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Solving the input data in error correc-tion of optical fabrication by finite Fourier coefficient algorithm

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Science China(Technological Sciences) 2006年第1期49卷 50-60页

作者： CHENG Haobo1,2. SUN Guozheng3.& FENG Zhijing2.1. Department of Optical Engineering, beijing Institute of Technology, beijing 100081, China 2. Department of Precision Instruments and Mechanology, Tsinghua University, beijing 100084, China 3. China North Industries Group Corporation, beijing 100089, China 1. Department of Optical Engineering Beijing Institute of Technology Beijing 100081 China 2. Department of Precision Instruments and Mechanology Tsinghua University Beijing 100084 China 3. China North Industries Group Corporation Beijing 100089 China

A free-form lens (FFL) is a special surface that is difficult to be fabricated. FFL are usually fabricated by computer-controlled optical surfacing (CCOS) technique. During CCOS, the material removal amount is determined by the unit removal function (URF) convoluting with the input data――the dwell time. When the removal amount and the URF are known, how to solve the input data involves the special algorithm――deconvolution. Usually, the input data are solved by virtue of low pass filter or iterative methods. However, an approximation solution would destroy the machining stability nec-essary to perform precisely CCOS. In this paper, to solve the input data, a new method that is based on the finite Fourier coefficient is put forward. It can give a continuous and accurate solution for fabricating choice. Several parameters are simulated, which influ-ence the process of CCOS, and evaluating on the effect of the method is also carried out. Experimental results verify that this method is suitable for guiding the manufacturing of high precision FFL.

关键词： optical fabrication, computer controlled optical surfacing, free-form lens, finite Fourier coefficient, error correction.

Discovery of Paleogene marine stratum along the southern side of Yarlung-Zangbo suture zone and its implications in tectonics

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Science China Earth Sciences 2005年第5期48卷 647-661页

作者： LI Guobiao 1 , WAN Xiaoqiao 1 , LIU Wencan 1 , LIANG Dingyi 1 & Hyesu Yun 2.1. China University of geosciences, beijing {2. China 2. Chungnam National University, Daejon, 3.5-3.0, Korea 1. China University of geosciences 100083 Beijing China 2. Chungnam National University 305-350 Daejon Korea

The Jiachala Formatiom is a new lithostratigraphic unit set up in this paper. This is the first report on the Paleogene marine sequences and microfaunas in Gyangze to the southern side of the Yarlung-Zangbo suture zone. On the basis of fossil abundance, species diversity, dominant species and first and last occurrences of key species, three dinoflagellate assemblages and three polynological assemblages were recognized in the Jiachala Formatiom. They are in ascending order as follows: Apectodinium quinquelatum-Apectodinium hyperacanthum, Cannin- gia chinensis-Palaeoperidinium pyrophorum and Cymatiosphaera reticulosa-Samlandia chla- mydophora dinoflagellate assemblages, and Arliaceoipollenites baculatus-Anacolosidites sub- trudens, Aglaoreidia cyclops-Pinuspollenites microinsigis, and Elaeangnacites asper-Ilexpol- lenites iliacus polynological Assemblages. According to the assemblages, the age of the Jiachala Formation is referred to Paleocene-early Eocene. The preliminary study on the Jiachala Forma- tion shows that this group of Paleogene deposits accumulated in an underfilled peripheral fore- land basin which was in response to the load of the crust thickening resulted from the Asia-India collision. The stratigraphic evidences provided by the evolution of foreland basin indicate that the India-Asia initional collision should occure near the Cretaceous/Paleogene boundary. The de- velopment and evolution of the southern Tibet foreland basin was under the control of the stress field from the subduct-collision between India and Asia and the structure pattern of the basement. The withering of Tethys Sea might occur after early Eocene in the Gyangze basin and should be after Priabonian of late Eocene in southern Tibet.

关键词： Paleogene marine strata, Jiachala Formation, microfossils, underfilled peripheral foreland basin, initional collision, Gyangze.

The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

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Science China Mathematics 2005年第9期48卷 1245-1259页

作者： ZHANG Xiaoxia~(1,2. & GUO Maozheng~(1,3. 1. School of Mathematical Sciences,Peking University,beijing 100871,China 2. Department of Mathematics,Yantai University,Yantai 2.4005,China 3. LMAM,Peking University,beijing 100871,China 1. School of Mathematical Sciences Peking University 100871 Beijing China 2. Department of Mathematics Yantai University 264005 Yantai China 3. LMAM Peking University 100871 Beijing China

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group ***,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative ***,an explicit description of the multiplicative unitary operator for C(SU_q(2. )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2. ) and the discrete group G.

关键词： multiplicative unitary operator, Woronowicz C*-algebra, crossed product.

On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2.and YU Yuanhong 3.1. Department of Applied Mathematics, beijing Institute of Technology, beijing 100081, China 2. Department of Mathematics, Yunnan University, Kunming 650091, China 3. Institute of Applied Mathematics, C Department of Applied Mathematics Beijing Institute of Technology Beijing China Department of Mathematics Yunnan University Kunming China Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

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. {3. Institute of Graphic Communication, {3. 102.00, China 2. Department of Mechanics & Engineering Science, Peking University, {3. 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.

On three-dimensional geological modeling and visualization

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Science China Earth Sciences 2004年第8期47卷 739-748页

作者： WU Qiang1 & XU Hua2.1. Department of Resource Exploitation Engineering, China University of Mining and Technology, beijing 100083. China 2. beijing Institute of Petrochemical Technology, beijing 102.17, China 1. Department of Resource Exploitation Engineering China University of Mining and Technology 100083 Beijing China 2. beijing Institute of Petrochemical Technology 102617 Beijing China

The technology of 3. geological modeling will bring about great changes in the methods of geological data acquiring, storing, processing and displaying. However, no perfect or convenient software systems have been developed up to now since the geologic data which re-flect geological entities bear the feature of diversity, uncertainty and complexity. Some supervoxel models, mathematical models of fault and geometrical models of fold have been contrived so as to show the space geometric configuration of the complicated geologic structures. The application-oriented system architecture for 3. geological modeling is established; and a novel design concept based on spatial data processing is also proposed with the technology of solid modeling as its core and the application of models as its objective. Theories and methods for 3. geological modeling will hopefully be enriched and developed. In the light of these theories and methods, a feature-based navigation visualization technique is also put forward in the paper. By integrating geo-database, graphics libraries and KBS with 3. dynamic simulation systems, geologists will be able to capture the partial characteristics and whole structure embodied in the geological data in a direct-viewing, figurative and accurate manner.

关键词： 3. geological modeling,geometrical model,system architecture,visualization

The crustal structure under Sanjiang and its dynamic implications:Revealed by seismic reflection/refraction profile between Zhefang and Binchuan,Yunnan

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Science China Earth Sciences 2005年第9期48卷 1329-1336页

作者： ZHANG Zhongjie1, BAI Zhiming1, WANG Chunyong2. TENG Jiwen1, Lü Qingtian3. LI Jiliang1, LIU Yifeng1 & LIU Zhenkuan4 1. Institute of Geology and Geophysics, Chinese Academy of Sciences, beijing 10002., China 2. Institute of Geophysics, China Seismological Bureau, beijing 100085, China 3. Institute of Deposition Resource, Chinese Academy of {2., beijing 10003., China 4. School of Exploration and Information, China University of {2., beijing 100083. China 1. Institute of Geology and Geophysics Chinese Academy of Sciences 100029 Beijing China 2. Institute of Geophysics China Seismological Bureau 100085 Beijing China 3. Institute of Deposition Resource Chinese Academy of Geosciences 100037 Beijing China 4. School of Exploration and Information China University of Geosciences 100083 Beijing China

The fault belts in Sanjiang mainly include Jinshajiang-Honghe fault, Lancangjiang fault and Nujiang fault (called Sanjiang faults) in western Yunnan Province, China. By interpreting the wide-angle seismic reflection/refraction profile between Zhefang and Binchuan, which crosses Tengchong and Baoshan blocks in Dianxi (western Yunnan) tectonic zone, we recon- struct the crustal structure with seismic traveltime tomography for crustal P-wave velocity and the seismic scattering image for crustal seismic reflection structure. In this paper, we firstly present the crustal structure images of P-wave velocity and seismic reflection under the wide-angle seismic profile. These results demonstrate that, the crustal velocity structure and seismic reflec- tion structure along the profile can be divided into 3.segments, and there is an obvious difference of crustal structure among the eastern, the western and the middle segment. Generally, crustal P-wave velocities in the Baoshan segment are 0.1―0.2.km/s slower and seismic reflection am- plitudes from Moho discontinuity are stronger than the other 2.segments. In the studied area, crustal thickness is about 40 km, and shows the thickening tendency from west to east along the profile. Additionally, it can be seen that there is one strong-amplitude seismic reflection event as bright points at the depths of 8―10 km, along the segment of 80―115 km of the profile (south- ward of Tengchong); and seismic reflection wave-field from Moho discontinuity varies obviously along the lateral direction. Finally, we make some discussions on the crustal thickening pattern in the Sanjiang fault belt, structural environment of earthquake development and the contact rela- tionship between the Tengchong block, Banshan block and Luxi trough.

关键词： Sanjiang area wide-angle seismic profile crustal structure.

Compression behavior of Zr_(41)Ti_(14)Cu_(12.5)Ni_(10)Be_(2..5) bulk metallic glass up to 2. GPa

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Science China(Physics,Mechanics & Astronomy) 2005年第3期48卷 319-324页

作者： LI Gong 1, 2., ZHAN Zaiji 2., LIU Jing 3., YUN Jinku 1 , SUN Liling 2., LIU Riping 1 , ZHANG Jun 2.& WANG Wenkui 1, 2.1. Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China 2. Center for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, beijing 100080, China 3. BSRF, Institute of High Energy Physics, Chinese Academy of Sciences, beijing 10003., China 1. Key Laboratory of Metastable Materials Science and Technology Yanshan University 066004 Qinhuangdao China 2. Center for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences 100080 Beijing China 3. BSRF Institute of High Energy Physics Chinese Academy of Sciences 100039 Beijing China

The compression of a Zr41Ti14Cu12.5Ni10Be2..5 bulk metallic glass (BMG) is investigated at room temperature up to 2. GPa using in-situ high pressure energy dispersive X-ray diffraction with a synchrotron radiation source. The pressure-induced structural relaxation is exhibited. It is found that below about 8 GPa, the existence of excess free volume contributes to the rapid structural relaxation, which gives rise to the rapid volumetric change, and the structural relaxation results in the structural stiffness under higher pressure.

关键词： bulk metallic glass, high pressure, structural relaxation, synchrotron radiation.

On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution

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Chinese Science Bulletin 1998年第6期43卷 450-458页

作者： JING Ping 1 and ZHU Lixing 2.1. Mathematics Lab, China University of Mining & Technology, beijing 100083. China 2. Probability Lab, Institute of Applied Mathematics, Chinese Academy of Sciences, beijing 100080, China Mathematics Lab China University of Mining & Technology Beijing China Probability Lab Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.

关键词： bootstrap approximation projection pursuit type statistic elliptical symmetry.