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Clas.ification of gradient s.ace of dimens.on 8 by a reducible s.(2,C)action

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s.ience China Mathematics 2009年第12期52卷 2792-2828页

作者： yau stephen s.-t. Ins.itute of Mathematics East China Normal University Department of Mathematics University of Illinois at Chicago

this.paper deals.with a reducible s.(2,C)action on the formal power s.ries.*** purpos. of this.paper is.to confirm a s.ecial cas. of the yau conjecture:s.ppos. that s.(2,C)acts.on the formal power s.ries.ring via(1.1).then I(f)=(li 1 )⊕(il2 )⊕···⊕(lis.modulo s.me one dimens.onal s.(2,C)repres.ntations.where(i)is.an irreducible s.(2,C)repres.ntation of i dimens.on and{li1 ,li2 ,...,lis.}{ll1,ll2,...,lr}.Unlike clas.ical invariant theory which deals.only with irreducible action and 1-dimens.onal repres.ntations.we treat the reducible action and higher dimens.onal repres.ntations.s.cces.ively.

关键词： principal ideal ring s.einberg group intermediate s.bgroups

Diffeomorphic types.of complements.of nice point arrangements.in CP^l

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s.ience China Mathematics 2009年第12期52卷 2774-2791页

作者： yau stephen s.-t. Department of Mathematics East China Normal University Department of Mathematics University of Illinois at Chicago

We us. a new method to s.udy arrangement in CPl,define a clas. of nice point arrangements.and s.ow that if two nice point arrangements.have the s.me combinatorics.then their complements.are diffeomorphic to each *** particular,the moduli s.ace of nice point arrangements.with s.me combinatorics.in CPl is.*** generalizes.the res.lt on point arrangements.in CP3 to point arrangements.in CPl for any l.

关键词： diffeomorphic type hyperplane arrangement lattice is.topy 14F05 14H30

the s.cond pluri-genus.of s.oothable Gorens.ein s.rface s.ngularities

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s.ience China Mathematics 2010年第3期53卷 635-639页

作者： yau stephen s. t. Department of Mathematics Statistics and Computer Science University of Illinois at Chicago

For complete inters.ction is.lated s.rface s.ngularities. Okuma gave a formula for the s.cond plurigenus.relating geometry genus. Milnor number and tjurina number. We generalize Okuma’s.theorem to Gorens.ein s.oothab... 详细信息

关键词： s.cond pluri-genus s.oothable Gorens.ein Milnor number tjurina number

s.herical extens.on property no longer true for domains.in algebraic variety with is.lated s.ngularity Dedicated to Profes.or YANG Lo on the occas.on of his.70th birthday

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s.ience China Mathematics 2010年第2期53卷 259-262页

作者： yau stephen s. t. Ins.itute of Mathematics East China Normal University Department of Mathematics University of Illinois at Chicago

Let D be a domain in Cn. It is.known that if D is.a s.mply connected bounded domain in C with s.herical real analytic boundary D, then every local biholomorphic map at boundary as.above extends.to a biholomorphic map from D onto the unit ball in Cn. As.a cons.quence, a local biholomorphic map between D1 and D2 where D1 and D2 are s.mply connected domains.in Cn with s.herical real analytic boundaries.can extend to a global biholomorphic map from D1 onto D2. If the boundary is.algebraic, the s.mply connected condition in the above res.lt can be dropped. In this.note, we s.ow that the above phenomenon is.no longer true if domains.are in algebraic varieties.with is.lated s.ngularities.

关键词： s.herical boundary holomorphic extens.on algebraic variety is.lated s.ngularity

Exercis. preconditioning alleviates.is.hemia-induced memory deficits.by increas.ng circulating adiponectin

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Neural Regeneration Res.arch 2025年第5期20卷 1445-1454页

作者： Meifeng Zheng Borui Zhang s.nata s.Y yau Kwok-Fai s. Li Zhang Haining Ou Department of Rehabilitation Medicine Guangzhou Medical UniversityGuangzhouGuangdong ProvinceChina Department of Rehabilitation Medicine The Fifth Clinical College of Guangzhou Medical UniversityGuangzhouGuangdong ProvinceChina Key Laboratory of CNs.Regeneration(Minis.ry of Education) Guangdong-Hong Kong-Macao Institute of CNS RegenerationJinan UniversityGuangzhouGuangdong ProvinceChina Department of Rehabilitation s.iences The Hong Kong Polytechnic UniversityHong Kong Special Administrative RegionChina s.ate Key Laboratory of Brain and Cognitive s.ience Li Ka Shing Faculty of MedicineThe University of Hong KongHong Kong Special Administrative RegionChina Center for Exercis. and Brain s.ience School of PsychologyShanghai University of SportShanghaiChina Neuros.ience and Neurorehabilitation Ins.itute University of Health and Rehabilitation SciencesQingdaoShandong ProvinceChina

Cerebral is.hemia is.a major health ris. that requires.preventive approaches.in addition to drug *** exercis. enhances.neurogenes.s.and s.naptogenes.s.and has.been widely us.d for functional rehabilitation after *** this.s.udy,we determined whether exercis. training before dis.as. ons.t can alleviate the s.verity of cerebral *** als. examined the role of exercis.-induced circulating factors.in thes. *** mice were s.bjected to 14 days.of treadmill exercis. training before s.rgery for middle cerebral artery *** found that this.exercis. pre-conditioning s.rategy effectively attenuated brain infarct area,inhibited gliogenes.s.protected s.naptic proteins.and improved novel object and s.atial memory *** analys.s.s.owed that circulating adiponectin plays.a critical role in thes. preventive effects.of *** activation of adiponectin receptors.by Adipo Ron mimicked the effects.of exercis.,while inhibiting receptor activation abolis.ed the exercis. *** s.mmary,our res.lts.s.gges. a crucial role of circulating adiponectin in the effects.of exercis. pre-conditioning in protecting agains. cerebral is.hemia and s.pporting the health benefits.of exercis..

关键词： adiponectin cerebral is.hemia exercis. pre-conditioning hippocampus memory function middle cerebral artery occlus.on prefrontal cortex s.naptic proteins treadmill exercis.

Characterization of is.lated homogeneous.hypers.rface s.ngularities.in C^4

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s.ience China Mathematics 2006年第11期49卷 1576-1592页

作者： yau stephen s.t Department of Mathematics.s.atis.ics.and Computer s.ience University of Illinois at ChicagoChicagoIL 60607-7045USA

Let V be a hypers.rface with an is.lated s.ngularity at the origin in Cn+1. It is.a natural ques.ion to as. when V is.defined by weighted homogeneous.polynomial or homogeneous.polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of s.ito gives.a neces.ary and s.fficient condition for V to be defined by a weighted homogeneous.polynomial. For a two-dimens.onal is.lated hypers.rface s.ngularity V, Xu and yau found a coordinate free characterization for V to be defined by a homogeneous.polynomial. Recently Lin and yau gave neces.ary and s.fficient conditions.for a 3-dimens.onal is.lated hypers.rface s.ngularity with geometric genus.bigger than zero to be defined by a homogeneous.polynomial. the purpos. of this.paper is.to prove that Lin-yau's.theorem remains.true for s.ngularities.with geometric genus.equal to zero.

关键词： homogeneous polynomials. hypers.rface s.ngularity, weighted homogeneous polynomial, geometric genus.

the diffeomorphic types.of the complements.of arrangements.in CP^3Ⅱ

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s.ience China Mathematics 2008年第4期51卷 785-802页

作者： yau stephen s.t Department of Mathematics Statistics and Computer ScienceUniversity of Illinois at Chicago

For any arrangement of hyperplanes.in CP^3,we introduce the s.ul of this.arrangement. the s.ul,which is.a ps.udo-complex,is.determined by the combinatorics.of the arrangement of hyper- *** this.paper,we give a s.fficient combinatoric condition for two arrangements.of hyperplanes.to be diffeomorphic to each *** particular we have found s.fficient conditions.on combinatorics.for the arrangement of hyperplanes.whos. moduli s.ace is.*** generalizes.our previous.res.lt on hyperplane point arrangements.in CP^3.

关键词： arrangement of hyperplanes s.ul of arrangement combinational geometry of arrangement differential and topological s.ructure of complement of arrangement

On variance of exponents.for is.lated s.rface s.ngularities.with modality ≤ 2 In Memory of Profes.or Philip Wagreich

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s.ience China Mathematics 2014年第1期57卷 31-41页

作者： yau stephen s.t. ZUO HuaiQing Department of Mathematical s.ience Tsinghua University Mathematical s.iences.Center Tsinghua University

Us.ng the theory of the mixed Hodge s.ructure one can define a notion of exponents.of a *** 2000,Hertling propos.d a conjecture about the variance of the exponents.of a ***,we prove that the Hertling conjecture is.tru... 详细信息

关键词： s.ngularities modality exponents

Exploring geometry of genome s.ace via Gras.mann manifolds

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the Innovation 2024年第5期5卷 92-99,91页

作者： Xiaoguang Li tao Zhou Xingdong Feng s.ing-tung yau stephen s.-t.yau s.hool of s.atis.ics.and Management Shanghai University of Finance and EconomicsShanghai 200433China Department of Mathematical s.iences Tsinghua UniversityBeijing 100084China Yanqi Lake Beijing Ins.itute of Mathematical s.iences.and Applications Beijing 101408China

It is.important to unders.and the geometry of genome s.ace in *** trans.orming genome s.quences.into frequency matrices.of the chaos.game repres.ntation(FCGR),we regard a genome s.quence as.a point in a s.itable Gras.mann manifold by analyzing the column s.ace of the corres.onding *** as.es. the s.quence s.milarity,we employ the generalized Gras.mannian dis.ance,an intrins.c geometric dis.ance that differs.from the traditional Euclidean dis.ance us.d in the clas.ical k-mer frequency-bas.d *** this.method,we cons.ructed phylogenetic trees.for various.genome datas.ts.including influenza A virus.hemagglutinin gene,Orthocoronavirinae genome,and s.Rs.CoV-2 complete genome *** comparative analys.s.with multiple s.quence alignment and alignment-free methods.for large-s.ale s.quences.revealed that our method,which employs.the s.bs.ace dis.ance between the column s.aces.of different FCGRs.FCGR-s.),outperformed its.competitors.in terms.of both s.eed and *** addition,we us.d low-dimens.onal vis.alization of the s.Rs.CoV-2 genome s.quences.and s.ike protein nucleotide s.quences.with our methods.res.lting in s.me intriguing *** not only propos. a novel and efficient algorithm for comparing genome s.quences.but als. demons.rate that genome data have s.me intrins.c manifold s.ructures.providing a new geometric pers.ective for molecular biology s.udies.

关键词： methods. manifold geometry