A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z_(2)-graded algebra E(θ),which corresponds to a noncommutative quadric hypersurface E^(!)/(z)for some central regular element z∈E_(2)^(...A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z_(2)-graded algebra E(θ),which corresponds to a noncommutative quadric hypersurface E^(!)/(z)for some central regular element z∈E_(2)^(!).It turns out that the bounded derived category D^(b)(gr_(Z_(2))E(θ))is equivalent to the stable category of the maximal Cohen-Macaulay modules over E^(!)/(z)provided that E!is noetherian.As a consequence,E^(!)/(z)is a noncommutative isolated singularity if and only if the corresponding Clifford deformation E(θ)is a semisimple Z_(2)-graded algebra.The preceding equivalence of triangulated categories also indicates that Clifford deformations of trivial extensions of a Koszul Frobenius algebra are related to Knörrer's periodicity theorem for quadric hypersurfaces.As an application,we recover Knörrer's periodicity theorem without using matrix factorizations.展开更多
Scale effect is one of the important aspects in the macro mechanical parame- ters’ research of rock mass, from a new point of view, by means of lab and field rock me- chanics test, establishment of E^Vp relation, cla...Scale effect is one of the important aspects in the macro mechanical parame- ters’ research of rock mass, from a new point of view, by means of lab and field rock me- chanics test, establishment of E^Vp relation, classification of engineering rock mass, nu- merical simulation test and back analysis based on surrounding rock’s displacement monitoring results of Shuibuya Project’s underground power station, rock mass deforma- tion module’s size effect of surrounding rock of Shuibuya Project’s undegroud power sta- tion was studied. It’s shown that rock mass deformation module’s scale effect of sur- rounding rock of Shuibuya Project’s undeground power station is obvious, the rock mass deformation module to tranquilization is 20% of intact rock’s. Finally the relation between rock mass deformation modules and the scale of research was established.展开更多
基金supported by ZJNSF(LY19A010011)NSFC(11971141,12371017)supported by NSFC(11971449,12131015,12371042).
文摘A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z_(2)-graded algebra E(θ),which corresponds to a noncommutative quadric hypersurface E^(!)/(z)for some central regular element z∈E_(2)^(!).It turns out that the bounded derived category D^(b)(gr_(Z_(2))E(θ))is equivalent to the stable category of the maximal Cohen-Macaulay modules over E^(!)/(z)provided that E!is noetherian.As a consequence,E^(!)/(z)is a noncommutative isolated singularity if and only if the corresponding Clifford deformation E(θ)is a semisimple Z_(2)-graded algebra.The preceding equivalence of triangulated categories also indicates that Clifford deformations of trivial extensions of a Koszul Frobenius algebra are related to Knörrer's periodicity theorem for quadric hypersurfaces.As an application,we recover Knörrer's periodicity theorem without using matrix factorizations.
文摘Scale effect is one of the important aspects in the macro mechanical parame- ters’ research of rock mass, from a new point of view, by means of lab and field rock me- chanics test, establishment of E^Vp relation, classification of engineering rock mass, nu- merical simulation test and back analysis based on surrounding rock’s displacement monitoring results of Shuibuya Project’s underground power station, rock mass deforma- tion module’s size effect of surrounding rock of Shuibuya Project’s undegroud power sta- tion was studied. It’s shown that rock mass deformation module’s scale effect of sur- rounding rock of Shuibuya Project’s undeground power station is obvious, the rock mass deformation module to tranquilization is 20% of intact rock’s. Finally the relation between rock mass deformation modules and the scale of research was established.
