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The Establishment of the Projections of Four to Seven-Dimensional Rectangular Coordinate Systems into the Three-Dimensional Space
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作者 Shi Kaida(Zhoushan Teachers’ College, Zhejiang, China) 《浙江海洋学院学报(人文科学版)》 1995年第1期1-8,共8页
Starting from the finite rotation group,the author makes a penetrating study of 4 to 7-dimensional hypercube so that we have acquired the projection models of 4 to 7-dimeneional spatial rectangular coordinate systems ... Starting from the finite rotation group,the author makes a penetrating study of 4 to 7-dimensional hypercube so that we have acquired the projection models of 4 to 7-dimeneional spatial rectangular coordinate systems into the three-dimensional space to have the 4 to 7-dimensional geometric figures demonstrated correctly. 展开更多
关键词 finite ROTATION group rectangular coordinate system hypercube.projection model.
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On Marginal Coordinate Test with Multivariate Responses
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作者 DONG Yuexiao LI Lei 《Journal of Systems Science & Complexity》 2026年第1期3-16,共14页
The authors extend the marginal coordinate test for predictor contribution(Cook,2004)to the case with multivariate responses.Instead of explicitly specifying the link functions between the responses and the predictors... The authors extend the marginal coordinate test for predictor contribution(Cook,2004)to the case with multivariate responses.Instead of explicitly specifying the link functions between the responses and the predictors,an asymptotic test is proposed under the normality assumption of the predictors as well as an asymmetry assumption about the unknown regression mean function.When these assumptions are violated,the asymptotic test with elliptical trimming and clustering is still valid with desirable numerical performances. 展开更多
关键词 Marginal coordinate hypotheses minimum volume ellipsoid K-means clustering ordinary least squares sufficient dimension reduction
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Quasi-real time inversion method of three-dimensional epicenter coordinate, trigger time, and magnitude based on CORS 被引量:1
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作者 Xiao Dongsheng Chang Ming +2 位作者 Su Yong Hu Qijun Yu Bing 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2016年第3期425-433,共9页
This study explores the quasi-real time inversion principle and precision estimation of three-dimensional coordinates of the epicenter, trigger time and magnitude of earthquakes with the aim to improve traditional met... This study explores the quasi-real time inversion principle and precision estimation of three-dimensional coordinates of the epicenter, trigger time and magnitude of earthquakes with the aim to improve traditional methods, which are flawed due to missing information or distortion in the seismograph records. The epicenter, trigger time and magnitude from the Lushan earthquake are inverted and analyzed based on high-frequency GNSS data. The inversion results achieved a high precision, which are consistent with the data published by the China Earthquake Administration. Moreover, it has been proven that the inversion method has good theoretical value and excellent application prospects. 展开更多
关键词 continuous operation reference station (CORS) trigger time three dimensional coordinate MAGNITUDE inversion
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Comprehensive two-dimensional river ice model based on boundary-fitted coordinate transformation method 被引量:1
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作者 Ze-yu MAO Jing YUAN +2 位作者 Jun BAO Xiao-fan PENG Guo-qiang TANG 《Water Science and Engineering》 EI CAS CSCD 2014年第1期90-105,共16页
River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal pro... River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy. 展开更多
关键词 two-dimensional river ice numerical model boundary-fitted coordinate technology river ice process freeze-up MacCormack scheme natural river
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One-dimensional (1D) europium coordination polymer wires:Synthesis,characterization and photoluminescence properties 被引量:1
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作者 罗龙飞 徐蓉 +1 位作者 赵东 钟声亮 《Journal of Rare Earths》 SCIE EI CAS CSCD 2010年第S1期106-110,共5页
1D europium coordination polymer wires were successfully prepared by reacting europium chloride with tributyl phosphate(TBP) at 160 oC for 12 h. The products were characterized by XRD,IR,TG,DTA,SEM,and EDS. SEM result... 1D europium coordination polymer wires were successfully prepared by reacting europium chloride with tributyl phosphate(TBP) at 160 oC for 12 h. The products were characterized by XRD,IR,TG,DTA,SEM,and EDS. SEM results showed that the wires were with diameters ranging from several hundreds of nanometers to ~5 μm and lengths going up to several hundreds of micrometers. Influencing factors such as the dosage of reactants and reaction time on the preparation were systematically investigated. Strong emission centering at 590 nm was realized in the coordination polymer wires on excitation at 395 nm. 展开更多
关键词 one dimensional solvothermal synthesis EUROPIUM coordination polymer rare earths
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Two-dimensional analyses of delamination buckling of symmetrically cross-ply rectangular laminates 被引量:5
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作者 薛江红 罗庆姿 +1 位作者 韩峰 刘人怀 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第5期597-612,共16页
The conventional approach to analysis the buckling of rectangular laminates containing an embedded delamination subjected to the in-plane loading is to simplify the laminate as a beam-plate from which the predicted bu... The conventional approach to analysis the buckling of rectangular laminates containing an embedded delamination subjected to the in-plane loading is to simplify the laminate as a beam-plate from which the predicted buckling load decreases as the length of the laminate increases. Two-dimensional analyses are employed in this paper by extending the one-dimensional model to take into consideration of the influence of the delamination width on the buckling performance of the laminates. The laminate is simply supported containing a through width delamination. A new parameterβ defined as the ratio of delamination length to delamination width is introduced with an emphasis on the influence of the delamination size. It is found that (i) when the ratio β is greater than one snap-through buckling prevails, the buckling load is determined by the delamination size and depth only; (ii) as the ratio β continues to increase, the buckling load will approach to a constant value. Solutions are verified with the well established results and are found in good agreement with the latter. 展开更多
关键词 two-dimensional analysis rectangular laminate DELAMINATION BUCKLING laminate theory
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Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method 被引量:1
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作者 Qiuhong Li Wenhao Huang +3 位作者 Joey Sanchez Ping Wang Qiang Ding Jiufa Wang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第3期2093-2121,共29页
Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved ... Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics. 展开更多
关键词 rectangular plate with cutouts the independent coordinate coupling method elastic boundary conditions free vibration analysis
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Intelligent Layout Method of the Powerhouse for Tank & Armored Vehicles Based on 3-Dimensional Rectangular Packing Theory 被引量:1
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作者 王延龙 毛明 +1 位作者 陆一平 别杰民 《Defence Technology(防务技术)》 SCIE EI CAS 2005年第1期17-24,共8页
Probes into a new and effective method in arranging the powerhouses of tank & armored vehicles. Theory and method of 3-dimensional rectangular packing are adapted to arrange effectively almost all the systems and ... Probes into a new and effective method in arranging the powerhouses of tank & armored vehicles. Theory and method of 3-dimensional rectangular packing are adapted to arrange effectively almost all the systems and components in the powerhouse of the vehicle, thus the study can be regarded as an attempt for the theory's engineering applications in the field of tank & armored vehicle design. It is proved that most parts of the solutions attained are reasonable, and some of the solutions are innovative. 展开更多
关键词 智能规划法 坦克装甲 三维矩形装填 电力管理装置
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NUMERICAL SIMULATION OF THREE DIMENSIONAL TURBULENT FLOW IN SUDDENLY EXPANDED RECTANGULAR DUCT
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作者 郭加宏 徐弘一 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第4期366-372,共7页
In this paper,to simulate the three dimensional turbulent flow in suddenly expanded rectangular duct numerically,the SIMPLEC algorithm is employed to solve the incompressible Navier-Stckes equation with k-εturbulenc... In this paper,to simulate the three dimensional turbulent flow in suddenly expanded rectangular duct numerically,the SIMPLEC algorithm is employed to solve the incompressible Navier-Stckes equation with k-εturbulence model.The numerical resulis show well the three dimensional turbulent flow field in the rectangular duct behind the sudden expansion cross-section. and agree.fairly well with the experimental result of the length of the main circumfluence.The numerical method of this paper can be applied to numerical analysis of this kind of turbulent flow. 展开更多
关键词 turbulent flow three dimensional numerical simulation suddenly expanded rectangular duct
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A One-dimensional Cd(Ⅱ)Coordination Polymer Constructed from 1,4-Benzene-dicarboxylic Acid and 3-(2,6-Di(pyrazin-2-yl)pyridin-4-yl)-1H-indole:Synthesis,Structure and Photoluminescence 被引量:2
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作者 谢玲 卢丽萍 朱苗力 《Chinese Journal of Structural Chemistry》 SCIE CAS CSCD 2016年第10期1606-1614,共9页
A new coordination polymer {[Cd(C_(21)H_(14)N_6)(C_8H_4O_4)]·H_2O}_n(1) was synthesized by an elaborate design via the reaction of 3-(2,6-di(pyrazin-2-yl)pyridin-4-yl)-1H-indole(bppi),1,4-benzene-... A new coordination polymer {[Cd(C_(21)H_(14)N_6)(C_8H_4O_4)]·H_2O}_n(1) was synthesized by an elaborate design via the reaction of 3-(2,6-di(pyrazin-2-yl)pyridin-4-yl)-1H-indole(bppi),1,4-benzene-dicarboxylic acid(H2bdc) and cadmium(Ⅱ) nitrate in CH_3OH/H_2O mixed solvents. Complex 1 crystallizes in orthorhombic,space group Ccca with a = 20.012(4),b = 31.881(6),c = 19.808(4) ?,V = 12638(4) ?~3,Z = 16,C_(29)H_(20)CdN_6O_5,M_r = 644.91,D_c = 1.356 g·cm^(-3),μ = 0.735 mm^(-1),F(000) = 5184,GOOF = 1.046,the final R = 0.0405 and wR = 0.1063 for 6870 observed reflections(I 〉 2σ(I)). The Cd(Ⅱ) centre is hepta-coordinated by three N and four O atoms from one bppi terminal ligand and two bdc2– ligands,respectively,displaying a capped trigonal prism geometry. Structure extension gives coordination polymeric chains,in which the bdc2– linkers connect Cd(Ⅱ) cations into a one-dimensional(1D) coordination polymer along the c axis,giving zigzag chains with the Cd···Cd separation of 11.178(1) ?. The adjacent bppi terminal ligands in the chains are anti-periplanar conformation. The three-dimensional(3D) structure is stabilized by π···π stacking and hydrogen-bonding interactions to form a supramolecular self-penetrating network with 1D channels. In 1,there are voids 2999.7 ?~3 with 23.7% of per unit cell volume. Thermal analysis indicates that the framework of 1 is stable until 651 K and the photoluminescence of 1 in the solid shows very weak fluorescence at 382 and 560 nm upon excitation at 310 nm. 展开更多
关键词 1 4-benzenedicarboxylic acid 3-(2 6-di(pyrazin-2-yl)pyridin-4-yl)-1H-indole one-dimensional cadmium(Ⅱ) coordination polymer π···π stacking interactions photoluminescence
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A New Two-dimensional Cd(Ⅱ) Coordination Polymer Constructed by Pyridine-2,5-dicarbohydrazide
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作者 张庆富 杨明 +2 位作者 熊克才 江飞龙 洪茂椿 《Chinese Journal of Structural Chemistry》 SCIE CAS CSCD 2009年第7期807-812,共6页
A new two-dimensional Cd(Ⅱ) coordination polymer, [Cd(2,5-pdch)(H2O)]n·2n(ClO4)·nH2O (2,5-pdch = pyridine-2,5-dicarbohydrazide), was prepared and characterized by elemental analysis, IR spectra an... A new two-dimensional Cd(Ⅱ) coordination polymer, [Cd(2,5-pdch)(H2O)]n·2n(ClO4)·nH2O (2,5-pdch = pyridine-2,5-dicarbohydrazide), was prepared and characterized by elemental analysis, IR spectra and single-crystal X-ray diffraction analysis. The crystal belongs to monoclinic, space group P21/c with a = 10.905(2), b = 11.602(1), c = 15.034(2) A, β = 117.794 (10°, V = 1682.8(4A3, Z = 4, C7H13CdCl2NsO12, Mr = 542.52, Dc = 2.141 g/cm^3,/μ = 1.691 mm^-1, F(000) = 1072, 2(MoKa) = 0.71073A, the final R = 0.0608 and wR = 0.1329 for 2972 observed reflections with I 〉 2σ(I). Single-crystal X-ray diffraction analysis reveals that the Cd(Ⅱ) atom displays a distorted pentagonal-bipyramidal geometry coordinated by three N atoms and three O atoms from three different 2,5-pdch ligands, and one water molecule. Interestingly, each two Cd(Ⅱ) atoms are bridged by two carbohydrazide groups of the 2,5-pdch ligands to form a dimeric unit, and such dimeric units are further connected by the 2,5-pdch ligand to generate a two-dimensional (4,4)-network. 展开更多
关键词 cadmium (Ⅱ) TWO-dimensional coordination polymer CARBOHYDRAZIDE
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Stability Analysis of Contact Scanning Probe for Micro/Nano Coordinate Measuring Machine 被引量:2
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作者 李瑞君 范光照 +3 位作者 钱剑钊 黄强先 龚伟 苗晋伟 《纳米技术与精密工程》 EI CAS CSCD 2012年第2期125-131,共7页
关键词 微纳米三坐标测量机 扫描探头 稳定性分析 传感哭喊中
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Enhanced hyperspectral imagery representation via diffusion geometric coordinates
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作者 何军 王庆 李滋刚 《Journal of Southeast University(English Edition)》 EI CAS 2009年第3期351-355,共5页
The concise and informative representation of hyperspectral imagery is achieved via the introduced diffusion geometric coordinates derived from nonlinear dimension reduction maps - diffusion maps. The huge-volume high... The concise and informative representation of hyperspectral imagery is achieved via the introduced diffusion geometric coordinates derived from nonlinear dimension reduction maps - diffusion maps. The huge-volume high- dimensional spectral measurements are organized by the affinity graph where each node in this graph only connects to its local neighbors and each edge in this graph represents local similarity information. By normalizing the affinity graph appropriately, the diffusion operator of the underlying hyperspectral imagery is well-defined, which means that the Markov random walk can be simulated on the hyperspectral imagery. Therefore, the diffusion geometric coordinates, derived from the eigenfunctions and the associated eigenvalues of the diffusion operator, can capture the intrinsic geometric information of the hyperspectral imagery well, which gives more enhanced representation results than traditional linear methods, such as principal component analysis based methods. For large-scale full scene hyperspectral imagery, by exploiting the backbone approach, the computation complexity and the memory requirements are acceptable. Experiments also show that selecting suitable symmetrization normalization techniques while forming the diffusion operator is important to hyperspectral imagery representation. 展开更多
关键词 hyperspectral imagery diffusion geometric coordinate diffusion map nonlinear dimension reduction
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Single Camera 3-D Coordinate Measuring System Based on Optical Probe Imaging 被引量:4
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作者 MAShu-ying YUZhi-jing 《Semiconductor Photonics and Technology》 CAS 2001年第4期235-240,共6页
A new vision coordinate measuring system--single camera 3 D coordinate measuring system based on optical probe imaging is presented. A new idea in vision coordinate measurement is proposed. A linear model is deduced w... A new vision coordinate measuring system--single camera 3 D coordinate measuring system based on optical probe imaging is presented. A new idea in vision coordinate measurement is proposed. A linear model is deduced which can distinguish six freedom degrees of optical probe to realize coordinate measurement of the object surface. The effects of some factors on the resolution of the system are analyzed. The simulating experiments have shown that the system model is available. 展开更多
关键词 Three dimensional measurement Vision coordinate measurement Optical probe Linear model
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DIGITAL GENERATION OF TWO-DIMENSIONAL FIELD OF TURBULENCE FOR FLIGHT SIMULATION 被引量:1
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作者 Yelun, Xiao 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 1990年第4期239-245,共7页
In some special cases of flight simulation (e.g. for formation flight, in-flight tanking) it is required to generate a two-dimensional field of turbulence, in which the turbulent wind speeds are stochastic functions o... In some special cases of flight simulation (e.g. for formation flight, in-flight tanking) it is required to generate a two-dimensional field of turbulence, in which the turbulent wind speeds are stochastic functions of two coordinates (e.g. x in the flight direction and y in the wing span direction). For this purpose a simple and efficient technique for the digital generation of a two-dimensional field of turbulence, i.e. for the production of turbulent speed sequences on a rectangular network, is proposed in this paper. The correlation of the turbulent field so generated is found to be in good agreement with the theoretical correlation of the turbulence model, and thus the feasibility of the proposed method is verified. Two possible operation modes (off-line and on-line) of the turbulence generator in flight simulation are also discussed. 展开更多
关键词 TURBULENCE TURBULENT coordinateS verified stochastic rectangular GENERATOR transformed MINIMIZATION intuitive
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Three-dimensional cooperative guidance laws against stationary and maneuvering targets 被引量:49
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作者 Zhao Jiang Zhou Rui Dong Zhuoning 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2015年第4期1104-1120,共17页
This paper presents the cooperative strategies for salvo attack of multiple missiles based on the classical proportional navigation(PN) algorithm.The three-dimensional(3-D) guidance laws are developed in a quite s... This paper presents the cooperative strategies for salvo attack of multiple missiles based on the classical proportional navigation(PN) algorithm.The three-dimensional(3-D) guidance laws are developed in a quite simple formulation that consists of a PN component for target capture and a coordination component for simultaneous arrival.The centralized algorithms come into effect when the global information of time-to-go estimation is obtained, whereas the decentralized algorithms have better performance when each missile can only collect information from neighbors.Numerical simulations demonstrate that the proposed coordination algorithms are feasible to perform the cooperative engagement of multiple missiles against both stationary and maneuvering targets.The effectiveness of the 3-D guidance laws is also discussed. 展开更多
关键词 coordination algorithms Maneuvering target Missile guidance Multiple missiles Three-dimensional (3-D)
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THREE-DIMENSIONAL ANALYSIS OF FUNCTIONALLY GRADED PLATE BASED ON THE HAAR WAVELET METHOD 被引量:2
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作者 Zhang Chun Zhong Zheng 《Acta Mechanica Solida Sinica》 SCIE EI 2007年第2期95-102,共8页
A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. Wit... A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. With good features in treating singularities, Haar series solution converges rapidly for arbitrary distributions, especially for the case where the material properties change rapidly in some regions. Through numerical examples the influences of the ratio of material constants on the top and bottom surfaces and different material gradient distributions on the structural response of the plate to mechanical stimuli are studied. 展开更多
关键词 functionally graded material rectangular plate Haar wavelet three-dimensional analysis
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A New Two-dimensional Copper(II) Complex with p-PhDTA Bridges 被引量:1
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作者 郑磊 倪中海 +4 位作者 黎文路 张丽芳 葛春华 崔爱莉 寇会忠 《Chinese Journal of Structural Chemistry》 SCIE CAS CSCD 北大核心 2008年第7期793-796,共4页
A new p-PhDTA bridged Cu(II) complex [Cu2(p-PhDTA)(DMSO)2]·4DMSO (p-PhDTA = p-phenylenediamine-N,N,N,N'-tetraacetic acid) has been synthesized and structurally characterized. The crystal belongs to ortho... A new p-PhDTA bridged Cu(II) complex [Cu2(p-PhDTA)(DMSO)2]·4DMSO (p-PhDTA = p-phenylenediamine-N,N,N,N'-tetraacetic acid) has been synthesized and structurally characterized. The crystal belongs to orthorhombic, space group Pca21 with a = 19.572(4), b = 19.552(4), c = 10.156(2)A, C26H48N2O14CU2S6, Mr = 932.10, V = 3886.4(13)A3, Z = 4, Dc = 1.593 g/cm^3, F(000) = 1936, λ(MoKa) = 0.71073A,μ = 1.480, R = 0.0487 and wR = 0.1151 for 8464 observed reflections (I 〉2σ(I)). In the complex, the oxygen atoms of carboxylate of p-PhDTA connect the Cu atoms in a syn-anti type, giving one-dimensional chains which are further linked by the benzene groups ofp-PhDTA to form a novel two-dimensional structure. 展开更多
关键词 COPPER TWO-dimensional coordination polymer CARBOXYLATE
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Three-dimensional tidal current numerical model of the Oujiang Estuary 被引量:2
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作者 LI Mengguo LI Wendan 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2009年第3期17-25,共9页
The characteristics of three-dimensional (3-D) tidal current in the Oujiang Estuary are investigated according to in situ observations. The Oujiang Estuary has features of irregular coastline, complex topography, ma... The characteristics of three-dimensional (3-D) tidal current in the Oujiang Estuary are investigated according to in situ observations. The Oujiang Estuary has features of irregular coastline, complex topography, many islands, moveable boundary, and submerged dyke, therefore, σ 3-D numerical model oil an unstructured triangular grid has been degeloped. The σ coordinate transforination, the moveable boundary and submerged dyke treatment techniques were employed in the model so it is suitable for the tidal simulations in the Oujing Estuary with submerged dyke and moveable boundary problems. The model is evaluated with the in situ data, and the results show that the calculated water elevations at 19 stations and currents at 19 profiler stations are in good agreement with measured data both in magnitude and phase. This numerical model is applied to the 3-D tidal circulation simulations of experiments in stopping flow transport through the South Branch of the Oujiang Estuary, and the feasibility to cutoff the flow in the South Branch of the Oujiang Estuary is demonstrated by numerical simulation experiments. The developed numerical model simulated the 3-D tidal current circulations in complicated coastal and estuarine waters very well. 展开更多
关键词 Oujiang Estuary three-dimensional tidal current mathematical model numerical simulation triangular grid σ coordinate transformation
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APPROXIMATION THEORY OF THREE DIMENSIONAL ELASTIC PLATES AND ITS BOUNDARY CONDITIONS WITHOUT USING KIRCHHOFF-LOVE ASSUMPTIONS
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作者 钱伟长 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第3期203-224,共16页
The classical small deflection theory of elastic plates id based on the Kirchhoff-Lore assumptions ̄[1,2].Ther are used on the basis of the thinness of plate and the smallness of deflection.In terms of Cartesian tens... The classical small deflection theory of elastic plates id based on the Kirchhoff-Lore assumptions ̄[1,2].Ther are used on the basis of the thinness of plate and the smallness of deflection.In terms of Cartesian tensor coordinates x_i(i=0, 12)these basic assumptions are:(1)the transversal normal strain may be neglected i.e._(00)=0;(2)the transversal shear strain may be neglected i.e.e_(0α)=0(α= 1, 2)(3)the transversal normal stress may be neglected i.e.. σ_(00)=0 .In classical theory of elastic plates,the strain-displacement relations and the corresponding stress-displacement relations are established on the basis of these assumptions. And the equations of the classical theory for a set of undetermined quantities defined on the middle surface are established through integrating the three dimensional equations of equilibrium of stress over the thickness.In the previous papers ̄[3,4,5],an approximation theory is given on the basis of Ihree dimensional theory of elastic plates without using Kirchhoff-Love assumptions。However,no uniqueness study is given,and also the boundary conditions have never been studied. In this paper.the same problems are studied on the basis of generalizedvariational principle of the three dimensional theory of elastic bodies ̄[6].The stationary conditions of variation give an unique and complete set of field equations and the related boundary conditions for the approximation theory.In this paper,the first order approximation theory is studied in detail. 展开更多
关键词 three dimensional elastic plates. Kirchhoff-Love assumptions.Cartesian TENSOR coordinateS
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