 

In their paper (Krishnamoorthy and Overstreet 1949), they considered reasonable for clay minerals a coordination index Z = 4, thus will have a value of 1 for univalent ions, 1.5 for divalent ions, and 2 for trivalent ions. Consequently, for a binary exchange K+-Mg +, the weighted fractions will be... 

In solids containing only one family of nodes, the atoms (or molecules) of the two components are placed on the nodes of the single lattice, the coordination index is the same for both components. For instance, with a binary solution of the solvent A and solute B, the crystalline lattice is that of the pure A and, at certain sites, atoms of B substitute atoms of A in the initial structiu e, but without modifying that structure. 

We have only looked at the case where the lattice was made up of all identical sites - i.e. sites which had the same coordination index. There is another kind of solid solution in which the coordination indices of the two components are not necessarily equal - that in which the atoms of each component are placed at the nodes of a distinct sublattice, so the lattice is formed of two families of nonidentical sites. This type of solution often gives us definite compounds, which frequently exhibit major deviations from stoichiometry (see Chapter 3). 

The crystalline lattice of the solid solution is very similar to the lattices of each of the pure solids A and B. In particular, these three solids exhibit the same coordination index z (say, 12 for the hexagonal lattice or the cubic, centered face lattice). 

This number z is the coordination index linked to the cell geometry. We shall suppose that the molecules occupy the sites of a cubic lattice with centered faces, and therefore the coordination index is z = 12. 

The mean number of vacancies neighboring a molecule (z is the coordination index of the lattice) would be ... 

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