Shapes Graph

Finally, titrate with dimethylglyoxime solution (0.02 M) using the standard general method and obtain a V-shaped graph. 

To learn that the end point in a redox titration is obtained as the point of inflection in the S-shaped graph produced by plotting em/ against volume of redox reagent . 

TOPOLOGICAL SHAPE GROUPS, SHAPE CODES, SHAPE GRAPHS, SHAPE MATRICES, AND SHAPE... 

Shape Codes, Shape Graphs, and Shape Matrices... 

Chain Molecule Shape Graphs and Shape Polynomials... 

Consider a MIDCO G(a) and a choice for the curvature parameter b, and assume that the shape domains of relative convexity of G(a) have been determined. By using an appropriate neighbor relation to describe the mutual arrangements of the domains along the MIDCO surface G(a), the corresponding shape matrix s(a,b) and the associated shape graph g (a,b) can be defined [109,110,158,193]. 

Figure 5.8 Three shape graphs, g(0.01,0), g(0.01,0.005), and g(0.01,-0.008), of the three shape domain partitionings of the allyl alcohol MIDCO G(O.Ol) of Figure 5.6 are shown. These shape graphs correspond to the three shape matrices s(0.01,0), 3(0.01,0.005), and...

Both the shape matrix s(a,b) and the shape graph g(a,b) give a detailed shape characterization of the MIDCO surface G(a), with respect to the selected reference curvature b. 

We have seen that a simple list of Betti numbers of the shape groups can serve as a numerical shape code for a partitioned molecular surface. Some of the alternative topological shape de.scriptors of molecular surfaces, such as the shape matrices s(a,b) and shape graphs g(a,b), can also serve as 3D topological shape codes 143,109,110,158,199]. In Chapter 6, several examples of shape codes are described and used as numerical shape similarity measures. 

P.G. Mezey, "The Topology of Molecular Surfaces and Shape Graphs", in Computational Chemical Graph Theory", D.H. Rouvray (Ed.), Nova, New York, 1990. 

As titrant is added to the flask containing the solution of unknown concentration, pH is measured. A distinctively shaped graph, called a titration curve, results when pH is plotted against titrant volume. Figure 18 shows a typical example. Because the curve is steep at the equivalence point, it is easy to locate the exact volume that corresponds to a pH of 7.00. 

Mezey, P.G. (1988c). Shape Group Studies of Molecular Similarity Shape Groups and Shape Graphs of Molecular Contour Surfaces. J.Math.Chem.,2,299. 

Mezey, P.G. (1989). The Topology of Molecular Surfaces and Shape Graphs. In Computational Chemical Graph Theory and Combinatorics (Rouvray, D.H., ed.). Nova Publications, New York (NY). 

Mezey, P.G. (1988c) Shape group studies of molecular similarity shape groups and shape graphs of molecular contour surfaces. /. Math. Chem., 2, 299. 

A hierarchical view is need to achieve the stratification. The concept of hierarchy is in fact a common feature of thinking about systems, so it is worth pursuing what Kumar, Smith, and Stefanelli were thinking as an example of what this means. The hierarchy is a tree-shaped graph that has several main components of a typical health organization or institution, namely its physical structures, its human resources, the tasks capable of being performed by these human resources, and the tasks recommended in the guidelines themselves. 

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