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A note on spline wavelets

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Chinese Science Bulletin 1997年第15期42卷 1250-1253页

作者： LIU YoumingDepartment of applied Mathematics, beijing Polytechnic University,{2.,{3. Department of applied Mathematics Beijing Polytechnic University Beijing China

THE B-spline wavelets Nm （x） play an important role in the approximation theory sincethey are piecewise polynomials so that they may be used to fit a function and its derivatives atthe integers. However, except for m=1, 2. they do not have the interpolating property (i.e. Nm（n） ≠δn0. In this work, we shall construct a family of scaling functions of fatherwavelets which have the interpolating property and whose Fourier transforms are spline func-tions. As usual, these functions can be orthogonalized by Meyer’s technique and the corre-sponding mother wavelets ψ may be found by the

关键词： wavelets scaling function cardinality.

Lie symmetry and conservation law of Birkhoffian system

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Chinese Science Bulletin 1999年第4期44卷 318-320页

作者： MEI FengxiangDepartment of applied Mechanics , beijing Institute of Technology, beijing 100081,{3. Department of applied Mechanics Beijing Institute of Technology Beijing China

The Lie symmetry of Birkhoffian system was studied, the condition under which the system admits the one-parameter Lie group of transformation with infinitesimal generator was given, and the structural equation and the... 详细信息

关键词： symmetry conservation law Birknoffian system.

Oscillatory periodic solutions of differential-delay equations with multiple lags

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Chinese Science Bulletin 1997年第6期42卷 444-447页

作者： GE WeigaoDepartment of applied Mathematics, beijing Institute of Technology, beijing 100081,{3. Department of applied Mathematics Beijing Institute of Technology Beijing 100081 China

BASED on the Nussbaum’s results, we studied in ref. [2. the conditions for the existence of oscillatory periodic solutions to the differential-delay equations (DDEs)

关键词： differential-delay equation periodic solution multiple lags.

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,{2.) 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+2.-2.(Ox 1) are linearly represented by φN(x), φN(x + 1),''', φN(x + 2. - 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

MD simulation of the effect of contact area and tip radius on nanoindentation

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Science china(Physics,Mechanics & Astronomy) 2004年第1期47卷 101-112页

作者： CHEN Shangda1,2.& KE Fujiu1,2.1. Department of applied Physics, beijing University of Aeronautics and Astronautics, beijing 100083.{3. 2. State Key Laboratory of Non-linear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, beijing 100080,{3. Correspondence should be addressed to Chen Shangda (email: chensd@***) Received August 2., 2.03 1. Department of applied Physics Beijing University of Aeronautics and Astronautics 100083 Beijing China 2. State Key Laboratory of Non-linear Mechanics (LNM) Institute of Mechanics Chinese Academy of Sciences 100080 Beijing China

Molecular dynamics simulations of nanoindentation are performed on monocrystal copper. A new contact atoms method is presented for calculating the contact area. Compared with conventional methods, this method can provide the contact area more accurately not only for sink-in but also for pile-up situation. The effect of tip radius on indentation is investigated too. The results indicate that the measured hardness of the material will become higher as the tip radius increases.

关键词： nanoindentation, molecular dynamics, contact area, zero point of penetration depth, nano- hardness.

Void damage model and service life prediction for solid high polymer

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Chinese Science Bulletin 2001年第21期46卷 1842-1845页

作者： SHEN TingfangDepartment of applied Physics, beijing Institute of Technology, beijing 100081,{3. Department of applied Physics Beijing Institute of Technology Beijing China

Based on the analysis of three void damage variety models, this note presents (i) a method that regards the void content as a damage variation of the grain and (ii) a geometric model for micro-unit of void damage. Equations of the void damage variety containing void content are analyzed. This work is focused on the measurement of internal damage level and the damage variety estimation is directly related to the life predication in the practical engineering applications. Nowadays, the critical service life of the solid grain/polymers is usually presumed at domestic and international level. The strength or strain reduction of 2.% or the stabilizer consumption of 50% is generally regarded as a critical storage life of the solid grain/polymers, and the service life is predicted by the extrapolation method on An-henius formula. The applications, however, show that the above method is unreliable and has significant errors. With the aid of the discontiguous automatic measuring device of real time volume

关键词： void content void damage thermal aging service life damage mechanics.

Accuracy of Lax-Wendroff scheme for discontinuous solutions of convection equations

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Chinese Science Bulletin 1997年第24期42卷 2047-2051页

作者： DING LijuanDepartment of applied Mathematics, beijing Institute of Technology, beijing 100081,{3. Department of applied Mathematics Beijing Institute of Technology Beijing China

IT is known from Brenner, Thomee and Wahlbin that the well-known second-order Lax-Wendroff scheme is stable in L^2. but unstable in L^p, p≠2. Generally speaking, if the initialdata is smooth enough and if a difference scheme, which is stable in L^p for some p, has orderof accuracy μ, then we can expect that the solution of the difference scheme converges to thesolution of the differential equation at the rate of order μ in L^p. But for discontinuous solu-tions, which are essential to hyperbolic equations, the above expectation is not true. Error es-timates for discontinuous solutions not only have theoretical meaning, but also practical value.

关键词： Lax-Wendroff scheme modlfled equation discontinuous solutions error estimate.

The State-of-Art and Development Trends of HSLA Steels in china

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Journal of Iron and Steel Research International 2011年第S1期18卷 1-13页

作者： WENG Yu-qing 1,YANG Cai-fu 2.SHANG Cheng-jia 3.(1.The Chinese Society for Metals,beijing,PR{2. 2.Centre Iron and Steel Research Institute,beijing,PR{2. 3.University of Science and Technology beijing,beijing,PR{2.) Chinese Soc Met Beijing Peoples R China Ctr Iron & Steel Res Inst Beijing Peoples R China Univ Sci & Technol beijing Beijing 100083 Peoples R China

During the last decade,the adjustment of product segments always is a very important task of iron industry,and upgrading of steel products has been impelled actively by Chinese iron and steel *** rapidly increasing of iron & steel production,a series of research achievements have been made in the technology area of high strengthtoughness steel,and also have been applied successfully in the actual production,*** technology of fine grain and ultra-fine grain steels,the technology for the control of microalloying ***,It is an important strategic goal of "Twelfth Five-year Plan" for Chinese iron and steel industry that the adjustment of steel product segments and meeting the requirements for upgrading of domestic and oversea equipment manufactory *** HSLA steel with better performance,instead of plain steel,could save steel consumption largely,and also release pressures from resource,energy and *** doubt,it is the only way to realize the sustained development of Chinese iron and steel industry by popularizing the application of HSLA steels vigorously.

关键词： HSLA steel microalloying technology Chinese iron and steel industry

Numerical simulation of strain localization and damage evolution in large plastic deformation using mixed finite element method

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Journal of University of Science and Technology beijing 2004年第3期11卷 273-277页

作者： Zhanghua Chen Jiajian Jin Jiumei Xiao applied Science School, University of Science and Technology beijing, beijing 100083.{3. applied Science School University of Science and Technology Beijing Beijing 100083 China

An investigation of computer simulation is presented to analyze the effectsof strain localization and damage evolution in large plastic deformation. The simulation is carriedout by using an elastic-plastic-damage coupling finite element program that is developed based onthe concept of mixed interpolation of displacement/pressure. This program has been incorporated intoa damage mechanics model as well as the corresponding damage criterion. To illustrate theperformance of the proposed approach, a typical strain localization problem has been simulated. Theresults show that the proposed approach is of good capability to capture strain localization andpredict the damage evolution.

关键词： strain localization mixed element truesdell stress rate material damage