For any ordinal $\lambda $ of uncountable cofinality, a $\lambda $-tree is a tree $T$ of height $\lambda $ such that $|T_{\alpha }|<{\rm cf}(\lambda )$ for each $\alpha <\lambda $, where $T_{\alpha }=\{x\in T\colon {\rm ht}(x)=\alpha \}$. In this note we get a Pressing Down Lemma for $\lambda $-trees and discuss some of its applications. We show that if $\eta $ is an uncountable ordinal and $T$ is a Hausdorff tree of height $\eta $ such that $|T_{\alpha }|\leq \omega $ for each $\alpha <\eta $, then the tree $T$ is collectionwise Hausdorff if and only if for each antichain $C\subset T$ and for each limit ordinal $\alpha \leq \eta $ with ${\rm cf}(\alpha )>\omega $, $\{{\rm ht}(c)\colon c\in C\} \cap \alpha $ is not stationary in $\alpha $. In the last part of this note, we investigate some properties of $\kappa $-trees, $\kappa $-Suslin trees and almost $\kappa $-Suslin trees, where $\kappa $ is an uncountable regular cardinal.
Obstructive sleep apnea (OSA) has been demonstrated to be
implicated in disorder of insulin secretion and diabetes mellitus.
In this study, we aimed to evaluate the protective role of tempol,
a powerful antioxidant, in chronic intermittent hypoxia
(IH)-induced pancreatic injury. The rat model of OSA was
established by IH exposure. The pathological changes, increased
blood-glucose level, and raised proinsulin/insulin ratio in
pancreatic tissues of rats received IH were effectively relieved
by tempol delivery. In addition, the enhanced levels of
pro-inflammatory cytokines, TNF-α, IL-1β, IL-6, and inflammatory
mediators, PGE2, cyclooxygenase-2 (COX-2), NO, and inducible
nitric oxide synthase (iNOS) in pancreatic tissue were suppressed
by tempol. Moreover, tempol inhibited IH-induced apoptosis in
pancreatic tissue as evidenced by upregulated Bcl-2 level, and
downregulated Bax and cleaved caspase-3 levels. Finally, the
abnormal activation of mitogen-activated protein kinase (MAPK)
and nuclear factor kappa-light-chain-enhancer of activated B cells
(NF-κB) signaling pathways induced by IH was restrained by
tempol administration. In summary, our study demonstrates that
tempol relieves IH-induced pancreatic injury by inhibiting
inflammatory response and apoptosis, which provides theoretical
basis for tempol as an effective treatment for OSA-induced
pancreatic injury.