Shape groups

A variety of shapes and sizes exists for the commercial M-magnets. Most M-ferrite products are flat owing to the relatively high and moderate B. Basic shape groups are rings, disks, plates, rods, cylinders, blocks, strips, and segments. Each shape-group in turn contains a number of products. The... 

Macropolycyclic ligands, 2,942 classification, 2,917 metal complexes binding sites, 2, 922 cavity size, 2,924 chirality, 2, 924 conformation, 2,923 dimensionality, 2, 924 electronic effects, 2, 922 shaping groups, 2,923 structural effects, 2,922 molecular cation complexes, 2,947 molecular neutral complexes, 2,952 multidentate, 2,915-953 nomenclature, 2,920 Macro tetrolide actins metal complexes, 2,973 Macrotricycles anionic complexes, 2,951 cylindrical... 

Walker, P. D., Maggiora, G. M., Johnson, M. A., Petke, J. D., and Mezey, P. G. (1995) Shape group-analysis of molecular similarity—Shape similarity of 6-membered aromatic ring-systems../. Chem. Inf. Comput. Sci. 35, 568-578. 

Speleands (20) are hollow, macropolycyclic molecules formed by the combination of polar binding units with rigid shaping groups. Speleate refers to the complex. 

The nature and, as a consequence, the selectivity of a particular macrocycle can be further manipulated by the selection of appropriate shaping groups and heteroatoms at the binding site. In general, saturated chains provide greater flexibility, particularly as chelate size (pertaining to the... 

The crystal and molecular structures of Pl Mg-TMEDA1 (3) (55) and of PlZnCl"TMEDA (4) (87) have been determined by X-ray diffraction. The dimethylpentadienyl groups in 3 retain a U shape, and the two double bonds are twisted relative to each other through 23°. The W-shaped group in 4 is, however, essentially planar. Bond lengths alternate as expected for t] -bonded pentadienyl groups. 

Pharmaceutical products such as tablets usually consist of active pharmaceutical ingredients. In the pharmaceutical industry, the API particle size has tended to become smaller in recent years and the needle shape has become very common. These small API particles usually belong to Group C according Geldart classification.2 3 It is well known that the needle-shaped Group C particles are very cohesive. They do not flow easily and mix poorly with other particles. 

Ribosomes are the site of protein synthesis and exist (1) in the cytoplasm as rosette-shaped groups called polysomes (in immature red blood cells there are usually five per group) (2) on the outer face of the RER or (3) in the mitochondrial matrix, although this last type is different in size and shape from ribosomes in the cytoplasm. Ribosomes are composed of RNA and protein and range in size from 15 to 20 nm. Their central role in protein synthesis is described in Chap. 16. 

Apparently, the concept of similarity plays an important role in the chemistry of functional groups. Motivated by the recent revival of interest in molecular similarity [7-39], we shall present a systematic approach towards a quantum chemical description of functional groups. There are two main components of the approach described in this report. The first component is shape-similarity, based on the topological shape groups and topological similarity measures of molecular electron densities[2,19-34], whereas the second component is the Density Domain approach to chemical bonding [4]. The topological Density Domain is a natural basis for a quantum... 

An important concern is the efficient detection of local shape changes introduced by chemical changes in remote locations of a molecule. One simple approach [20] applied a truncation method, compatible with the truncation process already used within the shape group methods for molecular shape analysis [41-44]. 

Skinny molecular range, [af, a< ) af is defined above, whereas is the maximum threshold at and below which all locally nonconvex domains on the surface of density domains are simply connected. In simpler terms, in the skinny molecular range all nuclei are found within a single density domain, but there are formal "neck regions on the surface of density domains. In the terminology of shape group analysis [2], rings of D) type can be found on the surface of density domains. 

For both types of FIDCO surfaces, the usual Shape Group method [2] of electron density shape analysis is applicable. The additional formal domain boundaries AD i(Ga b(3)) and AD i(GA(B)(a)) introduce one additional index -1, which can be treated the same way as relative curvature indices. The one-dimensional homology groups obtained by truncations using all possible index combinations are the shape groups of FIDCO surfaces. The (a,b)-parameter maps and shape codes are generated the same way as for complete molecules [2],... 

Since for the whole range of FIDCO surfaces of a given functional group there are only a finite number of topologically different truncated surfaces, consequently, there are only a finite number of shape groups characterizing the shape of a functional... 

The complete, three-dimensional shape of fuzzy electron densities can be described in detail using the Shape Group Methods, (SGM), reviewed in detail in a recent monograph [27], Here, only a brief summary of this method will be given. 

The results of the shape group analysis can be summarized using the Betti numbers. The distribution of various values of Betti numbers bPp(a,b) as a... 

The standard Shape Group Method is applicable for the analysis of the entire series of non-interacting RIDCOs, for a whole range of density thresholds a, with the provision of an additional domain type representing the connection of region R to the rest of the molecule within the actual RM system. This additional domain type D i is defined as... 

The Shape Group analysis can be carried out for all these regional electron densities using both the non-interacting and the interacting RIDCO formalisms. 

The effects of the pressure and the mineral shape groups on vacuum and pressure filtration are shown in Fig 3. The changes of the 1/Kc values as an indication of the filtration rate at different pressures for dolomite and quartz can be given as two results ... 

Figure 3. The effect of mineral shape groups on vacuum and pressure...

Whereas framework groups are more informative than point symmetry groups, they are able to describe only a rather restricted aspect of molecular shape. Alternative group theoretical methods, notably, the Shape Group Methods (SGM) of molecular topology, are more suitable for a detailed shape characterization. The shape groups will be discussed in Chapter 5 of this book. 

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