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science China Mathematics 2014年第1期57卷 31-41页

作者： yau stephen s.t. ZUO HuaiQing Department of Mathematical science Tsinghua University Mathematical sciences Center Tsinghua University

Using the theory of the mixed Hodge structure one can define a notion of exponents of a *** 2000,Hertling proposed a conjecture about the variance of the exponents of a ***,we prove that the Hertling conjecture is.t.u... 详细信息

关键词： singularities modality exponents

Exercise preconditioning alleviates ischemia-induced memory deficits by increasing circulating adiponectin

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Neural Regeneration Research 2025年第5期20卷 1445-1454页

作者： Meifeng Zheng Borui Zhang sonata s Y yau Kwok-Fai so 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(Ministry of Education) Guangdong-Hong Kong-Macao Institute of CNS RegenerationJinan UniversityGuangzhouGuangdong ProvinceChina Department of Rehabilitation sciences The Hong Kong Polytechnic UniversityHong Kong Special Administrative RegionChina state Key Laboratory of Brain and Cognitive science Li Ka Shing Faculty of MedicineThe University of Hong KongHong Kong Special Administrative RegionChina Center for Exercise and Brain science School of PsychologyShanghai University of SportShanghaiChina Neuroscience and Neurorehabilitation Institute University of Health and Rehabilitation SciencesQingdaoShandong ProvinceChina

Cerebral ischemia is a major health risk that requires preventive approaches in addition to drug *** exercise enhances neurogenesis and synaptogenesis,and has been widely used for functional rehabilitation after *** this study,we determined whether exercise training before disease ons.t.can alleviate the severity of cerebral *** also examined the role of exercise-induced circulating factors in these *** mice were subjected to 14 days of treadmill exercise training before surgery for middle cerebral artery *** found that this exercise pre-conditioning strategy effectively attenuated brain infarct area,inhibited gliogenesis,protected synaptic proteins,and improved novel object and spatial memory *** analysis showed that circulating adiponectin plays a critical role in these preventive effects of *** activation of adiponectin receptors by Adipo Ron mimicked the effects of exercise,while inhibiting receptor activation abolished the exercise *** summary,our results suggest a crucial role of circulating adiponectin in the effects of exercise pre-conditioning in protecting against cerebral ischemia and supporting the health benefits of exercise.

关键词： adiponectin cerebral ischemia exercise pre-conditioning hippocampus memory function middle cerebral artery occlusion prefrontal cortex synaptic proteins treadmill exercise

Characterization of isolated homogeneous hypersurface singularities in C^4

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science China Mathematics 2006年第11期49卷 1576-1592页

作者： yau stephen s t Department of Mathematics statistics and Computer science University of Illinois at ChicagoChicagoIL 60607-7045USA

Let V be a hypersurface with an isolated singularity at the origin in Cn+1. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface singularity V, Xu and yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. the purpose of this paper is.t. prove that Lin-yau's.t.eorem remains.t.ue for singularities with geometric genus equal to zero.

关键词： homogeneous polynomials, hypersurface singularity, weighted homogeneous polynomial, geometric genus.

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

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science 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 soul of this arrangement. the soul,which is a pseudo-complex,is determined by the combinatorics of the arrangement of hyper- *** this paper,we give a sufficient combinatoric condition for two arrangements of hyperplanes.t. be diffeomorphic to each *** particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is *** generalizes our previous result on hyperplane point arrangements in CP^3.

关键词： arrangement of hyperplanes soul of arrangement combinational geometry of arrangement differential and topological structure of complement of arrangement

thom-sebastiani properties of Kohn-Rossi cohomology of compact connected strongly pseudoconvex CR manifolds

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science China Mathematics 2017年第6期60卷 1129-1136页

作者： yau stephen s. t ZUO HuaiQing Department of Mathematical sciences Tsinghua University Beijing 100084 China yau Mathematical sciences Center Tsinghua University Beijing 100084 China

Let X1 and X2 be two compact connected strongly pseudoconvex embeddable Cauchy-Riemann （CR） manifolds of dimensions 2m - 1 and 2n - 1 in Cm＋l and Cn＋l, respectively. We introduce the thom- sebastiani sum X = X1 X2 which is a new compact connected strongly pseudoconvex embeddable CR manifold of dimension 2m＋2n＋ 1 in Cm＋n＋2. thus.t.e s.t.of all codimension 3 strongly pseudoconvex compact connected CR manifolds in C^n＋1 for all n ≥ 2 forms a semigroup. X is said to be an irreducible element in this semigroup if X cannot be written in the form X1 X2. It is a natural question to determine when X is an irreducible CR manifold. We use Kohn-Rossi cohomology groups.t. give a necessary condition of the above question. Explicitly, we show that if X = X1 X2, then the Kohn-Rossi cohomology of the X is.t.e product of those Kohn-Rossi cohomology coming from X1 and X2 provided that X2 admits a transversal holomorphic sl-action.

关键词： CR manifold Kohn-Rossi cohomology isolated singularity

Classification of gradient space of dimension 8 by a reducible sl(2,C)action

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science China Mathematics 2009年第12期52卷 2792-2828页

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

this paper deals with a reducible sl(2,C)action on the formal power series *** purpose of this paper is.t. confirm a special case of the yau conjecture:suppose that sl(2,C)acts on the formal power series ring via(1.1).then I(f)=(li 1 )⊕(il2 )⊕···⊕(lis)modulo some one dimensional sl(2,C)representations where(i)is an irreducible sl(2,C)representation of i dimension and{li1 ,li2 ,...,lis }{ll1,ll2,...,lr}.Unlike classical invariant theory which deals only with irreducible action and 1-dimensional representations,we treat the reducible action and higher dimensional representations successively.

关键词： principal ideal ring steinberg group intermediate subgroups

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

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science 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 use a new method to study arrangement in CPl,define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics.t.en their complements are diffeomorphic to each *** particular,the moduli space of nice point arrangements with same combinatorics in CPl is *** generalizes.t.e result on point arrangements in CP3 to point arrangements in CPl for any l.

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

the second pluri-genus of smoothable Gorenstein surface singularities

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science 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 intersection isolated surface singularities, Okuma gave a formula for the second plurigenus relating geometry genus, Milnor number and tjurina number. We generalize Okuma’s.t.eorem to Gorenstein smoothab... 详细信息

关键词： second pluri-genus smoothable Gorenstein Milnor number tjurina number

spherical extension property no longer true for domains in algebraic variety with isolated singularity Dedicated to Professor YANG Lo on the occasion of his 70th birthday

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science China Mathematics 2010年第2期53卷 259-262页

作者： yau stephen s. t. Institute 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 simply connected bounded domain in C with spherical real analytic boundary D, then every local biholomorphic map at boundary as above extends.t. a biholomorphic map from D onto the unit ball in Cn. As a consequence, a local biholomorphic map between D1 and D2 where D1 and D2 are simply connected domains in Cn with spherical real analytic boundaries can extend to a global biholomorphic map from D1 onto D2. If the boundary is algebraic, the simply connected condition in the above result can be dropped. In this note, we show that the above phenomenon is no longer true if domains are in algebraic varieties with isolated singularities.

关键词： spherical boundary holomorphic extension algebraic variety isolated singularity

Exploring geometry of genome space via Grassmann 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 shing-tung yau stephen s.-t.yau school of statistics and Management Shanghai University of Finance and EconomicsShanghai 200433China Department of Mathematical sciences Tsinghua UniversityBeijing 100084China Yanqi Lake Beijing Institute of Mathematical sciences and Applications Beijing 101408China

It is important to understand the geometry of genome space in *** transforming genome sequences into frequency matrices of the chaos game representation(FCGR),we regard a genome sequence as a point in a suitable Grassmann manifold by analyzing the column space of the corresponding *** assess.t.e sequence similarity,we employ the generalized Grassmannian distance,an intrinsic geometric distance that differs from the traditional Euclidean distance used in the classical k-mer frequency-based *** this method,we constructed phylogenetic trees for various genome datas.t.,including influenza A virus hemagglutinin gene,Orthocoronavirinae genome,and sARs-CoV-2 complete genome *** comparative analysis with multiple sequence alignment and alignment-free methods for large-scale sequences revealed that our method,which employs.t.e subspace distance between the column spaces of different FCGRs(FCGR-sD),outperformed its competitors in terms of both speed and *** addition,we used low-dimensional visualization of the sARs-CoV-2 genome sequences and spike protein nucleotide sequences with our methods,resulting in some intriguing *** not only propose a novel and efficient algorithm for comparing genome sequences but also demonstrate that genome data have some intrinsic manifold structures,providing a new geometric perspective for molecular biology studies.

关键词： methods. manifold geometry