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Unramified extensions of quadratic fields

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Progress in Natural Science:Materials International 2008年第3期18卷 323-324页

作者： Wei Li, Dong Yang, Xianke Zhang department of mathematical sciences, tsinghua university, beijing 100084, china department of mathematical sciences Tsinghua University Beijing 100084 China

Let K be a global quadratic field, then every unramified abelian extension of Kis proved to be absolutely Galois when Kis a number field or under some natural conditions when Kis a function field. The absolute Galois ... 详细信息

关键词： Global quadratic fields Unramified extensions

The Double Ringel-Hall Algebras of Valued Quivers

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Chinese Annals of Mathematics,Series B 2006年第6期27卷 701-722页

作者： Yanxin WANG Jie XIAO department of mathematical sciences Tsinghua University Beijing 100084 China College of mathematical Science Tianjin Normal University Tianjin 300384 China

这篇论文被奉献给双 Ringel-Hallalgebra D 的结构的学习(为无限的维的世袭代数学Λ的Λ)，它被给由一珍视发抖在一块有限的地上的Γ ，并且另外到 D 的关系的学习(与代表一起的Λ)模块珍视发抖Γ。

关键词： Ringel-Hall代数广义Kac-Moody代数 Drinfeld双精度近世代数

Twistor bundle theory and its application

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Science china Mathematics 2004年第4期47卷 605-616页

作者： PENG Chia-Kuei & TANG Zizhoudepartment of Mathematics, Graduate School of Chinese Academy of sciences, beijing 100039, china department of mathematical sciences, tsinghua university, beijing 100084, china department of Mathematics Graduate School of Chinese Academy of Sciences Beijing China department of mathematical sciences Tsinghua University Beijing China

Over an oriented even dimensional Riemannian manifold (M2m, ds2), in terms of the Levi-Civita connection form Ω and the canonical form Θ on the bundle of positive or→ J+(M, ds2) → M. The integrability on an almost complex structure J compatible with the metric and the orientation, is shown to be equivalent to the fact that the corresponding cross section of the twistor bundle is holomorphic with respect to J and the canonical almost complex structure J1 on J+(M, ds2), by using moving frame theory. Moreover, for various metrics and a fixed orientation on M, a canonical bundle isomorphism is established. As a consequence, we generalize a celebrated theorem of LeBrun.

关键词： almost complex structure, integrability, twistor bundle.

RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN SEMICONDUCTOR SCIENCE

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Acta Mathematica Scientia 2007年第2期27卷 437-448页

作者：黎勇 College of Applied Science beijing university of Technology

In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.

关键词： Hydrodynamic models nonisentropic Euler-Poisson momentum relaxation time limit energy relaxation time limit

Operator-Valued Fourier Multipliers on Multi-dimensional Hardy Spaces

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Chinese Annals of Mathematics,Series B 2011年第2期32卷 293-302页

作者： Shangquan BU department of mathematical sciences Tsinghua University Beijing 100084 China

The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces Hp(Td;X),where 1 ≤ p < ∞,d ∈ N,and X is an AUMD Banach space having the property (α).The suffcient condition on the multiplier is a Marcinkiewicz type condition of order 2 using Rademacher boundedness of sets of bounded linear *** is also shown that the assumption that X has the property (α) is necessary when d ≥ 2 even for scalar-valued *** the underlying Banach space does not have the property (α),a suffcient condition on the multiplier of Marcinkiewicz type of order 2 using a notion of d-Rademacher boundedness is also given.

关键词： Hardy空间算子集多维 Banach空间傅里叶充分条件乘子定理有界性

Extremal eigenvalues of measure differential equations with fixed variation

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Science china Mathematics 2010年第10期53卷 2573-2588页

作者： ZHANG MeiRong 1,2 1 department of mathematical sciences,tsinghua university,beijing 100084,china 2 Zhou Pei-Yuan Center for Applied Mathematics,tsinghua university,beijing 100084,china department of mathematical sciences Tsinghua University Beijing China Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing China

In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely *** taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth *** results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.

关键词： measure differential equation eigenvalue extremal value weak* topology Frechét derivative sub-differential

Effects of the Biot and the squirt-flow coupling interaction on anisotropic elastic waves

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Chinese Science Bulletin 2000年第23期45卷 2130-2138页

作者： YANG Dinghui & ZHANG Zhongjie department of mathematical sciences, tsinghua university, beijing 100084, china Institute of Geophysics, Chinese Academy of sciences, beijing 100101, china department of mathematical sciences Tsinghua University Beijing China Institute of Geophysics Chinese Academy of Sciences Beijing China

Considering the velocity anisotropy of the solid/fluid relative motion and employment of the BISQ theory based on the one-dimensional porous isotropic case, we establish a two-phase anisotropic elastic wave equation to simultaneously include the Biot and the squirt mechanisms in terms of both the basic principles of the fluid’s mass conservation and the elastic-wave dynamical equations in the two-phase anisotropic rock. Numerical results, while the Biot-flow and the squirt-flow effects are simultaneously considered in the transversely isotropic (Tl) poroelastic medium, show that the attenuation of the quasi P-wave and the quasi SV-wave strongly depend on the permeability anisotropy, and the attenuation behavior at low and high frequencies is contrary. Meanwhile, the attenuation and dispersion of the quasi P-wave are also affected seriously by the anisotropic solid/fluid coupling additional density.

关键词： two-phase anisotropy Biot flow squirt-flow elastic wave attenuation and dispersion BISQ model.

A GLOBAL LINEAR AND LOCAL QUADRATIC SINGLE-STEP NONINTERIOR CONTINUATION METHOD FOR MONOTONE SEMIDEFINITE COMPLEMENTARITY PROBLEMS

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Acta Mathematica Scientia 2007年第2期27卷 243-253页

作者：张立平 department of mathematical sciences tsinghua university

A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are：（i） it is well *** for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.

关键词： Semidefinite complementarity problem noninterior continuation method,global convergence local quadratic convergence

HARMONIC MAPS VERSUS POISSON EQUATIONS ON NONCOMPACT RIEMANNIAN MANIFOLDS

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Systems Science and mathematical sciences 2000年第3期13卷 333-336页

作者： MA Li(department of mathematical sciences, tsinghua university, beijing 100084, china) 清华大学数学系北京 100084

Suppose there is a map from a noncompact riemannian manifold into a nonpositively curved riemannian manifold such that its tension field is in a suitable Banach space. Then there exists an intimate relationship between harmonic maps and Poisson equations on the domain manifold. On the basis of this observation, we can extend some results of the previous work of Tam and Li.

关键词： Harmonic maps Poisson equations complete manifolds