As the national buildings in each climate zone and passive low energy consumption building demonstration projects expand,there has been a wave of innovation across the construction industry.China is also becoming a ho...As the national buildings in each climate zone and passive low energy consumption building demonstration projects expand,there has been a wave of innovation across the construction industry.China is also becoming a hot zone for energy-efficient and high-performance passive buildings.Along with the traditional passive building structure,steel structure passive construction,assembled PC structure passive construction such as the emergence of various types of passive construction,as well as a variety of new building materials,doors and Windows,and air conditioning air equipment,put forward a new challenge for building electrical engineering design personnel and requirements.展开更多
Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions ...Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions of simple atypical modules in the restricted supermodule category for W(n)are precisely calculated in this paper,and thereby the dimensions of all simple modules can be precisely given.Moreover,the restricted supermodule category for W(n)is proved to have one block.展开更多
Let g be a restricted Lie superalgebra of Cartan type W(n),S(n)or H(n)over an alge-braically closed field k of prime characteristic p>3,in the sense of modular version of Kac's definition in 1977.In this note,w...Let g be a restricted Lie superalgebra of Cartan type W(n),S(n)or H(n)over an alge-braically closed field k of prime characteristic p>3,in the sense of modular version of Kac's definition in 1977.In this note,we show that the restricted representation category over g has only one block(reckoning parities in).This phenomenon is very diff erent from the case of characteristic zero.展开更多
An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical.Such a semi-reductive algebraic group naturally arises and also plays a key role in the stud...An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical.Such a semi-reductive algebraic group naturally arises and also plays a key role in the study of modular representations of non-classical finite-dimensional simple Lie algebras in positive characteristic,and some other cases.Let G be a connected semi-reductive algebraic group over an algebraically closed field F and g=Lie(G).It turns out that G has many same properties as reductive groups,such as the Bruhat decomposition.In this note,we obtain an analogue of classical Chevalley restriction theorem for g,which says that the G-invariant ring F[g]~G is a polynomial ring if g satisfies a certain“positivity”condition suited for lots of cases we are interested in.As applications,we further investigate the nilpotent cones and resolutions of singularities for semi-reductive Lie algebras.展开更多
Let (g, [p]) be a restricted Lie algebra over an algebraically closed field of characteristic p 〉 O. Then the inverse limits of "higher" reduced enveloping algebras {uxs (g) I s ∈ N} with X running over g* ma...Let (g, [p]) be a restricted Lie algebra over an algebraically closed field of characteristic p 〉 O. Then the inverse limits of "higher" reduced enveloping algebras {uxs (g) I s ∈ N} with X running over g* make representations of g split into different "blocks". In this paper, we study such an infinite- dimensional algebra Ax (g) :=lim Uxs (g) for a given X C g*. A module category equivalence is built between subcategories of U(g)-rnod and Ax(g)-mod. In the case of reductive Lie algebras, (quasi) generalized baby Verma modules and their properties are described. Furthermore, the dimensions of projective covers of simple modules with characters of standard Levi form in the generalized x-reduced module category are precisely determined, and a higher reciprocity in the case of regular nilpotent is obtained, generalizing the ordinary reciprocity.展开更多
Microglia can modulate spinal nociceptive transmission.Yet,their role in spinal cord stimulation(SCS)-induced pain inhibition is unclear.Here,we examined how SCS affects microglial activation in the lumbar cord of rat...Microglia can modulate spinal nociceptive transmission.Yet,their role in spinal cord stimulation(SCS)-induced pain inhibition is unclear.Here,we examined how SCS affects microglial activation in the lumbar cord of rats with chronic constriction injury(CCI)of the sciatic nerve.Male rats received conventional SCS(50 Hz,80%motor threshold,180 min,2 sessions/day)or sham stimulation on days 18-20 post-CCI.SCS transiently attenuated the mechanical hypersensitivity in the ipsilateral hind paw and increased OX-42 immunoreactivity in the bilateral dorsal horns.SCS also upregulated the mRNAs of Ml-like markers,but not M2-like markers.Inducible NOS protein expression was increased,but brain-derived neurotrophic factor was decreased after SCS.Intrathecal minocycline(1μg-100μg),which inhibits microglial activation,dosedependently attenuated the mechanical hypersensitivity.Pretreatment with low-dose minocycline(1μg,30 min)prolonged the SCS-induced pain inhibition.These findings suggest that conventional SCS may paradoxically increase spinal M1-like microglial activity and thereby compromise its own ability to inhibit pain.展开更多
Let k be an algebraically closed field of characteristic p 〉 2, and gl(m|n) be the general linear Lie superalgebra over k. The Cartan invariants for the restricted supermodule category for gl(m|n) are presented.
文摘As the national buildings in each climate zone and passive low energy consumption building demonstration projects expand,there has been a wave of innovation across the construction industry.China is also becoming a hot zone for energy-efficient and high-performance passive buildings.Along with the traditional passive building structure,steel structure passive construction,assembled PC structure passive construction such as the emergence of various types of passive construction,as well as a variety of new building materials,doors and Windows,and air conditioning air equipment,put forward a new challenge for building electrical engineering design personnel and requirements.
基金supported by the National Natural Science Foundation of China(Nos.11126062,11201293,11226327,11271130)the Innovation Program of Shanghai Municipal Education Commission(Nos.12ZZ038,13YZ077)
文摘Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions of simple atypical modules in the restricted supermodule category for W(n)are precisely calculated in this paper,and thereby the dimensions of all simple modules can be precisely given.Moreover,the restricted supermodule category for W(n)is proved to have one block.
基金supported by the National Natural Science Foundation of China(Grant Nos.1160111611671138 and 11771279)+3 种基金Shanghai Key Laboratory of PMMP(Grant No.13dz2260400)the Scientific Research Foundation of Hebei Education Department(Grant No.QN2017090)the Doctoral Foundation of Hebei Normal University(Grant No.L2016B02)We thank the referees for their helpful comments.
文摘Let g be a restricted Lie superalgebra of Cartan type W(n),S(n)or H(n)over an alge-braically closed field k of prime characteristic p>3,in the sense of modular version of Kac's definition in 1977.In this note,we show that the restricted representation category over g has only one block(reckoning parities in).This phenomenon is very diff erent from the case of characteristic zero.
基金Supported by NSFC(Grant Nos.12071136,11671138,11771279,12101544)Shanghai Key Laboratory of PMMP(Grant No.13dz2260400)the Fundamental Research Funds of Yunnan Province(Grant No.2020J0375)。
文摘An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical.Such a semi-reductive algebraic group naturally arises and also plays a key role in the study of modular representations of non-classical finite-dimensional simple Lie algebras in positive characteristic,and some other cases.Let G be a connected semi-reductive algebraic group over an algebraically closed field F and g=Lie(G).It turns out that G has many same properties as reductive groups,such as the Bruhat decomposition.In this note,we obtain an analogue of classical Chevalley restriction theorem for g,which says that the G-invariant ring F[g]~G is a polynomial ring if g satisfies a certain“positivity”condition suited for lots of cases we are interested in.As applications,we further investigate the nilpotent cones and resolutions of singularities for semi-reductive Lie algebras.
基金Supported by National Natural Science Foundation of China (Grant Nos. 11126062,11201293 and 11271130)the Innovation Program of Shanghai Municipal Education Commission (Grant Nos. 12ZZ038 and 13YZ077)
文摘Let (g, [p]) be a restricted Lie algebra over an algebraically closed field of characteristic p 〉 O. Then the inverse limits of "higher" reduced enveloping algebras {uxs (g) I s ∈ N} with X running over g* make representations of g split into different "blocks". In this paper, we study such an infinite- dimensional algebra Ax (g) :=lim Uxs (g) for a given X C g*. A module category equivalence is built between subcategories of U(g)-rnod and Ax(g)-mod. In the case of reductive Lie algebras, (quasi) generalized baby Verma modules and their properties are described. Furthermore, the dimensions of projective covers of simple modules with characters of standard Levi form in the generalized x-reduced module category are precisely determined, and a higher reciprocity in the case of regular nilpotent is obtained, generalizing the ordinary reciprocity.
基金the Neurosurgery Pain Research Institute at the Johns Hopkins University and subsidized by the National Institutes of Health(Bethesda,Maryland,USA)(NS 110598)supported by an award from the China Scholarship Council for Chinese PhD candidates to study abroad。
文摘Microglia can modulate spinal nociceptive transmission.Yet,their role in spinal cord stimulation(SCS)-induced pain inhibition is unclear.Here,we examined how SCS affects microglial activation in the lumbar cord of rats with chronic constriction injury(CCI)of the sciatic nerve.Male rats received conventional SCS(50 Hz,80%motor threshold,180 min,2 sessions/day)or sham stimulation on days 18-20 post-CCI.SCS transiently attenuated the mechanical hypersensitivity in the ipsilateral hind paw and increased OX-42 immunoreactivity in the bilateral dorsal horns.SCS also upregulated the mRNAs of Ml-like markers,but not M2-like markers.Inducible NOS protein expression was increased,but brain-derived neurotrophic factor was decreased after SCS.Intrathecal minocycline(1μg-100μg),which inhibits microglial activation,dosedependently attenuated the mechanical hypersensitivity.Pretreatment with low-dose minocycline(1μg,30 min)prolonged the SCS-induced pain inhibition.These findings suggest that conventional SCS may paradoxically increase spinal M1-like microglial activity and thereby compromise its own ability to inhibit pain.
基金Supported partially by National Natural Science Foundation of China(Grant Nos.11271130,11201293,111126062)The Innovation Program of Shanghai Municipal Education Commission(Grant No.12zz038)Shanghai Science Foundation for Excellent Young Scholars(Grant No.yyy10046)
文摘Let k be an algebraically closed field of characteristic p 〉 2, and gl(m|n) be the general linear Lie superalgebra over k. The Cartan invariants for the restricted supermodule category for gl(m|n) are presented.