A fundamental theorem of Wolfe isometrically identifies the space of flat differential forms of dimension m in Rn with the space of flat m-cochains, that is, the dual space of flat chains of dimension m in Rn.
Chains of dimension k that have null boundary (i.e. chain in Z k := { c ∈ C k ; ∂ k (c ) = 0}) are called cycles (Z for Zykel, cycle in German) and k -chains that are the boundary of a k + 1 -chain (i.e. chains in B k := { b ∈ C k ; ∃ c ∈ C k + 1, b = ∂ k + 1(c )}) are called boundaries.
Predictions of the scaling theory were thus confirmed with additional detailed information on the state of confined chains in each regime of characteristic φ dependence of chain dimensions.
There is no contraction of chain dimensions in blends of linear and branched polyethylene chains.
Longitudinal studies in different populations are needed to disentangle the cause and effect chain between different dimensions of optimism and health-related behaviours.
This suggests that the hydrogen abstraction of S· depends on the chain dimension of unentangled polymer.
In view of the fact that the chain dimension of a long-branched polymer decreases with increasing branch density at the same molecular weight, the present results were consistently explicable.
It has been found by SEC-MALS that the chain dimension of the knotted ring polymers is evidently smaller than those of linear and the trivial ring polymer, while knotted polymer molecules have the same absolute molecular weight as the corresponding counterparts.
By comparison, the single chain dimension of the unsulfonated polystyrene at infinite dilution is 130Åin xylene.
The supply chain dimension of an EM is largely neglected and poorly managed, while basic logistics operation is currently hampering turnover and revenues.
Chain dimension of polystyrenes diluted with low molecular-weight homologues in semi-dilute solutions was investigated, referring to the results for solutions in benzene and styrene monomer, and its concentration dependence was clarified by small-angle neutron scattering (SANS) with a "contrast-matching" method.
