Graph-theory derived approach

Graph-Theory derived Approach Ideas derived from topology and graph-theory are used to model the skeleton chemical bonding in clusters. 29-33... 

A related approach can be used to compare the computed octahedral surface orbital energy parameters with the ideal values arising from the graph-theory-derived method. In this case, the ideal surface orbital energy parameters are the following, with /3s designating the surface orbital energy unit... 

The Formal Graph theory cannot follow this approach which contradicts itself in using time derivatives in steady state (even if time is carefully hidden under symbols such as e or y). This is because of the tight link in this science between flow and time, in which it is customary to distinguish between solids and fluids according to the time scale of relaxations or deformations (Phan-Tien 2002). 

The numbers of possible symbolic equatioas of each six monocyclic types in Figure 2 were derived by enumeration methods in graph theory and cover all possible variatioas. Zefirov also counts systematically all possible cases with more than one specific atom X and some general examples are found in Figure 2. His approach was expanded later by generating examples on the computer, continued in Section 2.3. 

In general, no simple, consistent set of analytical expressions for the resonance condition of all intradoublet transitions and all possible rhombicities can be derived with the perturbation theory for these systems. Therefore, the rather different approach is taken to numerically compute all effective g-values using quantum mechanics and matrix diagonalization techniques (Chapters 7-9) and to tabulate the results in the form of graphs of geff,s versus the rhombicity r = E/D. This is a useful approach because it turns out that if the zero-field interaction is sufficiently dominant over... 

The Method of Volkenstein and Goldstein. Volkenstein and Goldstein have applied the theory of graphs to the derivation of rate equations. Their approach has three main features the use of an auxiliary node, the compression of a path into a point, and the addition of parallel branches. These can be best explained by an example (Scheme 3). 

W. Borutzky and G. Dauphin-Tanguy. Incremental Bond Graph Approach to the Derivation of State Equations for Robustness Study. Simulation Modelling Practice and Theory, 12(1) 41-60,2004. 

Borutzky, W., Dauphin-Tanguy, G. (2004) Incremental bond graph approach to the derivation of state equations for robustness study, Simulation Modelling Practice and Theory 12(l) 41-60. 

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