Path matrix

Born-Oppenheimer approximation, matrix elements, 186-191 coordinate origins, 137-138 extended Born-Oppenheimer equations closed path matrix quantization, 171 — 173... 

Appendix N shows a 3rd catalyst bed heatup path matrix with these equations. It also shows several heatup path points. Figs. 16.3 and 16.4 show the entire heatup path. 

S03-in-feed-gas changes Chapter ll s heatup path matrix by introducing a new input variable ... 

The result of the Section 17.1.2-17.1.4 changes is heatup path matrix Table 17.1. 

C02 in feed gas introduces two new variables into the Table 17.1 heatup path matrix ... 

All of these changes are summarized in heatup path matrix Table 17.3. 

Table 17.3. Is1 catalyst bed heatup path matrix with S03 and C02 in feed gas". Cells D15 to H15 contain -H°9QK values. Cells 115 to M15 contain H°2QK values. All are calculated with Appendix G s enthalpy equations. 820 K part way down the catalyst bed is shown to be equivalent to oxidation of 46.7% of the feed gas s S02. 

Table 19.1. Heatup path matrix for after-intermediate-inSCri-making catalyst bed. The 1st three rows represent the equations ... 

Enthalpy Equations in Heatup Path Matrix Cells... 

A heatup path matrix is entered as described in Tables 11.2 and 1.1. Cells D28 to J28 contain enthalpy-as-a-function-of-temperature equations, Table 1.1. Cells C22 to C24 contain input kg-mole S02,02 and N2, Section 11.13. 

Heatup path matrix (In means fri feed aas. out means In intercept oasl ... 

Heatup path matrix (in means in feed gas, out means in intercept gas ) ... 

Table K.l shows a 2nd catalyst bed heatup path matrix with enthalpy-as-a-fiinction-of-temperature equations in cells D15 to K15. The only difference between this matrix and the Table 14.2 matrix is that Eqn. 14.9 in row 15 has been changed to ...

Table N.l. 3rd catalyst bed heatup path matrix with enthalpy equations in cells D15-K15. The numerical quantities in cells C8-C11 are Table M.2 s 2nd catalyst bed intercept quantities. 

A square symmetric matrix of dimension Ax A, A being the number of graph vertices, derived as the difference between the - distance-path matrix Dp and the distance matrix D [Diudea, 1996a Diudea et ai, 1997d Ivanciuc et al, 1998] ... 

The detour matrix A of a graph 5 (or maximum path matrix) is a square symmetric Ax A matrix, A being the number of graph vertices, whose entry i-j is the length of the longest path from vertex v, to vertex Vy [Buckley and Harary, 1990 Ivanciuc... 

The detour-path matrix Ap, analogously defined as the -> distance-path matrix Dp is a square symmetric matrix Ax A whose off-diagonal entry i-j is the count of all paths of any length m ( < m < A,) that are included within the longest path from vertex v, to vertex vy (A,y) [Diudea, 1996a]. The diagonal entries are zero. 

The hyper-detour index ww can be obtained applying the Wiener operator to the detour-path matrix, as ... 

For acyclic graphs, the hyper-detour index ww is equal to the index Dp obtained from the distance-path matrix Dp and to the WW obtained from the - Wiener matrix W. 

From the detour matrix and the distance matrix, a combined matrix, called detour/ distance matrix A/D (or maximum/minimum path matrix), is defined as [Ivanciuc and Balaban, 1994b] ... 

The hyper-distance-path index Dp can be obtained applying the - Wiener operator yv to the distance-path matrix ... 

For acyclic graphs the hyper-distance-path index Dp coincides with the - hyper-Wiener index WW derived from the - Wiener matrix and with the -> hyper-detour index derived from the detour-path matrix. Moreover, it was proposed as an extension of the hyper-Wiener index for any graph [Klein et al., 1995],... 

The reciprocal distance-path matrix Dp is a matrix whose elements are the reciprocal of the corresponding distance-path matrix elements ... 

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