a b s t r a c t N-Phthaloyl-chitosan O-prop-2-ynyl carbamate was prepared as a biopolymer amenable to undergo chemoselective conjugation by azide-alkyne coupling, while allowing upturn of chitosan's amines after dephthaloylation. N-phthaloylchitosan was prepared according to previously described methods and, due to its low solubility in current organic media, subsequent modifications were run in heterogeneous conditions. Activation of hydroxyls with carbonyl-1,1 -diimidazole and coupling to propargylamine yielded N-phthaloyl-chitosan O-prop-2-ynyl carbamate, then coupled to a model PEG-like azide by azide-alkyne coupling, giving the expected triazolyl conjugate. N-Dephthaloylation allowed recovery of the free amines, responsible for chitosan's bioadhesion and tissue-regeneration properties.The structures of all polymers were confirmed by Fourier-transformed infra-red (FT-IR) and X-ray photoelectron (XPS) spectroscopies, as well as by solid-state nuclear magnetic resonance (SSNMR). All chitosan derivatives were poorly soluble in both aqueous and organic media, which makes them suitable for topical applications or for removal of toxic substances from either the gastric intestinal tract or environmental sources.
Spin foam models are an approach to quantum gravity based on the concept of sum over states, which aims to describe quantum spacetime dynamics in a way that its parent framework, loop quantum gravity, has not as of yet succeeded. Since these models' relation to classical Einstein gravity is not explicit, an important test of their viabilitiy is the study of asymptotics -the classical theory should be obtained in a limit where quantum effects are negligible, taken to be the limit of large triangle areas in a triangulated manifold with boundary. In this paper we will briefly introduce the EPRL/FK spin foam model and known results about its asymptotics, proceeding then to describe a practical computation of spin foam and semiclassical geometric data for a simple triangulation with only one interior triangle. The results are used to comment on the "flatness problem" -a hypothesis raised by Bonzom (2009) suggesting that EPRL/FK's classical limit only describes flat geometries in vacuum. *
We show that, when an approximation used in this prior work is removed, the resulting improved calculation yields an alternative derivation, in the particular case studied, of the accidental curvature constraint of Hellmann and Kaminski. The result is at the same time extended to apply to almost all non-degenerate Regge-like boundary data and a broad class of face amplitudes. This resolves a tension in the literature.
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