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The localization of 1-cohomology of transitive Lie algebroids

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Science china Mathematics 2006年第2期49卷 277-288页

作者： CHEN Zhuo & LIU Zhangju department of Mathematics, Capital Normal university, beijing 100037, china School of Mathematical Science, peking university, beijing 100871, china 1. department of Mathematics Capital Normal University Beijing 100037 China 2. School of Mathematical Science Peking University Beijing 100871 China

For a transitive Lie algebroid A on a connected manifold M and its representation on a vector bundle F, we define a morphism of cohomology groups rk: Hk(A,F) → Hk(Lx,Fx), called the localization map, where Lx is the adjoint algebra at x ∈ M. The main result in this paper is that if M is simply connected, or H (LX,FX) is trivial, then T is injective. This means that the Lie algebroid 1-cohomology is totally determined by the 1-cohomology of its adjoint Lie algebra in the above two cases.

关键词： transitive Lie algebroid representation cohomology localization.

A numerical study for some efficient time-integration schemes using barotropic equations

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Acta Oceanologica Sinica 1989年第1期8卷 77-89页

作者： Han Wei and Zhang Yuling department of geophysics, peking university, beijing, china Dept. of geophysics Peking Univ. Beijing China. China

Three kinds of methods, i. e., explicit, semi-implicit, and semi-implicit and semi-Lagrangian method, are tested in the time-integration of shallow-water equations on rotating sphere. Helpful results are available fro... 详细信息

关键词： time A numerical study for some efficient time-integration schemes using barotropic equations

Analysis of the air-sea heat exchange during the El Nino event in 1983

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Acta Oceanologica Sinica 1990年第4期9卷 513-526页

作者： Zhu Yafen and Yang Dasheng geophysics department,peking university,beijing,china geophysics Dept. Peking Univ. Beijing China. China

In this paper,by using the ECMWF objective analysed data as well as CAC and NOAA grid point data of 1981 and 1983,the sensible and latent heat fluxes at the air and sea boundary surface within the range of 45°E-75°W, 35°N-35°S over the Pacific and the Indian Ocean are calculated. The purpose is to analyse the different revealing features during the mature stage and at the end of the 1982 -1983 El Nino event and to compare the difference of the features between thd El Nino and the normal. The result shows that the air and sea heat exchange west of the dateline over the central tropical Pacific during the EJ Nino period is more intense than that of the normal. However,the fluxes of the sensible and latent heat on the sea surface with strong warming of SSTneat by and on the south side of the equator east of 170°W are low and even negative,and the patterns of the sensible and latent heat fluxes over the Indian Ocean during the year of 1983 are similer to that of normal. Spatial patterns of the sensible heat ,the latent heat,SST,OLR and the wind speed exhibit large anomalies during the El Nino event. The corresponding relationships of the spatial distribution of the streng exchange of heat fluxes with regions of high SST and action convection or negative anomalies of OLR are relatively complicated. But the region of maximum air and sea heat exchange is in good coincidence with that of high value of the Vs. The strong heat exchange is weakened with the declining and the finishing of the El Nino event in the central tropical Pacific.

关键词： heat Analysis of the air-sea heat exchange during the El Nino event in 1983 Nino El

The LIL Convergence for Stationary Linear Random Field

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Acta Mathematica Sinica,English Series 1996年第4期12卷 385-397页

作者： He Shuyuan department of Probability and Statistics peking university beijing, 100871 china department of Probability and Statistics Peking University Beijing China

Let Y={Y_n;n∈N^2} be a stationary linear random field generated by a two- dimensional martingale difference. Where N^2 denotes the two dimensional integer lattice. The main purpose of this paper is to obtain the LIL ... 详细信息

关键词： Stationary linear random field 1/4 Martingale difference LIL convergency.

Role of atmospheric heat source/sink over the Qinghai-Xizang Plateau in quasi-4-year oscillation of atmosphere-land-ocean interaction

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Chinese Science Bulletin 2001年第3期46卷 241-245页

作者： ZHAO Ping & CHEN Longxundepartment of geophysics, peking university, beijing 100871, china Chinese Academy of Meteorological Sciences, beijing 100081, china department of geophysics Peking University Beijing China Chinese Academy of Meteorological Sciences Beijing China

Using 1961-1995 monthly atmospheric apparent heat source/sink over the Qinghai-Xizang Plateau (QXP)and reanalysis data of NCEP/NCAR, and 1961 ?1994 monthly SST of UK/GISST2, the statistical study is undertaken on the QXP heat source/sink in relation to both atmospheric circulation in Asia and El Nino/La Nina events. It is discovered that there exists noticeable interaction in aquasi-4-year period among the of the QXP, low-levelmeridional winds east of the QXP, low-level zonal winds in the equatorial Pacific, SST in the equatorial eastern Pacific, and the circulation at mid and high latitudes north of the QXP. They have difference in phase. The cold source intensity of the QXP in winter favours a low-level meridional wind anomaly to prevail in the mainland of china and its coast east of the QXP and to last until the subsequent autumn. The wind anomaly can induce a low-level zonal wind anomaly of the tropic Pacific that finally affects an El Nino/La Nina event in the autumn and subsequent winter.

关键词： Qinghai-Xizang Plateau thermal effect interannual variation atmosphere-land-ocean interaction.

On the boundary value problem for harmonic maps of the Poincaré disc

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Chinese Science Bulletin 1997年第24期42卷 2025-2045页

作者： LI Zhongdepartment of Mathematics, peking university, beijing 100871, china department of Mathematics Peking University Beijing China

The boundary value problem for harmonic maps of the Poincare disc is discussed. The emphasis is on the non-smoothness of the given boundary values in the problem. Let T . be a subspace of the universal Teichmüller space, defined as a set of normalized quasisymmetric homeomorphisms h of the unit circle S onto itself where h admits a quasiconformal extension to the unit disc D with a complex dilatation μ satisfyingwhere ρ(z)|dz|2 is the Poincare metric of D. Let B . be a Banach space consisting of holomorphic quadratic differentials φ in D with normsIt is shown that for any given quasisymmetric homeomorphism h : S1→S1∈ T . , there is a unique quasiconformal harmonic map of D with respect to the Poincare metric whose boundary corresponding is h and the Hopf differential of such a harmonic map belongs to B .

关键词： Harmonic maps quasiconfomial mappings universal Teichmüller spaces.

SYNTHESIS AND PROPERTIES OF NEW MESOGEN-JACKETED LIQUID CRYSTALLINE POLYMERS

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Chinese Journal of Polymer Science 2000年第2期18卷 139-148页

作者： Qi-ding Mi Qi-feng Zhou department of Polymer Science & Engineering, College of Chemistry peking university, beijing 100871, china peking Univ Coll Chem Dept Polymer Sci & Engn Beijing 100871 Peoples R China

Some new mesogen-jacketed liquid crystalline polymers (MJLCP) with polymer backbones, spacers, and mesogenic units of different structures were synthesized by radical polymerization. The mesomorphic behavior of these polymers was examined using differential scanning calorimetry (DSC) and polarizing optical microscopy (POM). Their liquid crystallinity is influenced by the variation of polymer backbone, spacer, mesogenic unit and its terminal groups. The results show that 1) a more flexible polymer main-chain is more favorable to the formation of a liquid crystal phase, while 2) a flexible spacer will decrease the 'Jacket Effect' and the liquid crystallinity and 3) a subtle modification of the terminal groups on the mesogenic unit may also have a significant influence on properties of the polymers.

关键词： mesogen-jacketed liquid crystalline polymers polymer backbones spacers mesogenic units liquid crystallinity

Recursive equations for compound distribution with the severity distribution of the mixed type

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Science china Mathematics 2005年第5期48卷 594-609页

作者： YANG Jingping, CHENG Shihong & WU Qin LMAM, department of Financial Mathematics, peking university, beijing 100871, china 1. LMAM Department of Financial Mathematics Peking University 100871 Beijing China

In this paper, recursive equations are obtained for compound distribution with the number of claims belonging to (a, b)-family and the severity distribution of the mixed type. Numerical methods to solve these equation... 详细信息

关键词： recursive equation compound distribution (a b)-family severity distribution of the mixed type.

THE APPLICATION OF DISCRETE ELEMENT METHOD IN SOLVING THREE-DIMENTIONAL IMPACT DYNAMICS PROBLEMS

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Acta Mechanica Solida Sinica 2003年第3期16卷 256-261页

作者： Liu Kaixin Gao Lingtian (department of Mechanics and Engineering Science,peking university,beijing 100871,china) department of Mechanics and Engineering Science Peking University Beijing 100871 China

A three-dimensional discrete element model of the connective type is presented. Moreover,a three-dimensional numerical analysis code,which can carry out the transitional pro- cess from connective model(for continuum)to contact model(for non-continuum),is developed for simulating the mechanical process from continuum to *** wave propagation process in a concrete block(as continuum)made of cement grout under impact loading is numer- ically simulated with this *** comparing its numerical results with those by LS-DYNA,the calculation accuracy of the model and algorithm is ***,the failure process of the concrete block under quasi-static loading is demonstrated,showing the basic dynamic tran- sitional process from continuum to *** results of calculation can be displayed by *** damage modes are similar to the experimental *** two numerical examples above prove that our model and its code are powerful and efficient in simulating the dynamic failure problems accompanying the transition from continuum to *** also shows that the discrete element method(DEM)will have broad prospects for development and application.

关键词： discrete element method three-dimensional model impact stress wave dynamic failure