Networks undefined

The principle of the second synthetic approach to polycatenanes, i.e. stepwise polycondensation, has been proposed by Shaffer and Tsay, but not experimentally demonstrated [42, 43], This approach has the advantage over multifunctional polycondensation that a linear polymer is formed before cyclization (Scheme 7). However, the second step, which consists of the cyclization of n macrocycles along the polymer chain 19, is likely, again, to give rise to an undefined network, containing some rotaxane and catenane units 21, similar to the multifunctional polycondensation approach. 

Stockmayer 25 subsequently developed equations relating to branched-chain polymer size distributions and gel formation, whereby branch connectors were of unspecified length and branch functionality was undefined. An equation was derived for the determination of the extent of reaction where a three-dimensional, network ( gel ) forms this relation was similar to Flory s, although it was derived using another procedure. Stockmayer likened gel formation to that of a phase transition and noted the need to consider (a) intramolecular reactions, and (b) unequal reactivity of differing functional groups. This work substantially corroborated Flory s earlier studies. 

Dissipation phenomena generally occur during measurement of the adherence of polymer materials, leading to an adherence energy function of both the number and nature of interfacial interactions (adhesion) and dissipative properties, mainly due to viscoelastic behavior [1-5]. Friction properties of polymers are also governed by interfacial interactions and dissipation mechanisms. Common phenomena (interfacial interaction and dissipation) therefore control adherence and friction behaviors. However, the relationship between the two phenomena is still vague or undefined. The first objective of this experimental work is then to compare adherence and friction of polydimethylsiloxane (PDMS) networks in order to establish relationships between these two properties. 

Any method can be implemented, no matter how complex, provided one has a complex enough network to perform such a task. A complex enough network usually means a network with at least three layers of nodes and nonlinear units and an undefined number of hidden units in the intermediate layer between input and output. 

Morphology Network Needles growing radially from Undefined Spherical... 

In practical applications a neural network can be used when the exact model is not known. It is a good example of a black-box technique. By no means, however, should the neural network be seen as the ultimate solution for problems with undefined or only partially defined models. The main reason is that it gives no additional information about the physical relationships and thus it will give no physical insight into the process. 

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