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SERIES REPRESENTATION OF DAUBECHIES' WAVELETS

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Journal of Computational Mathematics 1997年第1期15卷 81-96页

作者： X.G. Lu (department of Applied Mathematics, tsinghua university, beijing, china) 清华大学应用数学系北京

This paper gives a kind of series represeotation of the scaling functions φNand the associated wavelets . constructed by Daubechies. Based on Poission sununation formula, the functions gh. φN(x+N-1), φN (x+N),'''' φN (x+2N-2)(Ox 1) are linearly represented by φN(x), φN(x + 1),''', φN(x + 2N - 2) and some polynomials of order less than N, and φ0(x):= (φN (x), φN (x + 1),''', φN (x + N -2))t is translated into a solution of a nonhomogeneous vectorvalued functional equationwhere A0, A1 are (N - 1) x (N - 1)-dimensional matrices, the components of P0(x), P1 (x) are polynomials of order less than N. By iteration, .φ0(x) is eventualy represented as an (N - 1)-dimensional vector series with vector norm where and

关键词： Pro ER Math Si WAVELETS SERIES REPRESENTATION OF DAUBECHIES

The numerical method for three-dimensional impact with friction of multi-rigid-body system

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Science china(Physics,mechanics & Astronomy) 2006年第1期49卷 102-118页

作者： ZHAO Zhen1,2, LIU Caishan2 & CHEN Bin2 1. beijing Institute of Graphic Communication, beijing 102600, china 2. department of mechanics & engineering Science, Peking university, beijing 100871, china beijing Institute of Graphic Communication Beijing 102600 China department of mechanics & engineering Science Peking University Beijing 100871 China

The differential equations for planar impacts reduce to an algebraic form, and can be easily solved. For three dimensional impacts with friction, there is no closed-form solution, and numerical integration is required due to the swerve behavior of tangential impulse during collisions. The dynamic governing equations in the impact process are built up in impulse space based on the Lagrangian equation in this paper. The coefficient of restitution defined by Poisson is used as the condition of impact termination. A valid nu- merical method for solving three-dimensional frictional impact of multi-rigid body system is established. The singular cases of tangential movement in sticking point are especially noticed and analyzed. Several examples are present to reveal the different kinds of tan- gential movement modes varied with the normal impulse during collision.

关键词： multi-rigid body, impact, friction.

Dense coding scheme using superpositions of Bell-states and its NMR implementation

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Science china(Physics,mechanics & Astronomy) 2005年第1期48卷 57-67页

作者： ZHANG Jingfu, XIE Jingyi, DENG Zhiwei & LU Zhiheng Key Laboratory for Quantum Information and Measurements, department of Physics, tsinghua university, beijing 1.0084, china Center for Quantum Information, tsinghua university, beijing 1.0084, china department of Materials Science and engineering, beijing Normal university, beijing 100875, china Testing and Analytical Center, beijing Normal university, beijing 100875, china department of Physics, beijing Normal university, beijing 100875, china 1. Key Laboratory for Quantum Information and Measurements Department of Physics Tsinghua University 100084 Beijing China 2. Center for Quantum Information Tsinghua University 100084 Beijing China 3. department of Materials Science and engineering Beijing Normal University 100875 Beijing China 4. Testing and Analytical Center Beijing Normal University 100875 Beijing China 5. department of Physics Beijing Normal University 100875 Beijing China

Dense coding using superpositions of Bell-states is proposed. The generalized Grover's algorithm is used to prepare the initial entangled states, and the reverse process of the quantum algorithm is used to determine the entangled state in the decoding measurement. Compared with the previous schemes, the superpositions of two Bell-states are exploited. Our scheme is demonstrated using a nuclear magnetic resonance (NMR)quantum computer. The corresponding manipulations are obtained. Experimental results show a good agreement between theory and experiment. We also generalize the scheme to transmit eight messages by introducing an additional two-state system.

关键词： dense coding, superpositions of Bell-states, generalized Grover's algorithm, nuclear magnetic res-onance, quantum computer.

THE EXISTENCE OF J-HOLOMORPHIC CURVES AND APPLICATIONS TO THE WEINSTEIN CONJECTURE

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Chinese Annals of Mathematics,Series B 1999年第4期20卷 425-434页

作者： MA RENYI(department of Applied Mathmatics, tsinghua university, beijing 1.0084, china) tsinghua Univ Dept Appl Math Beijing 100084 Peoples R China

The author first proves the existences of J-holomorphic curves in the symplectizations of Legendre fibrations and then as an application confirms the Weinstein conjectures on contact manifolds of Legendre fibrations. As a corollary a new proof on the theorem due to Hofer,Viterbo, Gluck, Ziller, Weinstein and Ljusternik-Fet Theorem is provided, which is quite different from their original proofs.

关键词： Symplectic geometry J-holomorphic curves Periodic orbit

DYNAMIC AND KINEMATIC WAVE MODELSFOR 1-D RILL FLOW: A COMPARISON

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International Journal of Sediment Research 1999年第2期14卷 95-105页

作者： SHAO Xuejun (department of Hydraulic engineering, tsinghua university, beijing 1.0084, china)

Overland flows on hillslopes due to rainfall excess are numerically simulated with a simplified strip microtopography which has one single straight rill, and comparisons are made between predictions of a dynamic wave model (DWM) and a kinematic wave model (KWM). Overland flow on the strip is treated as one-dimensional and interrill flow is not simulated. The DWM is based on the Saint-Venant equation, and the KWM is derived using the Chezy formula. A numerical scheme is developed which solves the non-linear DWM equations in a similar way to that of solving the KWM equations, *** the basis of the method of characteristics. This scheme greatly reduces the complexity of the solution procedure and therefore allows the use of DWM in process-based catchment models involving a large number of topographical elements, i.e., hillslopes. Simulation result shows that. in terms of the predicted flow velocity V and depth h, the *** model is an accurate approximation to the dynamic one for broad sheet overland flows resulted from normal rainfall excess rates (1-3 mm/min). However. for small rill width, e.g. B20cm. or if the rainfal excess rate is extremely large (e.g.. 20 mm/min). differences of V and h between the two models will be significant. In general, the KWM tends to underestimate rill flow depth but overestimate its velocity, especially for small rill width. though it does give the same steady discharge per unit width, q =V h, as that predicted by DWM for steady rainfall excess rate. At the rising stage of the hydrograph, KWM predicts higher unit width discharge q, which leads to overestimation of rill detachment as a stream power function method is used.

关键词： Overland flow Rill flow Kinematic wave model Method of characteristics

Shrinkage Behaviour of Spheroidal Graphite Cast Iron in Green and Dry Sand Molds for the Benchmarking of Solidification Simulation

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Journal of Materials Science & Technology 2001年第6期17卷 610-614页

作者： Wenzhen LI and Baicheng LIU department of Mechanical engineering, tsinghua university, beijing 1.0084, china Jiarong LI beijing Institute of Aeronautical Materials, beijing 100095, china [Manuscri Tsing Hua Univ Dept Mech Engn Beijing 100084 Peoples R China beijing Inst Aeronaut Mat Beijing 100095 Peoples R China

The effects of metallurgical and processing parameters on the formation of shrinkage cavities and porosities in spheroidal graphite cast iron have been studied, considering the parameters of carbon equivalent, inoculation, casting modulus, mold type (green or dry) and pouring temperature within specific ranges of these variables. Based on the orthogonal experiments, the metallurgical and processing parameters of the minimum casting shrinkage and the maximum casting shrinkage were obtained, and the effects of metallurgical and processing parameters on the formation of shrinkage cavities and porosities in spheroids graphite cast iron castings were discussed. Finally, two regression equations relating these variables to the formation of shrinkage porosity were derived based upon the orthogonal experiments conducted.

关键词： Shrinkage Behaviour of Spheroidal Graphite Cast Iron in Green and Dry Sand Molds for the Benchmarking of Solidification Simulation Graphite Simulation Cast

Studies of the unsteady supersonic base flows around three afterbodies

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Acta Mechanica Sinica 2009年第4期25卷 471-479页

作者： Zhixiang Xiao Song Fu School of Aerospace engineering,tsinghua university, 1.0084 beijing, china School of Aerospace engineering Tsinghua University 100084 Beijing China

Unsteady supersonic base flows around three afterbodies, cylindrical （Cy）, boattailed （BT） and three-step （MS）, are investigated in this paper. Reynolds-averaged Navier-Stokes （RANS） and two RANS/LES （large-eddy simulation） hybrid methods, detached eddy simulation （DES） and delayed-DES （DDES）, are used to predict the base flow characteristics around the baseline Cy afterbody. All the RANS and hybrid methods are based on the two-equation SST （shear-stress transport） model with compressible corrections （CC）. According to the comparison of measurements, both DES and DDES can produce more satisfactory results than RANS. RANS can only present the ＂stable＂ flow pat- terns, while the hybrid methods can demonstrate unsteady flow structures. DDES and DES results are little different from one another although the latter exhibits better agreement with the experiment. DES is taken to investigate the 5° BT and three-step afterbodies. The mean flow data and the instantaneous turbulent coherent structures are compared against available measurements.

关键词： Cylindrical Boattailed and three-stepafterbodies DES and DDES Unsteady flow

The Influence of Preheat Temperature of Steel Plate on Steel-mushy Cu-graphite Bonding

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Journal of Wuhan university of Technology(Materials Science) 2006年第3期21卷 12-14页

作者：张鹏 department of Mechanical engineering Beijing Jiaotong UniversityBeijing 100044China

The pressing bonding of steel plate to QTi3.5-3.5 graphite slurry was conducted. Under the conditions of 530 ℃ for the preheat temperature of dies, 45% for the solid fraction of QTi3.5- 3.5 graphite slurry, 50 MPa for the pressure and 2 min for the pressing time, the relationship between the preheat temperature of steel plate and interfacial mechanical property of bonding plate was studied. The results show that when the preheat temperature of steel plate is lower titan 618 ℃ , the interfacial shear strength of bonding plate increases with the increasing of the preheat temperature of steel plate. When the preheat temperature of steel plate is higher than 618 ℃ , the interfacial shear strength decreases with the increasing of the preheat temperature of steel plate. When the preheat temperature of steel plate is 618 ℃ , the highest interfacial shear strength of bonding plate of 127.8 MPa can be got.

关键词： steel-mushy QTi3.5-3.5 graphite pressing bonding interfacial shear strength preheat temperature of steel plate

VISUALIZATION AND ANALYSIS OF LONGITUDINAL VORTICES AT CURVED WALLS OF 2D LAMINAN AND TURBULENT CHANNEL FLOWS

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Acta Mechanica Sinica 1988年第1期4卷 1-7页

作者： Zhang Zhaoshun Wang Xilin department of engineering mechanics, tsinghua university, beijing 1. department of engineering mechanics Tsinghua University Beijing

The 3D structure of longitudinal vortices at the curved walls of both laminar andturbulent channel flows are visualized by the hydrogen bubble technique. Together with theconditional sampling of the turbulent characte... 详细信息

关键词： turbulence coherent structure visualization.