Statistical network analysis formulation

Statistical analysis and neural networks optimization of formulations. CHEMiCALC... 

The mathematical background for the computation and the analysis are formulated in the adjustment calculation approach which is basically linear. The observables are assumed to be a sample, in the sense of statistics, of the true absolutely correct values and their deviations from these true values follow certain statistical laws of distribution. However, for the observational types of distances and directions there is a non-linear relationship between the observations and the coordinates of the network s points. Initial values are needed in order to linearize the non-linear observational equations. 

Ladder studies are often conducted var3dng the stoichiometric ratios and other factors to determine the optimum formulations. Statistical design of experiment (DOE) methodology has been used to efficiently carry out ladder studies (141). Information concerning network structures can be obtained using dynamic mechanical analysis (DMA) (142,143) and chemorheology to guide formulation development (144,145). 

For convenience of mathematical formulation, the junctions at the termini of chains were shown as the sites of entanglements. The term constraints on junctions was used with the understanding that these constraints were derived directly from local intermolecular entanglements among chains. The dependence of these constraints on strain, obtained by a statistical analysis of the local geometry about the junctions, forms the basis of the Flory theory of elasticity of real networks. The predictions obtained by... 

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