Lactic acid fermentation of green coffee beans is a new strategy for coffee flavor modulation, creating novel aroma characteristics. © 2018 Society of Chemical Industry.

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In this paper, motivated by the works of Bakry et. al in finding sharp Li-Yau type gradient estimate for positive solutions of the heat equation on complete Riemannian manifolds with nonzero Ricci curvature lower bound, we first introduce a general form of Li-Yau type gradient estimate and show that the validity of such an estimate for any positive solutions of the heat equation reduces to the validity of the estimate for the heat kernel of the Riemannian manifold. Then, a sharp Li-Yau type gradient estimate on the three dimensional hyperbolic space is obtained by using the explicit expression of the heat kernel and some optimal Li-Yau type gradient estimates on general hyperbolic spaces are obtained.2010 Mathematics Subject Classification. Primary 35K05; Secondary 53C44.

Celluclast pretreatment of PK followed by roasting may be a promising new way of improving PKO aroma. © 2017 Society of Chemical Industry.

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