A Geometric Model for Odd Differential K-theory

Odd $K$-theory has the interesting property that it admits an infinite number of inequivalent differential refinements. In this paper we provide a bundle theoretic model for odd differential $K$-theory using the caloron correspondence and prove that this refinement is unique up to a unique natural isomorphism. We characterise the odd Chern character and its transgression form in terms of a connection and Higgs field and discuss some applications. Our model can be seen as the odd counterpart to the Simons-Sullivan construction of even differential $K$-theory. We use this model to prove a conjecture of Tradler-Wilson-Zeinalian regarding a related differential extension of odd $K$-theoryComment: 36 page

Purification of prostaglandin E2-9-oxoreductase from human decidua vera

AbstractProstaglandin E2-9-oxoreductase (PGE2-9-OR), the enzyme which converts prostaglandin E2 (PGE2) to prostaglandin F2α (PGF2α), has been detected in human decidua vera. A 105-fold purification was achieved when the centrifuged homogenate was fractionated sequentially by DEAE—Trisacryl, hydroxyapatite—agarose gel, ultrogel AcA 44 and Matrex gel blue A gel chromatographies. The following kinetic constants for PGE2-9-OR have been obtained. The equilibrium constant with respect to PGE2 is 83 μM, the Michaelis constant, Km, for PGE2 is 80 μM, for NADPH 1.6 μM. The maximal velocity for the forward reaction is V1 = .203 pmol/min. The enzyme was inhibited by progesterone, oestradiol-17β, cortisol and pharmaceutical drugs. An activating effect could be demonstrated with Ca2+ and oxytocin. The occurrence of PGE2-9-OR in the decidua vera suggests that this enzyme may be responsible for the transformation of PGE2 to PGF2α in these tissues. This may be an important mechanism for the initiation and maintenance of uterine contractions