Network irregular

Theoretically, branched molecules are soluble in some solvent, and are thus distinguishable from cross-linked networks. Conversely, however, not all insoluble polymers are cross-linked networks. Irregular cross-linked networks are the result of either certain uncontrolled, nonstereospecific reactions, or they are produced by the subsequent cross-linking of linear or branched molecules. For network formation to occur, it is essential that each macromolecule be cross-linked at two or more sites to two other polymer chains. 

The calculations were performed for e = 29.8 and = 6.1, assuming as in Ref. [3] the same dielectric anisotropy for the polymer network. The Cy versus y characteristics for three samples (A, B, and C) with R/a = 3 and same polymer concentration ( 9%), but different network topography, is shown in Fig. 10. In Prtedericksz-like geometry where the external field is strictly perpendicular to fibers (samples A and B), the orientational transition happens abruptly at a well-defined threshold (r/ and t]b, respectively, with r/ > r/s). In sample C network irregularities further decrease the switching threshold (r/cl not well-defined anymore), yet keep the reorientational process relatively sudden. The thresholds for... 

Characterization of folded proteins Characterization of DNA sequences Characterization of t-RNA Characterization of proteins Characterization of molecular shape Characterization of chirality Characterization of graph and network centrality Characterization of network irregularities Recognition of molecular docking Numerical characterization of proteome maps DNA and protein alignment... 

Interest in irregular networks revived since the 1980s when an additional two measures for irregularity of networks were proposed based on the variance of vertex degrees [52] and on the sum of absolute values of differences in degrees of adjacent vertices [53]. We should mention that the index that BeU used as a measure of network irregularities was introduced about 10 years before by Snijders [54] as a... 

Let us return to the Estrada approach to characterization of network irregularities. He generalized the difference between the reciprocal square roots of the vertex degrees to... 

Recommendations on additional aspects of macromolecular nomenclature such as that of regular double-strand (ladder and spiro) and irregular single-strand organic polymers continue to be pubHshed in I ure and Applied Chemistty (100,101). Recommendations on naming nonlinear polymers and polymer assembHes (networks, blends, complexes, etc) are expected to be issued in the near future. 

Because thermosetting plastics have an irregular form they are amorphous and because of the network structure are invariably rigid. They do not dissolve without decomposition but may swell in appropriate solvents, the amount of swelling decreasing with increased cross-link density. 

Covalent polymeric networks which are completely disordered. Continuity of structure is provided by an irregular three-dimensional network of covalent links, some of which are crosslinks. The network is uninterrupted and has an infinite molecular weight. Examples are vulcanized rubbers, condensation polymers, vinyl-divinyl copolymers, alkyd and phenolic resins. 

Particulate, disordered structures. These include flocculent precipitates where particles generally consist of fibres in brush-heap disarray or connected in irregular networks. 

A growing neural gas has an irregular structure. A running total is maintained of the local error at each unit, which is calculated as the absolute difference between the sample pattern and the unit weights when the unit wins the competition to match a sample pattern. Periodically, a new unit is added close to the one that has accumulated the greatest error, and the error at the neighbors to this node share their error with it. The aim is to generate a network in which the errors at all units are approximately equal. 

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