In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especi...In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especially, we discuss the existence of locally linear pseudofree C9 action on this kind of 4-manifolds.展开更多
Let N be a closed,orientable 4-manifold satisfying H<sub>1</sub>（N,Z）=0,and M be a closed,connected,nonorientable surface embedded in N with normal bundle v.The Euler class e（v）ofv is an element of H&l...Let N be a closed,orientable 4-manifold satisfying H<sub>1</sub>（N,Z）=0,and M be a closed,connected,nonorientable surface embedded in N with normal bundle v.The Euler class e（v）ofv is an element of H<sub>2</sub>（M,（?））,where （?） denotes the twisted integer coefficients determined byw<sub>1</sub>（v）=w<sub>1</sub>（M）.We study the possible values of e（v）[M],and prove H<sub>1</sub>（N-M）=Z<sub>2</sub> or 0.Underthe condition of H<sub>1</sub>（N-M,Z）=Z<sub>2</sub>,we conclude that e（v）[M]can only take the followingvalues:2σ（N）-2（n+β<sub>2</sub>）,2σ（N）-2（n+β<sub>2</sub>-2）,2σ（N）-2（n+β<sub>2</sub>-4）,…,2σ（N）+2（n+β<sub>2</sub>）,where σ（N） is the usual index of N,n the nonorientable genus of M and β<sub>2</sub> the 2nd real Bettinumber.Finally,we show that these values can be actually attained by appropriate embeddingfor N=homological sphere.In the case of N=S<sup>4</sup>.this is just the well-known Whitney conjectureproved by W.S.Massey in 1969.展开更多
Let N be a closed, nonorientable surface, M be a simply connected 4-manifold. f: N→M is an embedding with normal bundle v<sub>f</sub>. The normal Euler class e（v<sub>f</sub>） of f is an elem...Let N be a closed, nonorientable surface, M be a simply connected 4-manifold. f: N→M is an embedding with normal bundle v<sub>f</sub>. The normal Euler class e（v<sub>f</sub>） of f is an element in H<sup>2</sup>（N,）, where is the local coefficient determined by w<sub>1</sub>（v<sub>f</sub>） =w<sub>1</sub>（N）. It is very important to determine e（v<sub>f</sub>）[N] for all embeddings. This problem is closely related to whether a two-dimensional homology class can be represented by a smooth embedded sphere. In this note, we determine all the possible normal Euler numbers of embedding real projective plane into indefinite 4-manifolds.展开更多
A foundamental problem in 4-dimensional differential topology iS to find a surface with minimal genus that can represent a given two-dimensional homology class. Hsiang, Rohlin have got some results about the homologic...A foundamental problem in 4-dimensional differential topology iS to find a surface with minimal genus that can represent a given two-dimensional homology class. Hsiang, Rohlin have got some results about the homological l-connected manifolds. This note will discuss this problem under the condition that H<sub>1</sub>（N<sup>4</sup>） is finite. Under this assumption, the possible normal Euler numbers of embedding nonorientable surfaces in 4-manifolds are also determined.展开更多
Letπ=π_(1)(M)for a compact 3-manifold M,andχ_(4),p and q^(*)be the invariants of Hausmann and Weinberger(1985),Kotschick(1994)and Hillman(2002),respectively.For a certain class of compact 3-manifolds M,including al...Letπ=π_(1)(M)for a compact 3-manifold M,andχ_(4),p and q^(*)be the invariants of Hausmann and Weinberger(1985),Kotschick(1994)and Hillman(2002),respectively.For a certain class of compact 3-manifolds M,including all those not containing two-sided RP2’s,we determineχ_(4)(π).We address when p(π)equalsχ_(4)(π)and when q^(*)(π)equalsχ_(4)(π),and answer a question raised by Hillman(2002).展开更多
Parkinson's disease is primarily caused by the loss of dopaminergic neurons in the substantia nigra compacta.Ferroptosis,a novel form of regulated cell death characterized by iron accumulation and lipid peroxidati...Parkinson's disease is primarily caused by the loss of dopaminergic neurons in the substantia nigra compacta.Ferroptosis,a novel form of regulated cell death characterized by iron accumulation and lipid peroxidation,plays a vital role in the death of dopaminergic neurons.However,the molecular mechanisms underlying ferroptosis in dopaminergic neurons have not yet been completely elucidated.NADPH oxidase 4 is related to oxidative stress,however,whether it regulates dopaminergic neuronal ferroptosis remains unknown.The aim of this study was to determine whether NADPH oxidase 4 is involved in dopaminergic neuronal ferroptosis,and if so,by what mechanism.We found that the transcriptional regulator activating transcription factor 3 increased NADPH oxidase 4 expression in dopaminergic neurons and astrocytes in an 1-methyl-4-phenyl-1,2,3,6 tetrahydropyridine-induced Parkinson's disease model.NADPH oxidase 4 inhibition improved the behavioral impairments observed in the Parkinson's disease model animals and reduced the death of dopaminergic neurons.Moreover,NADPH oxidase 4 inhibition reduced lipid peroxidation and iron accumulation in the substantia nigra of the Parkinson's disease model animals.Mechanistically,we found that NADPH oxidase 4 interacted with activated protein kinase Cαto prevent ferroptosis of dopaminergic neurons.Furthermore,by lowering the astrocytic lipocalin-2 expression,NADPH oxidase 4 inhibition reduced 1-methyl-4-phenyl-1,2,3,6 tetrahydropyridine-induced neuroinflammation.These findings demonstrate that NADPH oxidase 4 promotes ferroptosis of dopaminergic neurons and neuroinflammation,which contribute to dopaminergic neuron death,suggesting that NADPH oxidase 4 is a possible therapeutic target for Parkinson's disease.展开更多
Multiple sclerosis(MS)is the most common chronic disease of the central nervous system(CNS)in young adults and represents the first cause of severe handicap,originally non-traumatic(Oh et al.,2018).MS is chara cterize...Multiple sclerosis(MS)is the most common chronic disease of the central nervous system(CNS)in young adults and represents the first cause of severe handicap,originally non-traumatic(Oh et al.,2018).MS is chara cterized by the infiltration of auto reactive lymphocytes specific to myelin through the blood-brain barrier,which results in the appearance of inflammatory demyelinating lesions caused by the death of the central nervous system myelinating cells,oligodendrocytes(Oh et al.,2018).There is a prevalence sexual with a ratio of three times more affected women than men.展开更多
Geometry optimization of p-C_(6)H_(4)-connected cyclo[20]carbon(p-C_(6)H_(4)-C_(20))was carried out at M062X/6-311G(d,p)level,three kinds of bond orders(Mayer,Laplacian,and Wiberg),electron-hole distributions,localize...Geometry optimization of p-C_(6)H_(4)-connected cyclo[20]carbon(p-C_(6)H_(4)-C_(20))was carried out at M062X/6-311G(d,p)level,three kinds of bond orders(Mayer,Laplacian,and Wiberg),electron-hole distributions,localized orbital locators(LOL),and infrared(IR)spectrum were also performed at the same level.Based on TD-DFT M062X/6-311G(d,p)method,the first 20 excited states and ultraviolet(UV)spectra of p-C_(6)H_(4)-C_(20) were calculated.Calculation results of π-electron delocalization analyses prove thatπ-electron delocalization of p-C_(6)H_(4)-C_(20) is more likely to occur on shorter C-C bonds rather than longer C-C bonds,and inside/outside of the ring plane rather than above/below the ring plane.Two absorption peaks of p-C_(6)H_(4)-C_(20) locate at about 319 nm and 236 nm,respectively.展开更多
基金The Science and Technology Program(20110035) of Shanghai Maritime University
文摘In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especially, we discuss the existence of locally linear pseudofree C9 action on this kind of 4-manifolds.
文摘Let N be a closed,orientable 4-manifold satisfying H<sub>1</sub>（N,Z）=0,and M be a closed,connected,nonorientable surface embedded in N with normal bundle v.The Euler class e（v）ofv is an element of H<sub>2</sub>（M,（?））,where （?） denotes the twisted integer coefficients determined byw<sub>1</sub>（v）=w<sub>1</sub>（M）.We study the possible values of e（v）[M],and prove H<sub>1</sub>（N-M）=Z<sub>2</sub> or 0.Underthe condition of H<sub>1</sub>（N-M,Z）=Z<sub>2</sub>,we conclude that e（v）[M]can only take the followingvalues:2σ（N）-2（n+β<sub>2</sub>）,2σ（N）-2（n+β<sub>2</sub>-2）,2σ（N）-2（n+β<sub>2</sub>-4）,…,2σ（N）+2（n+β<sub>2</sub>）,where σ（N） is the usual index of N,n the nonorientable genus of M and β<sub>2</sub> the 2nd real Bettinumber.Finally,we show that these values can be actually attained by appropriate embeddingfor N=homological sphere.In the case of N=S<sup>4</sup>.this is just the well-known Whitney conjectureproved by W.S.Massey in 1969.
文摘Let N be a closed, nonorientable surface, M be a simply connected 4-manifold. f: N→M is an embedding with normal bundle v<sub>f</sub>. The normal Euler class e（v<sub>f</sub>） of f is an element in H<sup>2</sup>（N,）, where is the local coefficient determined by w<sub>1</sub>（v<sub>f</sub>） =w<sub>1</sub>（N）. It is very important to determine e（v<sub>f</sub>）[N] for all embeddings. This problem is closely related to whether a two-dimensional homology class can be represented by a smooth embedded sphere. In this note, we determine all the possible normal Euler numbers of embedding real projective plane into indefinite 4-manifolds.
基金the National Natural Science Foundation of China.
文摘A foundamental problem in 4-dimensional differential topology iS to find a surface with minimal genus that can represent a given two-dimensional homology class. Hsiang, Rohlin have got some results about the homological l-connected manifolds. This note will discuss this problem under the condition that H<sub>1</sub>（N<sup>4</sup>） is finite. Under this assumption, the possible normal Euler numbers of embedding nonorientable surfaces in 4-manifolds are also determined.
基金supported by Simons Collaborations in Mathematics and the Physical Sciences(Grant No.615229).
文摘Letπ=π_(1)(M)for a compact 3-manifold M,andχ_(4),p and q^(*)be the invariants of Hausmann and Weinberger(1985),Kotschick(1994)and Hillman(2002),respectively.For a certain class of compact 3-manifolds M,including all those not containing two-sided RP2’s,we determineχ_(4)(π).We address when p(π)equalsχ_(4)(π)and when q^(*)(π)equalsχ_(4)(π),and answer a question raised by Hillman(2002).
基金supported by the National Natural Science Foundation of China,Nos.82271444(to JP),82271268(to BZ),and 82001346(to YL)the National Key Research and Development Program of China,No.2022YFE0210100(to BZ)。
文摘Parkinson's disease is primarily caused by the loss of dopaminergic neurons in the substantia nigra compacta.Ferroptosis,a novel form of regulated cell death characterized by iron accumulation and lipid peroxidation,plays a vital role in the death of dopaminergic neurons.However,the molecular mechanisms underlying ferroptosis in dopaminergic neurons have not yet been completely elucidated.NADPH oxidase 4 is related to oxidative stress,however,whether it regulates dopaminergic neuronal ferroptosis remains unknown.The aim of this study was to determine whether NADPH oxidase 4 is involved in dopaminergic neuronal ferroptosis,and if so,by what mechanism.We found that the transcriptional regulator activating transcription factor 3 increased NADPH oxidase 4 expression in dopaminergic neurons and astrocytes in an 1-methyl-4-phenyl-1,2,3,6 tetrahydropyridine-induced Parkinson's disease model.NADPH oxidase 4 inhibition improved the behavioral impairments observed in the Parkinson's disease model animals and reduced the death of dopaminergic neurons.Moreover,NADPH oxidase 4 inhibition reduced lipid peroxidation and iron accumulation in the substantia nigra of the Parkinson's disease model animals.Mechanistically,we found that NADPH oxidase 4 interacted with activated protein kinase Cαto prevent ferroptosis of dopaminergic neurons.Furthermore,by lowering the astrocytic lipocalin-2 expression,NADPH oxidase 4 inhibition reduced 1-methyl-4-phenyl-1,2,3,6 tetrahydropyridine-induced neuroinflammation.These findings demonstrate that NADPH oxidase 4 promotes ferroptosis of dopaminergic neurons and neuroinflammation,which contribute to dopaminergic neuron death,suggesting that NADPH oxidase 4 is a possible therapeutic target for Parkinson's disease.
基金supported by a grant from the French Multiple Sclerosis Society(ARSEP,Grant Number:R20163LL)(to AMG)。
文摘Multiple sclerosis(MS)is the most common chronic disease of the central nervous system(CNS)in young adults and represents the first cause of severe handicap,originally non-traumatic(Oh et al.,2018).MS is chara cterized by the infiltration of auto reactive lymphocytes specific to myelin through the blood-brain barrier,which results in the appearance of inflammatory demyelinating lesions caused by the death of the central nervous system myelinating cells,oligodendrocytes(Oh et al.,2018).There is a prevalence sexual with a ratio of three times more affected women than men.
文摘Geometry optimization of p-C_(6)H_(4)-connected cyclo[20]carbon(p-C_(6)H_(4)-C_(20))was carried out at M062X/6-311G(d,p)level,three kinds of bond orders(Mayer,Laplacian,and Wiberg),electron-hole distributions,localized orbital locators(LOL),and infrared(IR)spectrum were also performed at the same level.Based on TD-DFT M062X/6-311G(d,p)method,the first 20 excited states and ultraviolet(UV)spectra of p-C_(6)H_(4)-C_(20) were calculated.Calculation results of π-electron delocalization analyses prove thatπ-electron delocalization of p-C_(6)H_(4)-C_(20) is more likely to occur on shorter C-C bonds rather than longer C-C bonds,and inside/outside of the ring plane rather than above/below the ring plane.Two absorption peaks of p-C_(6)H_(4)-C_(20) locate at about 319 nm and 236 nm,respectively.
