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Arithmetic of Shimura curves

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Science China mathematics 2010年第3期53卷 573-592页

作者： ZHANG Shou-Wu department of mathematics, Columbia {2., {3. york, ny 1002., usa 1. department of mathematics Columbia University New York NY 10027 USA

This is the note for a series of lectures that the author gave at the Centre de Recerca Matemtica (CRM), Bellaterra, Barcelona, Spain on October 19–2., 2.09. The aim is to give a comprehensive description of some recent work of the author and his students on generalisations of the Gross-Zagier formula, Euler systems on Shimura curves, and rational points on elliptic curves.

关键词： Shimura curves CM-points L-series

On the Birch-Swinnerton-Dyer Conjecture of Elliptic Curves E_D:y^2.x^3.D^2.

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Acta Mathematica Sinica,English Series 2000年第2期16卷 229-236页

作者： Delang Li department of mathematics,Sichuan Union {2.,Chengdu 610064,P.R.China Ye Tian department of mathematics,Columbia {2.,new york,ny 1002.,usa department of mathematics Sichuan Union University Chengdu 610064 P. R. China department of mathematics Columbia University New York NY 10027 USA

We prove in this paper that the BSD conjecture holds for a certain kind of elliptic curves.

关键词： Elliptic curve BSD conjecture Graph 2.component

Summary of a Life in Observational Ultraviolet/Optical Astronomy

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Research in Astronomy and Astrophysics 2024年第1期24卷 1-43页

作者： Donald G.york department of Astronomy and Astrophysics The University of Chicago5801 South Ellis Ave.Chicago 60637ILUSA

I reminisce on my early life in Section 1;on my education in Sections 2.and 3.on the years at Princeton as a research astronomer in Section 4;on the years on the faculty at Chicago in Section 5;on research on Diffuse Interstellar Bands(DIBs) in Section 6;on construction of the 3.5 m telescope at Apache Point Observatory(APO)in Section 7;on work on the Sloan Digital Sky Survey(SDSS) in Section 8;on work in public education in Chicago in Section 9;and on my travels in Section 10. My main science research is of an observational nature,concerning Galactic and intergalactic interstellar gas. Highlights for me included my work on the orbiting telescope Copernicus, including the discovery of interstellar deuterium;early observations of absorption associated with fivetimes ionized oxygen;and discoveries concerning the phases of gas in the local interstellar medium, based on previously unobservable interstellar UV spectral lines. With other instruments and collaborations, I extended interstellar UV studies to the intergalactic cool gas using quasi-stellar object QSO absorption lines redshifted to the optical part of the spectrum;provided a better definition of the emission and morphological character of the source of absorption lines in QSO spectra;and pursued the identification of the unidentified DIBs. For several of these topics, extensive collaborations with many scientists were essential over many years. The conclusions developed slowly, as I moved from being a graduate student at Chicago, to a research scientist position at Princeton and then to a faculty position at Chicago. At each stage of life, I was exposed to new technologies adaptable to my science and to subsequent projects. From high school days, I encountered several management opportunities which were formative. I have been extremely fortunate both in scientific mentors I had and in experimental opportunities I encountered.

关键词： Interstellar Medium(ISM) Nebulae (galaxies:)quasars:absorption lines ultraviolet:stars

Randomization of Q_(p) spaces on the unit ball of C^(n)

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Science China mathematics 2005年第z1期48卷 306-317页

作者： LI Bo & OUYANG Caiheng department of mathematics, State {2. of {3. york at Buffalo, Buffalo, ny 142.0, usa Wuhan Institute of Physics and mathematics, Chinese Academy of Sciences, Wuhan 43.071, China SUny Buffalo Dept Math Buffalo NY 14260 USA Chinese Acad Sci Wuhan Inst Phys & Math Wuhan 430071 Peoples R China

In this paper, we study the random power series of several complex variables,and give some sufficient conditions for random power series to belong to Qp and Qp,0spaces by means of their characterizations of Carleson m... 详细信息

关键词： random power series, function spaces, the unit ball.

Aggregation and assembly of crescent foldamers

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Science China Chemistry 2010年第1期53卷 45-51页

作者： GONG Bing department of Chemistry,university at Buffalo,The State university of {3. york,Buffalo,{3. york 142.0,usa 1. department of Chemistry University at Buffalo The State University of New York Buffalo New York 14260 USA

Recent studies have started to provide initial insights into the aggregation and assembly of two classes of back-rigidified foldamers with flat,curved backbones consisting of aromatic *** their persistent shape that presents large,well-defined aromatic surface areas,these crescent foldamers were found to undergo size-dependent aggregation in solution and pack into 1D assemblies in the solid *** aromatic oligoamides undergo stacking interactions not only in polar solvents but also in nonpolar ones,a unique property that is not associated with many other molecules that associate via π-π stacking *** stacking of oligo(m-phenylene ethynylenes) is similar to aromatic hydrocarbons,being promoted in polar solvents such as methanol while being discouraged in nonpolar solvents such as *** ready synthetic availability of crescent foldamers makes it possible to directly control the intermolecular interaction by tuning surface ***,the columnar assembly of these cavity-containing molecules provides a new strategy for constructing supramolecular nanotubular structures.

关键词： foldamer folding hydrogen bond π-π stacking aggregation assembly

On the Uniqueness of Heat Flow of Harmonic Maps and Hydrodynamic Flow of Nematic Liquid Crystals

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Chinese Annals of mathematics,Series B 2010年第6期31卷 921-938页

作者： Fanghua LIN Changyou WANG Courant Institute of Mathematical Sciences New York University New York NY 10012 USA department of mathematics University of Kentucky Lexington KY 40506 USA.

For any n-dimensional compact Riemannian manifold (M,g) without boundary and another compact Riemannian manifold (N,h), the authors establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0,T),W1,n). For the hydrodynamic flow (u,d) of nematic liquid crystals in dimensions n = 2.or 3. it is shown that the uniqueness holds for the class of weak solutions provided either (i) for n = 2. u ∈ Lt∞ L2.∩L2.Hx1, ▽P∈ Lt4/3.Lx4/3., and ▽d∈ L∞t Lx2.Lt2.x2. or (ii) for n = 3. u ∈ Lt∞ Lx2.L2.Hx1∩ C([0,T),Ln), P ∈ Ltn/2.Lxn/2., and ▽d∈ L2.Lx2.∩ C([0,T),Ln). This answers affirmatively the uniqueness question posed by Lin-Lin-Wang. The proofs are very elementary.

关键词： Hydrodynamic flow Harmonic maps Nematic liquid crystals Uniqueness

Surface roughness and removal rate in magnetorheological finishing of a subsurface damage free surface

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Progress in Natural Science:Materials International 2005年第6期15卷 538-544页

作者： CHENG Haobo1*, WANG Yingwei2. FENG Zhijing1 and CHENG Kai3.1. State Key Laboratory of Tribiology, Tsinghua university, Beijing 100084, China 2. {3. of Material Sciences, Changchun university of Science and Technology, Changchun 13.02., China 3. Faculty of Information and Engineering Systems, city Campus, Leeds LS1 3.E, UK) State Key Laboratory of Tribiology Tsinghua University Beijing 100084 China department of Material Sciences Changchun University of Science and Technology Changchun 130021 China Faculty of Information and Engineering Systems City Campus Leeds LS1 3HE UK

Based on computer-controlled optical surfacing, a new technique called magnetorheological finishing (MRF), is presented. The new technique combines the features of conventional loose abrasive machining with a wheel shaped polishing tool. The tool incorporates a host of features and has unprecedented fabricating versatility. The pre-polishing and fine polishing processes can be performed only by adjusting different parameters. The material removal function is studied theoretically and the results of simulation present a Gaussian distribution feature. Based on the established theoretical model, material removal rate experiments involving a parabolic mirror are designed and carried out to determine the effect of controllable parameters on size of the gap between the workpiece and the polishing wheel, rotating speed of the polishing wheel, concentration of volume fraction of non-magnetic particles and polishing time. Further experiments are carried out on the surface microstructure of the workpiece, the final surface roughness with an initial value of 10.98 nm reaches 1.2. nm root mean square (RMS) after 2. min of polishing. The subsurface damage experiment and the atomic force microscopy (AFM) measurement on the polished surface can also verify the feasibility of the MRF technique.

关键词： magnetorheological finishing surface roughness computer controlled optical surfacing subsurface damage removal function.

Correlation of zeros of automorphic L-functions

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Science China mathematics 2008年第7期51卷 1147-1166页

作者： LIU Jianya1 & YE YangBo1,2.1 School of mathematics,Shandong university,Jinan 2.0100, China 2.2. of mathematics,The university of Iowa,Iowa city,IA 52.42.1419,usa 1. School of mathematics Shandong University Jinan 250100 China 2. department of mathematics The University of Iowa Iowa City IA 52242-1419 USA

We compute the n-level correlation of normalized nontrivial zeros of a product of Lfunctions: L(s, π1) … L(s, π k ), where πj, j = 1, …, k, are automorphic cuspidal representations of GL mj (?A). Here the sizes of the groups GL mj (?A) are not necessarily the same. When these L(s, π j ) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s, π j ) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m 1, …, m k ? 4, but are under Hypothesis H in other cases.

关键词： automorphic L-function zero correlation Selberg’s orthogonality conjecture 11F70 11M2. 11M41

A conceptual evolutionary aseismic decision support framework for hospitals

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Earthquake Engineering and Engineering Vibration 2012年第4期11卷 499-512页

作者： Yufeng Hu Gary F. Dargush Xiaoyun Shao department of Civil and Construction Engineering Western Michigan UniversityKalamazoo department of Mechanical and Aerospace Engineering University at BuffaloState University of New YorkBuffalo

In this paper, aconceptual evolutionary framework for aseismic decision support for hospitalsthat attempts to integrate a range of engineering and sociotechnical models is presented. Genetic algorithms are applied to find the optimal decision sets. A case study is completed to demonstrate how the frameworkmay applytoa specific *** simulations show that the proposed evolutionary decision support framework is able to discover robust policy sets in either uncertain or fixed environments. The framework also qualitatively identifies some of the characteristicbehavior of the critical care organization. Thus, by utilizing the proposedframework, the decision makers are able to make more informed decisions, especially toenhance the seismic safety of the hospitals.

关键词： decision making seismic engineering hospital genetic algorithms