The Concept of Nodes

In HAZOP studies and What-If analyses, the review team must first identify the areas or components of the system that will each be analyzed during the review process. In the chemical industry, these individual components are typically referred to as nodes. There are three basic criteria for identilying the nodes to be reviewed (Nolan 1994). 

Divide the facility into process systems and subsystems 

Follow the process flow of the system under study 

Isolate subsystems into major components which achieve a single objective (i.e., increase pressure, remove water, separate gases). 

---

C[ and Cj are the concepts of nodes i and j in the two schemas, as generated in the first step and C is the conjunction of all the relations that hold between concepts of labels mentioned in C, and Cj (this includes all nodes on the path to nodes i and j). This is done by using a SAT solver to test unsatisfiability. It is worth noting that the unsatisfiability problem is known to be CO-NP, yet modern SAT solvers have shown very good performance in solving such problems. To reason about relations between concepts of nodes, a set of premises (axioms) is built as a conjunction of the concepts of labels computed in the third step. For example, R. Card Info, type will be defined to be subsumed by S. Card Information while an equivalence semantic relationship is defined between R. Card Info, type and S.Cardlnformation.type. 

The presence of (non-)reactive singular points i.e. pure components and (non-)reactive azeotropes) in ROMs allows the division of the (transformed) composition diagram into separate (reactive) distillation regions by introducing (reactive) distillation separatrices, which connect two singular points in the composition space. The explanatory note 5.1 gives a brief overview of the concepts of nodes and saddle points, as features of singular points. 

Let us illustrate the concept of "tree-like" with a few simple examples. Suppose G is tree-like with entry node e and there is a direct connection from n to m. Situations (1), (2) and (3) below are permissible ... 

In actual practice a number of tests must be passed at various nodes before final classification takes place. Also, a prohibitive time would be required to search a large database of models for ones which most closely approximated the actual data set. For this reascxi the concept of similarity nets is introduced. In this case, a more general model is first chosen, one which is clearly not conpletely absurd. A subset of other models which are variations of this first general model then provides the index for the final choice of model. Such a reduction in the model lists greatly reduces the search space for the closest fit. 

The concept of the size of an atom is not well defined within quantum mechanics. An atom has no sharp boundary the probability of finding an electron decreases exponentially with distance from the atom s centre. Nevertheless, a useful measure of the size of the core is provided by the position of the outer node of the valence electron s radial function, since we have seen that the node arises from the constraint that the valence state... 

These concepts of the classical physics of standing waves have important implications in photophysics, in particular for the understanding of orbital symmetries and laser light emission. In the case of a standing wave the propagation velocity does not exist, and the important relationship defines the wavelengths as a function of the distance between the boundaries and the number of nodes in the wavefunction... 

The most dramatic result of the preferential attachment growth rule is the appearance of highly connected nodes called hubs. The scale-free networks do not have typical nodes with average number of edges. The concept of average connectivity does not have meaning for these nets. 

The central point is that use of the concepts of thermal resistance and capacitance enables us to write the forward-difference equation for all nodes and boundary conditions in the single compact form of Eq. (4-41). The setup for a numerical solution then becomes a much more organized process which can be adapted quickly to the computational methods at hand. 

In this respect I wish to point out, first for the simplest case of the hydrogen atom, that the usual rules of quantum mechanics may be replaced by another postulate in which there is no mention of whole numbers. The introduction of quantisation then follows naturally as, for instance, in the solution of the problem of a vibrating string when the number of nodes must be a whole number. I he new conception may be generalised and touches I believe, very deeply, the true nature of quantum laws. 

To facilitate rule deflnition, parameters can be set at deflnition time as well. This can be compared to the concept of genericity as contained in some modern programming languages. We plan to allow different kinds of parameters, ranging from integer values, or node types, to complex graph patterns. 

The concept of a sentinel lymph node (SLN) was spawned by Cabanas in his study of penile carcinoma. 

---