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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.

Bacteriophage secondary infection

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Virologica Sinica 2015年第1期30卷 3-10页

作者： stephen t Abedon Department of Microbiology the Ohio State University OH 44906 USA

Phages are credited with having been first described in what we now, officially, are commemorating as the 100 th anniversary of their discovery. those one-hundred years of phage history have not been lacking in excitement, controversy, and occasional convolution. One such complication is the concept of secondary infection, which can take on multiple forms with myriad consequences. the terms secondary infection and secondary adsorption, for example, can be used almost synonymously to describe virion interaction with already phage-infected bacteria, and which can result in what are described as superinfection exclusion or superinfection immunity. the phrase secondary infection also may be used equivalently to superinfection or coinfection, with each of these terms borrowed from medical microbiology, and can result in genetic exchange between phages, phage-on-phage parasitism, and various partial reductions in phage productivity that have been termed mutual exclusion, partial exclusion, or the depressor effect. Alternatively, and drawing from epidemiology, secondary infection has been used to describe phage population growth as that can occur during active phage therapy as well as upon phage contamination of industrial ferments. Here primary infections represent initial bacterial population exposure to phages while consequent phage replication can lead to additional, that is, secondary infections of what otherwise are not yet phage-infected bacteria. Here I explore the varying meanings and resultant ambiguity that has been associated with the term secondary infection. I suggest in particular that secondary infection, as distinctly different phenomena, can in multiple ways influence the success of phage-mediated biocontrol of bacteria, also known as, phage therapy.

关键词： lysis from without lysis inhibition coinfection parallel secondary infection phage therapy pharmacology serial secondary infection superinfection

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 to 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

From foraging to autonoetic consciousness： the primal self as a consequence of embodied prospective foraging

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Current Zoology 2015年第2期61卷 368-381页

作者： thomas t. HILLS stephen BUttERFILL Department of Psychology University of Warwick CV4 7AL Coventry UK Department of Philosophy University of Warwick CV4 7AL Coventry UK

the capacity to adapt to resource distributions by modulating the frequency of exploratory and exploitative behaviors is common across metazoans and is arguably a principal selective force in the evolution of cognition. Here we （I） review recent work investigating behavioral and biological commonalities between external foraging in space and internal foraging over envi- ronments specified by cognitive representations, and （2） explore the implications of these commonalities for understanding the origins of the self. Behavioural commonalities include the capacity for what is known as area-restricted search in the ecological literature： this is search focussed around locations where resources have been found in the past, but moving away from locations where few resources arc found, and capable of producing movement pattems mimicking L6vy flights. Area-restricted search shares a neural basis across metazoans, and these biological commonalities in vertebrates suggest an evolutionary homology be- tween external and internal foraging. Internal foraging, and in particular a form we call embodied prospective foraging, makes available additional capacities for prediction based on search through a cognitive representation of the external environment, and allows predictions about outcomes of possible future actions. We demonstrate that cognitive systems that use embodied prospec- tive foraging require a primitive sense of self, needed to distinguish actual from simulated action. this relationship has implica- tions for understanding the evolution of autonoetic consciousness and self-awareness.

关键词： Self-projection Mental time travel Episodic future thinking Foraging Consciousness

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： 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,then their complements are diffeomorphic to each *** particular,the moduli space of nice point arrangements with same combinatorics in CPl is *** generalizes the result on point arrangements in CP3 to point arrangements in CPl for any l.

关键词： diffeomorphic type hyperplane arrangement lattice isotopy 14F05 14H30

Double negative regulatory t cells in transplantation and autoimmunity:recent progress and future directions

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Journal of Molecular Cell Biology 2012年第1期4卷 48-58页

作者： stephen C.Juvet Li Zhang Division of Respirology and Clinician-Scientist training Program Department of MedicineInstitute of Medical ScienceUniversity of TorontoTorontoONCanada toronto General Research Institute University Health NetworkMedical Discovery TowerRoom 2-807101 College StreetTorontoONCanada Department of Immunology University of TorontoTorontoONCanada Department of Laboratory Medicine and Pathobiology University of Toronto and Toronto General Research InstituteUniversity Health NetworkTorontoONCanada

t lymphocytes bearing the ab t cell receptor(tCR)but lacking CD4,CD8,and markers of natural killer(NK)cell differentiation are known as‘double-negative’(DN)t cells and have been described in both humans and rodent *** and others have shown that DN t cells can act as regulatory t cells(tregs)that are able to prevent allograft rejection,graft-versus-host disease,and autoimmune *** the last few years,new data have revealed evidence of DN treg function in vivo in rodents and ***,significant advances have been made in the mechanisms by which DN tregs target antigen-specific t *** major limitation of the field is the lack of a specific marker that can be used to distinguish truly regulatory DN t cells(DN tregs)from non-regulatory ones,and this is the central challenge in the coming ***,we review recent progress on the role of DN tregs in transplantation and autoimmunity,and their mechanisms of *** also provide some perspectives on how DN tregs compare with Foxp31 tregs.

关键词： double-negative t cells regulatory t cells transplantation autoimmunity graft-versus-host disease type 1 diabetes mellitus

transport mechanism in chemically reactive hybrid nanofluid flow containing gyrotactic micro-organisms over a curved oscillatory surface

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Applied Mathematics and Mechanics(English Edition) 2025年第1期46卷 177-192页

作者： M.NAVEED M.IMRAN t.ASGHAR Z.ABBAS Department of Mathematics Division of Science and TechnologyUniversity of Education Department of Mathematics The Islamia University of Bahawalpur

this paper examines the transport analysis, including both heat transfer and mass transfer, in hybrid nanofluid flow containing gyrotactic microorganisms towards a curved oscillatory surface. the influence of magnetic fields is also inspected in terms of their physical characteristics. to depict the phenomena of transport, modified versions of both Fick's and Fourier's laws are used. Additionally, the characteristics of both heterogeneous and homogeneous chemical reactions are also incorporated. Utilizing a curvilinear coordinate system, the flow problem is formulated as partial differential equations(PDEs)for momentum, concentration, microorganism field, and energy. An analytical solution to the obtained flow equations is achieved utilizing the homotopy analysis method(HAM).the effects of significant flow parameters on the pressure and microorganism fields, velocity, oscillation velocity, concentration, and temperature distributions are shown via graphs. Furthermore, the variations in skin friction, mass transfer rate, heat transfer rate, and local motile number due to different involved parameters are presented in tables and are analyzed in detail. Graphical results indicate that the curves of velocity and temperature fields are enhanced as the values of the solid volume fraction variables *** is also verified that the concentration rate field decreases as the values of the homogeneous reaction strength parameter and the radius of curvature parameter increase, and it increases with the Schmidt number and the heterogeneous reaction strength *** outcomes show a favorable response of the motile number to advanced values of the Peclet number, the Schmidt number, the microorganism difference parameter, and the bio-convective Lewis number.

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