We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.
The purpose of this review is to analyze the involvement of protein kinases in the cardioprotective mechanism induced by chronic hypoxia. It has been reported that chronic intermittent hypoxia contributes to increased expression of the following kinases in the myocardium: PKCδ, PKCα, p-PKCε, p-PKCα, AMPK, p-AMPK, CaMKII, p-ERK1/2, p-Akt, PI3-kinase, p-p38, HK-1, and HK-2; whereas, chronic normobaric hypoxia promotes increased expression of the following kinases in the myocardium: PKCε, PKCβII, PKCη, CaMKII, p-ERK1/2, p-Akt, p-p38, HK-1, and HK-2. However, CNH does not promote enhanced expression of the AMPK and JNK kinases. Adaptation to hypoxia enhances HK-2 association with mitochondria and causes translocation of PKCδ, PKCβII, and PKCη to the mitochondria. It has been shown that PKCδ, PKCε, ERK1/2, and MEK1/2 are involved in the cardioprotective effect of chronic hypoxia. The role of other kinases in the cardioprotective effect of adaptation to hypoxia requires further research.