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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 to prove that Lin-yau's theorem remains true for singularities with geometric genus equal to zero.

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

New results on the geometry of the moduli space of Riemann surfaces

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Science china Mathematics 2008年第4期51卷 632-651页

作者： yau Shing-Tung center of Mathematical Sciences Zhejiang University

We briefly survey our recent results about the Mumford goodness of several canonical metrics on the moduli spaces of Riemann surfaces, including the Weil-petersson metric, the Ricci metric, the perturbed Ricci metric and the Kahler-Einstein metric. We prove the dual Nakano negativity of the Weil-petersson metric. As applications of these results we deduce certain important results about the L 2-cohomology groups of the logarithmic tangent bundle over the compactified moduli spaces.

关键词： moduli spaces canonical metrics good metrics L 2-cohomology 14D20 14H20 32G13 53c55

Model-Based Adaptive predictive control with Visual Servo of a Rotary crane System

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Journal of Electronic Science and Technology 2018年第2期16卷 169-174页

作者： Zhi-Ren Tsai yau-Zen chang Department of computer Science and Information Engineering Asia UniversityTaichung 41354 Department of Mechanical Engineering Chang Gung UniversityTaoyuan 33302 with the Department of Medical Research China Medical University HospitalChina Medical UniversityTaichung 41354 Department of Neurosurgery Chang Gung Memorial HospitalChiayi 61363

This paper investigated the implementation of an adaptive predictive controller using nonlinear dynamic echo state neural （ESN） model for a rotary crane system by the visual servo method. The control sequences within the control horizon were described using cubic spline interpolation to enlarge the predictive horizon. Verification of the proposed scheme in the face of exogenous disturbances and modeling error with inaccurate string length was demonstrated by both simulations and experiments.

关键词： Adaptive predictive controller echo state neural(ESN) model exogenous disturbances modeling error rotary crane

Enhancing Design of Visual-Servo Delayed System

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Journal of Electronic Science and Technology 2018年第3期16卷 232-240页

作者： Zhi-Ren Tsai yau-Zen chang the Department of computer Science and Information Engineering Asia University the Department of Medical Research China Medical University Hospital China Medical University the Department of Mechanical Engineering Chang Gung University the Department of Neurosurgery Chang Gung Memorial Hospital

A robust adaptive predictor is proposed to solve the time-varying and delay control problem of an overhead crane system with a stereo-vision servo. The predictor is based on the use of a recurrent neural network(RNN) with tapped delays, and is used to supply the real-time signal of the swing angle. There are two types of discrete-time controllers under investigation, i.e., the proportional-integral-derivative(pID) controller and the sliding controller. Firstly, a design princ.p.e of the neural predictor is developed to guarantee the convergence of its swing angle estimation. Then, an improved version of the particle swarm optimization algorithm, the parallel particle swarm optimization(ppSO) method is used to optimize the control parameters of these two types of controllers. Finally, a homemade overhead crane system equipped with the Kinect sensor for the visual servo is used to verify the proposed scheme. Experimental results demonstrate the effectiveness of the approach, which also show the parameter convergence in the predictor.

关键词： parallel particle swarm optimization robust adaptive predictor stereo-vision servo time-varying delay

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 the set 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 to 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 the 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 to 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： princ.p.l ideal ring Steinberg group intermediate subgroups

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 to 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

progress of china＇s Market Institution： Requiring a Stringent Implementation of policies

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Fudan Journal of the Humanities and Social Sciences 2014年第4期7卷 601-619页

作者： Laurence chin yau Yuen c/o Fuxiang Bay Hengqin New Area Zhuhai 519031 Guangdong China

Since reform, china＇s market institution has been gradually evolving, but is still facing insufficient competition owing to lower transparency, administrative interventions, and territorial limitations in certain areas. This paper reviews the applicability of market hypotheses to china, and analyzes the implications with respect to various markets and the resolution of the Third plenary Session of the Eighteenth central committee congress. It is vital for the relevant authorities to reinforce implementation of the resolution＇s initiatives. Following the new policies, it is expected that the market institution will be advanced to a higher level.

关键词： Resolution Market institution Markets chinese enterprise Rural land

Epidemiological study of hypertensive retinopathy in the primary care setting: Retrospective cross-sectional review of retinal photographs

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Family Medicine and community Health 2016年第4期4卷 13-21页

作者： Lap-kin chiang Michael K.c.yau cheuk-wai Kam Lorna V.Ng Benny c.Y.Zee Family Medicine and General Outpatient Department Kwong Wah HospitalHospital AuthorityHong KongChina The Jockey club School of public Health and primary care The Chinese University of Hong KongHong KongChina

Objective:The objective is to estimate the prevalence and grading of hypertensive retinopa-thy in the primary care setting;examine the patient characteristics associated with hypertensive retinopathy;and examine the association of hypertensive retinopathy and other hypertension ***:This is a retrospective cross-sectional *** included adult hypertensive patients with available and gradable retinal ***:Two hundred fifty-six male hypertensive patients(34.3%)and 491 female hyper-tensive patients(65.7%)were *** average duration of hypertension was 7.2 years,and 49.8%and 41.2%of patients were taking one or two antihypertensive medications *** 1491 qualified retinal photographs(744 right eye and 747 left eye),24.9%,62.6%,and 12.5%were classified as showing normal,mild,and moderate hypertensive retinopathy *** three commonest retinal signs were generalized or focal arteriolar narrowing(650 cases,43.6%),hard exudates(168 cases,11.3%),and opacity(c.p.er or silver wiring)of the arteriolar wall(166 cases,11.1%).patients older than 61 years,having hypertension for more than 15 years,or taking three or more antihypertensive medications were significantly associated with hyperten-sive retinopathy(pconclusion:In a primary care clinic in Hong Kong,77.1%of hypertensive patients had hypertensive *** hypertensive retinopathy was the commonest target organ damage for hypertensive patients in a primary care clinic.

关键词： Hypertensive retinopathy retinal photograph primary care