Ordering index

Figure 7.9 EJfect of mean residence time on mean crystal size parameter i = hjg, the relative nucleation to growth order index)...

Profound line profile analysis is possible if a set of reflections is observed, i.e., peaks from several crystallographic orders indexed by (h) are accessible. With respect to a principal reflection found at the position, V(, the positions of the higher orders are... 

Note that the bond order index defined by Mayer accounts for the covalent contribution to the bond (this is why of late it is often mentioned as shared electron pair density index, SEDI). As such, the index cannot be expected to produce the integer values corresponding to the Lewis picture if a bond has a significant ionic contribution. The bond order index defined in this way measures the degree of correlation of the fluctuation of electron densities on the two atoms in question [7]. 

The inclusion of higher order indices, such as the sixth order index used here, indicates that a critical dimension or number of atoms in a chain is influential... 

The second connection index considers three adjacent molecules at a time, and there are four choices (1,3,2), (3,2,1), (1,3,1), and (1,3,2). The second-order index has the value of... 

Another important consideration is that all results reported here are based on the calculation of zero- and first-order connectivity indexes only. It is possible that die inclusion of higher-order indexes, which in turn means more detailed... 

Here we report similar studies on 2GT polyester and 66 polyamide fibers and define local order indexes. 

As can be seen from the table, the values of gRP do indeed remedy the insufficiency of the first order index r and correctly predict the reaction preferred... 

We are able to apply successively the relation in Eq. (13-66) and thereby we determine the higher-order index transformed integrals, e.g.,... 

Inverted forms of the chemical names (parent index headings) are used for most entries in the alphabetically ordered index. Organic names are listed at the parent based on Rule C-10, Nomenclature of Organic Chemistry, 1979 Edition. Coordination compounds, salts and ions are listed once at each metal or central atom parent index heading. Simple salts and binary compounds are entered in the usual uninverted way, e.g.. Sulfur oxide (SxO), Lira-nium( V) chloride (UCL). 

Two main definitions of bond order indices are reported below. Moreover, the term fractional bond order was suggested to refer to the inverse of any bond order index. Fractional bond order permits individual treatment of a and it molecular systems a bonds give simple graphs, while jt bonds introduce a weighted molecular framework with weights less than one [Randic et al, 1980]. 

Referring to the subgraph order, rth order indices can be defined as -+ count descriptors, i.e. the number of rth order subgraphs in the graph The zero order index is simply the - atom number A, i.e. the number of graph vertices 1 order index is the -> bond number B, i.e. the number of graph edges 2" order index is the... 

Interestingly, despite the greater electron affinity of carbon than boron, the calculated bond orders/indices of the cage bonds from the equatorial or tropical boron atoms to the axial atoms in systems [B H ] , [CB iH ], and C2B 2H change little as axial carbon atoms replace axial boron atoms. However, axial carbon atoms reduce the electron density and so the bond order/index between equatorial or tropical boron atoms, ... 

Alternatively, the ordering index may be continuous so that, for example, x(v) is a random variable for each real v. We say that x(v) is a random function of v a random function assigns a random variable to each value of its argument(s). The corresponding joint probability density / [x(v)] is a functional of this function. 

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