Topologically invariant

In the microemulsion the role of A is played by the period of damped oscillations of the correlation functions (Eq. (7)). The surface-averaged Gaussian curvature Ky, = 2t x/ S is the topological invariant per unit surface area. Therefore the comparison between Ryyi = Kyy / in the disordered microemulsion and in the ordered periodic phases is justified. We calculate here R= Since K differs for diffused films from cor-... 

Molecular similarity analysis has developed substantially over the years, especially as digital computers became faster, more compact, and widely available to scientists. Handling large sets of molecules is generally not a problem. The main problem confronting MSA is the problem of the lack of topological invariance of the chemistry spaces induced by the various similarity measures. Unfortunately, this problem may be fundamentally related to the inherent subjectivity of similarity and thus cannot be addressed in any simple manner. 

Ciolowski J (1990) Scaling Properties of Topological Invariants. 153 85-100 Cohen MH (1996) Strenghtening the Foundations of Chemical Reactivity Theory. 183 143-173... 

We define the topological invariant of the link J f as the (normalized) expectation value... 

For the convenience of the discussion, these indices are classified according to their logical derivation from topological invariants, rather than according to their chronological development. 

Table 12.10 C60H36 fullerane topological characterization for each isomer topological invariants W, p and NMR theoretical spectrum are given, being l multiplicity of resonance lines. Highly symmetric Th molecule, in bold, has low W, p values...

Adjacency Matrix, Spectral Density Function and Topological Invariants 87... 

Lower and Upper Bounds to Reduced Topological Invariants. 97... 

In practice, it is much more convenient to use some quantities derived from A instead of the matrix itself. These quantities are usually called topological invariants. For example, the Tt-electron energy in the variable p calculations can be accurately approximated by topological invariants [6]... 

In this review we discuss the scaling properties of topological invariants and the relations between them. First, we recall the basic concepts of the chemical graph theory. Then, we introduce reduced topological invariants and discuss the problem of size extensivity. Following a brief overview of the known approximate relations between topological invariants, we move to considerations of their scaling properties. Finally, we discuss some practical aspects of the present formalism. 

Knowledge of T allows us to calculate most of the topological invariants that are of interest for chemists. They include [7, 8] ... 

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