Complete node

Number of complete node-hy node searches required 15... 

Number of complete node-by-node searches required 19 Would you like to add the structure as a now concept (y yes)... 

Potential physical reactions can only be identified with any assurance of completeness after the complete specification of the chemical species set, CSS. This is a result of Postulate 1, n + 2) defining variables must be known before a thermodynamic state can be specified. Since incomplete specification of n leads to incomplete specification of potential states, a complete node description is required before physical reactions can be identified completely. 

The nodes M form a barrier between G and the rest of G- For this reason M is referred to as a barrier set and is a special case of a separating set [95], One important special case of a barrier set is the set of complete nodes of a graph, referred to henceforth as a complete barrier set. 

In this section we present several results concerning the eigenvalues and eigenvectors of Jg for graphs with complete nodes or completely connected subgraphs. See [305] for proofs of the following theorems. 

Theorem 13.11 Consider a network ofnjeactors represented by a graph Q and let Vj Mg be a complete node. Ifk e ct(J( )) with eigenvector z, then k e cr(Jg) with eigenvector z such that... 

When m [Pg.390]

We showed above that reactors that are coupled to all other reactors play a special role. In a similar way, the presence of completely connected subgraphs influences pattern formation in networks of diffusively coupled monostable elements. The following five theorems address the consequences of the presence of completely connected subgraphs with respect to a nonempty set of nodes M. In the latter three results, 7 is a set of complete nodes. These results address the possibility of localized and buffered patterns in networks of diffusively coupled reactors. We demonstrate the existence of such patterns for networks with Lengyel-Epstein kinetics in Sect. 13.4.2. 

Theorem 13.15 implies that if an edge or node, which is not a complete node, is added to or deleted from t/j, then the effect on the eigenvalues and eigenvectors will primarily be manifested only in. ... 

The simplest case of a network with a complete node is a star graph. We start our exploration of the nonlinear dynamical behavior of Lengyel-Epstein networks with a 10-node star graph, namely of Fig. 13.3a. Theorem 13.17 implies that F = 1, 10. Choosing r = = 1, we expect from (13.125) that a coupling strength... 

The hilar lymph nodes, which are encountered within the lung at the bifurcations of the large bronchi, are complete nodes with a subcapsular sinus and follicles. From the hilar nodes, the lymph drains via extensively anastomosing channels through tracheobronchial lymph nodes clustered alongside the main stem bronchi, beneath the Carina, and along the course of the trachea. In the me-... 

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