Mason rule

On the other hand, Vol kenstein and Gol dshtein actively applied graph theory methods in a series of the studies in the 1960s [2-4] and introduced this relationship by analogy with the known Mason rule from electrical engineering. 

A strict substantiation for this analogy and derivation of this relationship in terms of the Mason rule [5] can be found in refs. 6 and 7. In our monograph [7] we also give proofs for the fact that the terms of eqn. (11) obtained using the Kramer rule are spanning tree weights of various nodes. A brief substantiation for eqn. (11) will be given below. 

Let us prove the validity of the "Mason rule formulated above [see eqn. (11)] for linear mechanisms with many cycles (routes). 

Let us prove this theorem proceeding from the Mason rule [5], For this purpose let us rewrite eqns. (32) as... 

The application of graph theory methods for deriving kinetic equations of heterogeneous catalytic reactions is based upon the so-called Rule of Mason this is also known in American literature as the Shannon-Mason Rule of Cycles. Although established by Shannon in 1941 (23), the rule acquired great popularity after its rediscovery by Mason in 1955 (24.25). A strict proof for the validity of the Rule of Mason for multiroute linear mechanisms was presented only recently by Evstigneev and Yablonskii (26), where both an inductive proof and a proof based on the Rule of Krammer are set forth. 

Mason and coworkers10 studied the chiral bicyclic derivatives 2, 3, 33 and 34, having known absolute configuration. These molecules possess a planar s-cis diene chromophore and formally their chirality is due to the presence of the D or CH3 substituents, which rule out all the symmetry planes. However, it is interesting to point out a peculiar structural... 

And even before their ultimate ascension, his true disciples had the capacity to rid themselves of the taint of original sin and reach toward spiritual perfection and eternal life. But to attain such moral purity, they must be prepared to overcome terrible ordeals that would be strewn in their path. Only seventy-two Masons could achieve the first grade, forty-eight the second, and so on up to the final grade, where a dozen immortals would eventually reign forever as spiritual rulers of the world. Masons must realize, however, that the devils necromancers were constantly at work to divert them from this true path with temptations—earthly greed and cupidity. As a rule of thumb, they should trust spirits whose names ended in er, and shun those whose names ended in el. ... 

As has already been shown, graph theory methods were first used in chemical kinetics by King and Altman who applied them to linear enzyme mechanisms [1] to derive steady-state kinetic equations. Vol kenshtein and Gol dshtein in their studies during the 1960s [2 1] also elaborated a new formalism for the derivation of steady-state kinetic equations based on graph theory methods ("Mason s rule , etc.). 

Application of the Rule of Mason in chemical kinetics was made for the first time in the work of Vol kenshtein and Gordshtein (3,4) and leads, by analogy to electrotechnics, to the foDowing expression for the concentrations of the ISCs participating in the studied mechanism ... 

We now give an expressions for the rate of a catalytic reaction obtained from the Rule of Mason. 

According to the Rule of Mason, the base determinant of a given vertex includes only spanning trees that end on this vertex. The number of needed spanning trees is actually smaller than that given by equation (69). 

Maricondi and Maricondi (13) have shown that Mason s hexadecadal regional rule can be applied to predict the experimentally observed sign of the low energy CD transition for... 

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