Connected nodes

Obviously a block is a single entry flow diagram and the basic blocks are tree-like. We need only see that the operations of block composition and block iteration preserve the property of being tree-like. If B is fearned by directly connecting node n of block by block composition to entry node of block Bj, clearly n is an ancestor of ej, so that if both and Bj are treelike, clearly B is tree-like. If B is formed by block iteration by directly connecting exit node n of Block B to entry node of, then n remains a descendant of in B, so if is tree-like then B is also tree-like. 

Next, we will open a page and show how to connect nodes of a circuit on one page to nodes on another page. Double-click on the text My First PdQe to open the schematic ... 

To connect nodes on different pages we use the offpage connectors. Select Place and then Off-Page Connector from the menus ... 

Figure 14. Schematic representation of the two parallel interpenetrating (4,4) nets in [Mn43](C104)2 showing the polyrotaxane-polycate-nane associations. 6-connecting nodes are provided by 6-coordinate Mn and node-to-node connections by ligand 4.

Figure 17. Inclined interpenetration (actually perpendicular) of two (4,4) nets in [M(4,4 -bipy)2(H20)2](SiF6). 4-Connecting nodes are provided by M which has two pendant trans H20 ligands not shown here and connections between nodes are provided by 4,4 -bipy.

A related example involving (6,3) rather than (4,4) nets, in which any 6-gon has components of two independent inclined sheets passing through it is noteworthy in the context of this book in that the connecting rods themselves are encircled in rotaxane fashion by bead-like cucurbituril components, as in structure 5. The 3-connecting nodes of the (6,3) nets are provided by Ag1 each of which is linked to three others by bridging ligands of type 5 [22]. 

Figure 20. Structure of [Cu(4,4 -bipy)X], X is Cl, Br, or I. Circles represent Cu. Each short connection shown here is provided by two p2 X bridges. Long connections are provided by bipy, some of which are present in close side-by-side pairs. The 3-connecting nodes of the (6,3) net are located at the mid-points of the Cu(X)2Cu 4-gons i.e. at the mid-points of the short connections shown here. A 6-gon of one horizontal sheet is shown here in heavy black and three independent inclined nets are seen passing through it, a central one represented by fine lines and a front and a back one by open connections.

Figure 25. (a) Three interpenetrating (10,3)-b nets with T-shaped 3-connecting nodes in the structure of [Ag(bipy)]N03. Circles represent Ag atoms. Long connections are via bridging bipy units and short connections are direct Ag... Ag interactions, (b) An idealized version of the mode of interpenetration of three (10,3)-b nets, of the type seen in [Ag(bipy)]N03. 

In Na[Ti2(PS4)3] the Tirv centers act as 3-connecting nodes, being chelated by three bidentate PS4- ligands which in turn act as /i2-ligands [29], generating an extended net with the (8,3)-c topology [1]. Two of these then interpenetrate [1]. 

The friction equation P,-Pj = ( p/gcn 2)fjLljQl/Dfj applies to the line connecting node i with... 

Figure 10.91 The simplest kind of ravel based on a 3-connected vertex. While none of the three threads are knotted or catenated, pulling on all three of them simultaneously results in an entangled unit distinct from the analogous unravelled 3-connected node.110...

It must be noted that the former correspond to elementary reactions and not to steps. It means that one reversible step corresponds to two nodes. Edges connect nodes -substances and nodes reactions provided that the substances take part in the reaction. Edges will be oriented from substance A, to reaction - E/J. A if A, is the initial reactant (a, 0) and vice... 

The structure of material 6 is a 2D coordination network of twofold interpenetration, in which cubane-like Cu4I4 clusters act as connecting nodes and the dps ligands as the spacer. The intramolecular Cu—Cu distances range from 2.563(1) to 2.734(2) A. Like in the case of [ Cu(p,-I)2Cu (dps)2]ra 5, ligation... 

The position of the methyl substituent of 1,4-bis(tolylthio)butane plays also a major role for the control of the nuclearity. This was evidenced by mixing Cul with l,4-bis(o-tolylthio)butane (Scheme 10). The 2D network of the reaction product [(CuI)2 p,-o-TolS(CH2)4STol-o 2]ra 20 (Fig. 35) contains discrete dinuclear Cu(p2-I)2Cu rhomboids as connecting nodes, similar to the bonding situation encountered in [(CuBr)2 p,-p-TolS(CH2)4STol-p 2] 19. The Cu-Cu separation of 2.796(3) A matches closely with the sum of the van der Waals radii of two Cu atoms. 

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