Frechet expansion

An example of (d) is the memory-integral expansion , which results from a Frechet expansion of the stress tensor given as a general functional of the strain history the general term in this expansion is an n-fold integral involving all various n-tuple products of the relative finite strain tensors... 

In one of several important studies on dendronized polymers [4c, 4d]. Schluter and coworkers explored the stiffening of polystyrene chains through the incorporation of Frechet-type dendrons as side chains [28, 29]. While the G-l and G-2 dendrons were not sufficiently bulky to effectively stiffen the polystyrene chain, the G-3 dendron provides enough steric bulk to force the hybrid polymer into adopting a cylindrical shape in solution [28b], In a complementary study, Neubert and Schluter demonstrated that adding charges to the dendritic wedges leads to an expansion of the chains of the hybrid copolymer in aqueous solution [29],... 

The accuracy of the averaged model truncated at order p9(q 0) thus depends on the truncation of the Taylor series as well as on the truncation of the perturbation expansion used in the local equation. The first error may be determined from the order pq 1 term in Eq. (23) and may be zero in many practical cases [e.g. linear or second-order kinetics, wall reaction case, or thermal and solutal dispersion problems in which / and rw(c) are linear in c] and the averaged equation may be closed exactly, i.e. higher order Frechet derivatives are zero and the Taylor expansion given by Eq. (23) terminates at some finite order (usually after the linear and quadratic terms in most applications). In such cases, the only error is the second error due to the perturbation expansion of the local equation. This error e for the local Eq. (20) truncated at 0(pq) may be expressed as... 

Boydston AJ, Holcombe TW, Unmh DA, Frechet JMJ, Gmbbs RH (2009) A direct route to cyclic organic nanostmctures via ring-expansion metathesis polymerization of a dendronized macromonomers. J Am Chem Soc 131 5388-5389... 

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