In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles ...In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.展开更多
A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorph...A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorphism and δ an α- derivation of a ring R. We prove that （1） If R is an （α, δ）-compatible and weakly 2-primal ring, then R[x; α, δ] is weakly semicommutative; （2） If R is （α, δ）-compatible, then R is weakly 2-primal if and only if R[x; α, δ] is weakly 2-primal.展开更多
Leaf veins play an important role in plant growth and development,and the bundle sheath(BS)is believed to greatly improve the photosynthetic efficiency of C_(4) plants.The OBV mutation in tomato(Solanum lycopersicum)r...Leaf veins play an important role in plant growth and development,and the bundle sheath(BS)is believed to greatly improve the photosynthetic efficiency of C_(4) plants.The OBV mutation in tomato(Solanum lycopersicum)results in dark veins and has been used widely in processing tomato varieties.However,physiological performance has difficulty explaining fitness in production.In this study,we confirmed that this mutation was caused by both the increased chlorophyll content and the absence of bundle sheath extension(BSE)in the veins.Using genome-wide association analysis and map-based cloning,we revealed that OBV encoded a C_(2)H_(2) L domain class transcription factor.It was localized in the nucleus and presented cell type-specific gene expression in the leaf veins.Furthermore,we verified the gene function by generating CRISPR/Cas9 knockout and overexpression mutants of the tomato gene.RNA sequencing analysis revealed that OBV was involved in regulating chloroplast development and photosynthesis,which greatly supported the change in chlorophyll content by mutation.Taken together,these findings demonstrated that OBV affected the growth and development of tomato by regulating chloroplast development in leaf veins.This study also provides a solid foundation to further decipher the mechanism of BSEs and to understand the evolution of photosynthesis in land plants.展开更多
We deal with the (2 + 1)-extension of classical Boussinesq system,which can reduce to several meaningful(1 + 1)-dimensional systems.By studying its Lax pair,we put forward invariances of Lax pair at first,then a recur...We deal with the (2 + 1)-extension of classical Boussinesq system,which can reduce to several meaningful(1 + 1)-dimensional systems.By studying its Lax pair,we put forward invariances of Lax pair at first,then a recursionformula depending on an arbitrary function is derived.At last,some solutions of the (2 + 1)-extension of classicalBoussinesq system are digged out by using the formula.展开更多
In this article, we study the (2+1)-extension of Burgers equation and the KP equation. At first, based on a known Backlund transformation and corresponding Lax pair, an invariance which depends on two arbitrary functi...In this article, we study the (2+1)-extension of Burgers equation and the KP equation. At first, based on a known Backlund transformation and corresponding Lax pair, an invariance which depends on two arbitrary functions for (2+1)-extension of Burgers equation is worked out. Given a known solution and using the invariance, we can find solutions of the (2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgers equation which cannot be directly obtained by constraining the invariance of the (2+ 1)-extension of Burgers equation.Furthermore, we reveal that the invariance for finding the solutions of Burgers equation can help us find the solutions of KP equation. At last, based on the invariance of Burgers equation, the corresponding recursion formulae for finding solutions of KP equation are digged out. As the application of our theory, some examples have been put forward in this article and some solutions of the (2+ 1)-extension of Burgers equation, Burgers equation and KP equation are obtained.展开更多
基金the National Natural Science Foundation of China(11688101 and 11431013)the National Natural Science Foundation of China(12022110,11201347 and 11671306).
文摘In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.
基金The NSF(11071097,11101217)of Chinathe NSF(BK20141476)of Jiangsu Province
文摘A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorphism and δ an α- derivation of a ring R. We prove that （1） If R is an （α, δ）-compatible and weakly 2-primal ring, then R[x; α, δ] is weakly semicommutative; （2） If R is （α, δ）-compatible, then R is weakly 2-primal if and only if R[x; α, δ] is weakly 2-primal.
基金This research was supported by The National Key Research and Development Program of China(Grant No.2019YFD1000301)the Fundamental Research Funds for Central Nonprofit Scientific Institution(Grant No.IVF-BRF2018006)+1 种基金the Key Laboratory of Biology and Genetic Improvement of Horticultural Crops,Ministry of Agriculture,Chinathe Science and Technology Innovation Program of the Chinese Academy of Agricultural Sciences(Grant No.CAAS-ASTIP-IVFCAAS).
文摘Leaf veins play an important role in plant growth and development,and the bundle sheath(BS)is believed to greatly improve the photosynthetic efficiency of C_(4) plants.The OBV mutation in tomato(Solanum lycopersicum)results in dark veins and has been used widely in processing tomato varieties.However,physiological performance has difficulty explaining fitness in production.In this study,we confirmed that this mutation was caused by both the increased chlorophyll content and the absence of bundle sheath extension(BSE)in the veins.Using genome-wide association analysis and map-based cloning,we revealed that OBV encoded a C_(2)H_(2) L domain class transcription factor.It was localized in the nucleus and presented cell type-specific gene expression in the leaf veins.Furthermore,we verified the gene function by generating CRISPR/Cas9 knockout and overexpression mutants of the tomato gene.RNA sequencing analysis revealed that OBV was involved in regulating chloroplast development and photosynthesis,which greatly supported the change in chlorophyll content by mutation.Taken together,these findings demonstrated that OBV affected the growth and development of tomato by regulating chloroplast development in leaf veins.This study also provides a solid foundation to further decipher the mechanism of BSEs and to understand the evolution of photosynthesis in land plants.
文摘We deal with the (2 + 1)-extension of classical Boussinesq system,which can reduce to several meaningful(1 + 1)-dimensional systems.By studying its Lax pair,we put forward invariances of Lax pair at first,then a recursionformula depending on an arbitrary function is derived.At last,some solutions of the (2 + 1)-extension of classicalBoussinesq system are digged out by using the formula.
文摘In this article, we study the (2+1)-extension of Burgers equation and the KP equation. At first, based on a known Backlund transformation and corresponding Lax pair, an invariance which depends on two arbitrary functions for (2+1)-extension of Burgers equation is worked out. Given a known solution and using the invariance, we can find solutions of the (2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgers equation which cannot be directly obtained by constraining the invariance of the (2+ 1)-extension of Burgers equation.Furthermore, we reveal that the invariance for finding the solutions of Burgers equation can help us find the solutions of KP equation. At last, based on the invariance of Burgers equation, the corresponding recursion formulae for finding solutions of KP equation are digged out. As the application of our theory, some examples have been put forward in this article and some solutions of the (2+ 1)-extension of Burgers equation, Burgers equation and KP equation are obtained.
