Extended adjacency index

EAmax index -> eigenvalue-based descriptors (O extended adjacency matrix indices)... 

They are two molecular descriptors calculated from -+ extended adjacency matrices EA [Yang et al, 1994], The first is the sum of the absolute eigenvalues of the EA matrix, called the EAI index ... 

This matrix is a special case of —> distance degree matrices obtained by the parameter combination a = 0, (3 = 0, y=l. The row sum of the additive adjacency matrix is the —> extended connectivity of first-order EC defined by Morgan. This local invariant was used to calculate the eccentric adjacency index. A modification of this matrix, which accounts for heteroatoms, is the additive chemical adjacency matrix. 

H -state index = hydrogen electrotopological state index electrotopological state indices > heteroatom-corrected extended adjacency matrix —> extended adjacency matrices... 

Recently Hu and Xu proposed a highly discriminating molecular topological index based on the extended adjacency matrix. The extended adjacency matrix is computed by... 

Surface plasmon waves (SPW) have been explored almost half a century ago (23, 24). These are surface-bound electromagnetic waves propagating on the dielectric-metal interface. The existence of SPW strongly depends on the refiuctive index of the dielectric medium adjacent to the metal, so it is commonly known that the electromagnetic field of SPW is extended into the medium only to a depth of 200 nm or so (25, 26). Therefore, SPW is very suitable for the measurement of small changes in refractive index of dielectric medium in the vicinity of metal for detecting bio-molecules interaction (26-30). 

D denotes the degrees of the atoms i and j of a molecular graph, and the sum goes over all adjacent atoms. The exponent was originally chosen by Randic to be -1/2 however, it has been used to optimize the correlation between the descriptor and particular classes of organic compounds. The connectivity index was later extended by Kier and Hall to applications with connected subgraphs [22],... 

The lowest level structure descriptor is simply the count of atoms. However, only in alkanes are the properties even roughly proportional to the number of atoms. More information-rich structure indicators are needed. In the earliest topological methods, numerical indexes were developed simply by counting the number of edges or pairs of adjacent edges. Wiener,Platt,and others " developed structure indexes that produced interesting correlations to some properties of saturated hydrocarbons. As impressive as this work is, it could not be readily or usefully extended to unsaturated compounds or to heteroatom-... 

Finally, there is one particular topological descriptor that should be mentioned because it has found considerable utility in a number of studies. This property, originally called a chemically intuitive molecular index by its inventor, Frank Burden, is based on a modified molecular adjacency matrix. The approach was extended by Pearlman " to take account of atomic charge, polarisability and hydrogen bonding ability, properties which are termed BCUT descriptors. BCUTs are available in a number of software packages and in addition to their utility in QSAR modelling, they have been shown to be useful measures of chemical similarity. 

The analysis of the step-profile fiber is readily extended to multilayered fibers with a uniform refractive index in each layer. An example of this is the W fiber, which has three layers with a smaller index in the centre layer than in the two adjacent layers [6], The modal fields and eigenvalue equations for such structures are constructed from the appropriate solution of Eq. (12-11) in each layer, ensuring that the tangential fields are continuous at each interface. 

---