L_(ν)operator is an important extrinsic differential operator of divergence type and has profound geometric settings.In this paper,we consider the clamped plate problem of L2νoperator on a bounded domain of the comp...L_(ν)operator is an important extrinsic differential operator of divergence type and has profound geometric settings.In this paper,we consider the clamped plate problem of L2νoperator on a bounded domain of the complete Riemannian manifolds.A general formula of eigenvalues of L_(ν)^(2)operator is established.Applying this general formula,we obtain some estimates for the eigenvalues with higher order on the complete Riemannian manifolds.As several fascinating applications,we discuss this eigenvalue problem on the complete translating solitons,minimal submanifolds on the Euclidean space,submanifolds on the unit sphere and projective spaces.In particular,we get a universal inequality with respect to the L_(II) operator on the translating solitons.Usually,it is very difficult to get universal inequalities for weighted Laplacian and even Laplacian on the complete Riemannian manifolds.Therefore,this work can be viewed as a new contribution to universal estimate.展开更多
This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the g...This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.展开更多
Chloroplasts overproduce reactive oxygen species(ROS)under unfavorable environmental conditions,and these ROS are implicated in both signaling and oxidative damage.There is mounting evidence for their roles in transla...Chloroplasts overproduce reactive oxygen species(ROS)under unfavorable environmental conditions,and these ROS are implicated in both signaling and oxidative damage.There is mounting evidence for their roles in translating environmental fluctuations into distinct physiological responses,but their targets,signaling cascades,and mutualism and antagonism with other stress signaling cascades and within ROS signaling remain poorly understood.Great efforts made in recent years have shed new light on chloroplast ROS-directed plant stress responses,from ROS perception to plant responses,in conditional mutants of Arabidopsis thaliana or under various stress conditions.Some articles have also reported the mechanisms underlying the complexity of ROS signaling pathways,with an emphasis on spatiotemporal regulation.ROS and oxidative modification of affected target proteins appear to induce retrograde signaling pathways to maintain chloroplast protein quality control and signaling at a whole-cell level using stress hormones.This review focuses on these seemingly interconnected chloroplast-to-nucleus retrograde signaling pathways initiated by ROS and ROS-modified target molecules.We also discuss future directions in chloroplast stress research to pave the way for discovering new signaling molecules and identifying intersectional signaling components that interact in multiple chloroplast signaling pathways.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11861036 and 11826213)the Natural Science Foundation of Jiangxi Province(Grant No.20224BAB201002)。
文摘L_(ν)operator is an important extrinsic differential operator of divergence type and has profound geometric settings.In this paper,we consider the clamped plate problem of L2νoperator on a bounded domain of the complete Riemannian manifolds.A general formula of eigenvalues of L_(ν)^(2)operator is established.Applying this general formula,we obtain some estimates for the eigenvalues with higher order on the complete Riemannian manifolds.As several fascinating applications,we discuss this eigenvalue problem on the complete translating solitons,minimal submanifolds on the Euclidean space,submanifolds on the unit sphere and projective spaces.In particular,we get a universal inequality with respect to the L_(II) operator on the translating solitons.Usually,it is very difficult to get universal inequalities for weighted Laplacian and even Laplacian on the complete Riemannian manifolds.Therefore,this work can be viewed as a new contribution to universal estimate.
基金This research is supported by the Natural Science Foundation of the Educational Committee of Jiang Su Province.
文摘This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.
基金Research in the Kim laboratory has been supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(grant XDB27040102)the 100-Talent Program of the Chinese Academy of Sciences,and the National Natural Science Foundation of China(grant 31871397 to C.K.).
文摘Chloroplasts overproduce reactive oxygen species(ROS)under unfavorable environmental conditions,and these ROS are implicated in both signaling and oxidative damage.There is mounting evidence for their roles in translating environmental fluctuations into distinct physiological responses,but their targets,signaling cascades,and mutualism and antagonism with other stress signaling cascades and within ROS signaling remain poorly understood.Great efforts made in recent years have shed new light on chloroplast ROS-directed plant stress responses,from ROS perception to plant responses,in conditional mutants of Arabidopsis thaliana or under various stress conditions.Some articles have also reported the mechanisms underlying the complexity of ROS signaling pathways,with an emphasis on spatiotemporal regulation.ROS and oxidative modification of affected target proteins appear to induce retrograde signaling pathways to maintain chloroplast protein quality control and signaling at a whole-cell level using stress hormones.This review focuses on these seemingly interconnected chloroplast-to-nucleus retrograde signaling pathways initiated by ROS and ROS-modified target molecules.We also discuss future directions in chloroplast stress research to pave the way for discovering new signaling molecules and identifying intersectional signaling components that interact in multiple chloroplast signaling pathways.
