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“尺规”往事
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作者 钱俊 陈月圆 《中学生数理化(八年级数学)(华师大版)》 2009年第3期43-44,共2页
在我国古代又把“尺规”叫做“规矩”.有句俗语,叫做“不以规矩,不成方圆”.那么究竟什么叫“规”?什么叫“矩”呢?
关键词 画圆工具 中学 数学教学 “尺规”
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新课标视域下小学数学“尺规作图”教学实践
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作者 陈秋蓉 《教育界》 2024年第20期5-7,共3页
“尺规作图”是新课标中“图形与几何”领域的重要内容。明确课标内“尺规作图”的内容体系、探寻教学中“尺规作图”的教育价值、探究课堂上“尺规作图”的教学路径,能引导学生在实践操作中感受数学的严谨性和精确性,进而促进其几何直... “尺规作图”是新课标中“图形与几何”领域的重要内容。明确课标内“尺规作图”的内容体系、探寻教学中“尺规作图”的教育价值、探究课堂上“尺规作图”的教学路径,能引导学生在实践操作中感受数学的严谨性和精确性,进而促进其几何直观和推理意识的良好发展。 展开更多
关键词 小学数学 新课标 “尺作图” 三角形 核心素养
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A New Three-Level Hierarchical Control Algorithm for Large-Scale Systems
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作者 解三明 吴沧浦 许钟灵 《Journal of Beijing Institute of Technology》 EI CAS 1996年第2期211+205-211,共8页
This paper presents a new three-level hierarchical control parallel algorithm for large-scale systems by spatial and time decomposition. The parallel variable metric (PVM)method is found to be promising third-level al... This paper presents a new three-level hierarchical control parallel algorithm for large-scale systems by spatial and time decomposition. The parallel variable metric (PVM)method is found to be promising third-level algorithm. In the subproblems of second-level, the constraints of the smaller subproblem requires that the initial state of a subproblem equals the terminal state of the preceding subproblem. The coordinating variables are updated using the modified Newton method. the low-level smaller subproblems are solved in parallel using extended differential dynamic programmeing (DDP). Numerical result shows that comparing with one level DDP. the PVM /DDP algorithm obtains significant speed-ups. 展开更多
关键词 hierarchical control differential dynamic programming parallel variable metric
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The Possibility of Angle Trisection (A Compass-Straightedge Construction) Kimuya M Alex
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作者 Kimuya M Alex 《Journal of Mathematics and System Science》 2017年第1期25-42,共18页
The objective of this paper is to provide a provable solution of the ancient Greek problem of trisecting an arbitrary angle employing only compass and straightedge (ruler). (Pierre Laurent Wantzel, 1837) obscurely... The objective of this paper is to provide a provable solution of the ancient Greek problem of trisecting an arbitrary angle employing only compass and straightedge (ruler). (Pierre Laurent Wantzel, 1837) obscurely presented a proof based on ideas from Galois field showing that, the solution of angle trisection corresponds to solution of the cubic equation; x3 - 3x - 1 = 0, which is geometrically irreducible [1]. The focus of this work is to show the possibility to solve the trisection of an angle by correcting some flawed methods meant for general construction of angles, and exemplify why the stated trisection impossible proof is not geometrically valid. The revealed proof is based on a concept from the Archimedes proposition of straightedge construction [2, 3]. 展开更多
关键词 Angle trisection COMPASS Ruler (Straightedge) Classical Construction GeoGebra Software Greek's geometry Cubic equation Plane geometry Solid geometry
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Scaling Analysis and its Applications of Electrostatic Micromotors
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作者 王欣利 程树康 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2004年第2期177-180,共4页
An electrostatic micromotor is compared with a conventional electromagnetic mieromotor, and the scaling effect of driving forces is analysed according to their different operation principles. Characteristic dimension ... An electrostatic micromotor is compared with a conventional electromagnetic mieromotor, and the scaling effect of driving forces is analysed according to their different operation principles. Characteristic dimension L represents the linear scale of micromotors. Electromagnetic driving force is proportional to high-order power of characteristic dimension L whereas electrostatic driving force is not. So, in micro domain, the effect of electrostatic force is larger than that of electromagnetic force, which makes electrostatic micromotor more competitive against electromagnetic alternative in MEMS. In assessing the performance of a micromotor, the power per unit volume and efficiency are the two most important criteria. Hence, the two kinds of micromotors are further compared from these two aspects. The results indicate that electrostatic a micromotor has higher power per unit volume and efficiency, moreover, its structure is simple, it can be made sufficiently small. For those advantages of electrostatic micromotors, they can be used in optical devices, aerospace equipment and medical instruments. 展开更多
关键词 MEMS scaling effect characteristic dimension micro domain
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A new procedure for determining dry density of mixed soil containing oversize gravel
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作者 Hamed Farshbaf AGHAJANI Masoud Ghodrati YENGEJEH +1 位作者 Amirmohammad KARIMZADEH Hossein SOLTANI-JIGHEH 《Journal of Central South University》 SCIE EI CAS CSCD 2018年第12期2841-2856,共16页
This paper presents a novel computational procedure for the maximum dry density of mixed soils containing oversize particles.At first,the large-scale compaction test data for mixed soils are analyzed by an artificial ... This paper presents a novel computational procedure for the maximum dry density of mixed soils containing oversize particles.At first,the large-scale compaction test data for mixed soils are analyzed by an artificial neural network to determine the main factors affecting the compaction.These factors are then imposed on a genetic programming method and a new mathematical equation emerges.The new equation has more conformity with the experimental data in comparison with the previous correction methods.Besides,the mixed soil dry density is associated with most base soil and oversize fraction specifications.With regard to the sensitivity analyses,if the mixed soil contains high percentages of oversize fraction,the mixed soil composition is governed by the specification of oversized grains,such as specific gravity and the maximum grain size and by increasing these factors,the mixed soil dry density is increased.In mixed soil with a low content of oversize,the base soil specification mainly controls the compaction behavior of mixed soil.Furthermore,if the base soil is inherently compacted with greater dry density,adding the oversize slightly improves the mixed soil dry density.In contrast,adding oversized grains to the base soil with a lower dry density produces a mixed soil with greater dry density.By increasing the maximum grain size difference between the oversize fraction and base soil,the dry density of mixed soil is enhanced. 展开更多
关键词 mixed soil oversize COMPACTION genetic programming artificial neural network
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RESEARCH ON SOME THEORETICAL PROBLEMS OF MAP DATA HANDLING USING FRACTAL APPROACH
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作者 WANG Qiao 《Geo-Spatial Information Science》 2000年第1期34-38,共5页
Some theoretical problems of fractal geographical map data handling are dis- cussed and some new methods about fractal dimension introducing, developing, comparing and estimating are proposed in this paper.
关键词 fractals fractal dimension SELF-SIMILARITY scale interval
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Effects of Formulation Parameters and Process Variables on the Properties of Granules Obtained by Reactive Granulation 被引量:2
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作者 Leping Dang Xiaojun Lang +1 位作者 Xu Li Hongyuan Wei 《Transactions of Tianjin University》 EI CAS 2018年第3期224-233,共10页
In this work, granulation between dodecyl-benzenesulfonic acid and sodium carbonate was investigated in a laboratory-scale high shear mixer. The effects offormulation parameters and process variables, including primar... In this work, granulation between dodecyl-benzenesulfonic acid and sodium carbonate was investigated in a laboratory-scale high shear mixer. The effects offormulation parameters and process variables, including primary carbonate size, binder content, impeller speed, and operating temperature, were correlated to the properties ofthe product granules. Design ofexperiment and analysis ofvariance were combined to analyze the experimentaldata, and results showed that larger granule sizes with fewer fine particles can be obtained by employing higher binder contents and larger sodium carbonate sizes. The shear force ofthe impeller can extensively break oversized granules. The binder content exerted a contrasting effect on the flowability ofgranules formed with two kinds ofsodium carbonate, likely because ofdifferences in the liquid saturation ofthe solids. The dissolution rate determined by in-line size analysis showed that high binder contents were beneficialto dissolution performance, and the relationships between Hunter color and tested parameters were evaluated. The results ofthis work can be used as a reliable guidance for process controland optimization in powder detergent manufacturing. 展开更多
关键词 Dry neutralization GRANULATION Size FLOWABILITY Dissolution rate Color
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Measurement of Earthquake Size
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作者 Chen Zhangli Chen Hanlin +3 位作者 Zhao Cuiping Wang Qincai Hua Wei Zhou Lianqing 《Earthquake Research in China》 2014年第3期285-298,共14页
The paper begins with a brief review of the research history of earthquake size measurement. On this basis, the author pointed out the following points: ① In recent decades, ML, mb (mH ), Ms magnitude scales are w... The paper begins with a brief review of the research history of earthquake size measurement. On this basis, the author pointed out the following points: ① In recent decades, ML, mb (mH ), Ms magnitude scales are widely used as measures of earthquake size. However, these magnitude scales have a deficiency of "overgeneralization" and "magnitude saturation". Moreover, since they do not fully take into account the regional difference of seismic attenuation, especially the difference of site effects on the amplification of ground motion, these magnitude scales are but inaccurate measures of earthquake size. ② Seismic moment M0 not only has clear physical meaning, but also overcomes the deficiencies existing in ML, mb (mB ) and Ms magnitude scales, so it is the most suitable physical quantity for measuring earthquake size scientifically. In order to continue to use the term "magnitude", Kanamori defined the moment magnitude scale Act. Although its prerequisite assumptions remain to be studied, it is still a reasonable scale used as a measure of the relative size of an earthquake. ③ For measuring the earthquake size more scientifically, we must make full use of a large amount of waveform data from modern regional digital seismograph networks, strengthen the research on seismic wave attenuation characteristics, site effect, calculation of source parameters and the related scaling relations. In improving the measurement methods for ML, mb (mB ) and Ms magnitude, we should focus on the improvement of Mw scale and carry forward the work as gradually taking Mw magnitude scale as the uniform physical quantity to measure the relative size of earthquakes, so as to lay a more solid foundation for research in earthquake science and earthquake prediction. 展开更多
关键词 EARTHQUAKE MEASUREMENT MAGNITUDE Seismic moment ENERGY Stressdrop
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Numerical Modeling and Analysis of Gas Entrainment for the Ventilated Cavity in Vertical Pipe
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作者 向敏 江振宇 +1 位作者 张为华 屠基元 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2014年第3期252-260,共9页
A semi-empirical gas entrainment model was proposed for the ventilated cavity in vertical pipe, based on which, a complete numerical scheme was established by coupling with the Eulerian-Eulerian two-fluid model to pre... A semi-empirical gas entrainment model was proposed for the ventilated cavity in vertical pipe, based on which, a complete numerical scheme was established by coupling with the Eulerian-Eulerian two-fluid model to predict the multiscale flow field created by ventilated cavity. Model predictions were validated against experimental measurements on void fraction and bubble size distributions. Simulations were carried out to explore the effect of ventilation rate and inlet turbulence intensity on the macroscale cavity shape and the bubbly flow downstream of the ventilated cavity. As the ventilation rate increasing, a reverse trend was observed for the void fraction and bub-ble size distributions. It is concluded that the average void fraction in the pipe flow region is determined by the vo-lumetric ratio between liquid and gas. However, the bubble size evolution is dominated by the breakage effect induced by turbulence in the vortex region. Furthermore, simulations were conducted to analyze geometric scale effect based upon Froude similitude. The results imply that the velocity distributions were properly scaled. Slight scale effect was seen for the void fraction caused by faster dispersion of bubbles in the larger size model. The comparatively greater bubble size was predicted in the smaller model, implying significant scale effects in terms of tur-bulence and surface tension effect. It reveals that empirical correlations valid in wide range are required for the extrapolation from small-size laboratory models. 展开更多
关键词 ventilated cavity gas entrainment bubbly flow SIMULATION
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Nano-microbubble flotation of fine and ultrafine chalcopyrite particles 被引量:31
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作者 Ahmadi Rahman Khodadadi Darban Ahmad +1 位作者 Abdollahy Mahmoud Fan Maoming 《International Journal of Mining Science and Technology》 SCIE EI 2014年第4期559-566,共8页
As is well known to mineral processing scientists and engineers, fine and ultrafine particles are difficult to float mainly due to the low bubble-particle collision efficiencies. Though many efforts have been made to ... As is well known to mineral processing scientists and engineers, fine and ultrafine particles are difficult to float mainly due to the low bubble-particle collision efficiencies. Though many efforts have been made to improve flotation performance of fine and ultrafine particles, there is still much more to be done. In this paper, the effects of nano-microbubbles (nanobuhbles and microbubbles) on the flotation of fine (-38 + 14.36 μm) and ultrafine (-14.36 + 5μm) chalcopyrite particles were investigated in a laboratory scale Denver flotation cell. Nano-microbubbles were generated using a specially-designed nano- microbubble generator based on the cavitation phenomenon in Venturi tubes. In order to better under- stand the mechanisms of nano-microbubble enhanced froth flotation of fine and ultrafine chalcopyrite particles, the nano-microbubble size distribution, stability and the effect of frother concentration on nano- bubble size were also studied by a laser diffraction method. Comparative flotation tests were performed in the presence and absence of nano-microbubbles to evaluate their impact on the fine and ultrafine chalcopyrite particle flotation recovery. According to the results, the mean size of nano-microbubbles increased over time, and decreased with increase of frother concentration. The laboratory-scale flotation test results indicated that flotation recovery of chalcopyrite fine and ultrafine particles increased by approximately 16-21% in the presence of nano-microbubbles, depending on operating conditions of the process. The presence of nano-microbubbles increased the recovery of ultrafine particles (-14.36 + 5 μm) more than that of fine particles (-38 + 14.36 μm). Another major advantage is that the use of nano-microbubbles reduced the collector and frother consumptions by up to 75% and 50%, respectively. 展开更多
关键词 Nanobubbles Nano-microbubble Bubble size distribution Chalcopyrite Froth flotation Fine particles
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A new kind of wavelet-based method for spectrum deconvolution
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作者 肖跃 崔一平 《Journal of Southeast University(English Edition)》 EI CAS 2003年第1期22-25,共4页
To subtract the slit function from the measured spectrum, a wavelet-based deconvolution method is proposed to obtain a regularized solution of the problem. The method includes reconstructing the signal from the wavele... To subtract the slit function from the measured spectrum, a wavelet-based deconvolution method is proposed to obtain a regularized solution of the problem. The method includes reconstructing the signal from the wavelet modulus maxima. For the purpose of maxima selection, the spatially selective noise filtration technique was used to distinguish modulus maxima produced by signal from the one created by noise. To test the method, sodium spectrum measured at a wide slit was deconvolved. He-Ne spectrum measured at the corresponding slit width was used as slit function. Sodium measured at a narrow slit was used as the reference spectrum. The deconvolutton result shows that this method can enhance the resolution of the degraded spectrum greatly. 展开更多
关键词 DECONVOLUTION slit function wavelet local maxima
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Simulation and Discussion on the Decreasing Flow Stress Scale Effect
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作者 申昱 于沪平 +3 位作者 董湘怀 郭斌 单德彬 李澍 《Journal of Shanghai Jiaotong university(Science)》 EI 2012年第3期306-311,共6页
The miniaturization of products requires the mass production of microparts.The microforming can well meet this requirement.Due to the emergence of decreasing flow stress scale effect in the micro scale,the traditional... The miniaturization of products requires the mass production of microparts.The microforming can well meet this requirement.Due to the emergence of decreasing flow stress scale effect in the micro scale,the traditional forming process and theory may fail.Based on the crystal plasticity theory,upsetting tests of micro copper cylinders with different dimensions and grain sizes were simulated,and the decreasing flow stress scale effect was studied and discussed.Results show that with the decrease of billet dimensions,the flow stress is gradually decreased,and the decreasing flow stress scale effect is emerged;with the increase of grain size,the decreasing flow stress scale effect is more remarkable.It can also be seen that the decreasing flow stress scale effect can be well simulated with the crystal plasticity theory,and the necessary relevant information is provided for deeper understanding on this scale effect,as well as the design of processes and die structures in the microforming. 展开更多
关键词 MICROFORMING scale effect crystal plasticity numerical simulation
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Effect of size on mechanical behavior of Au pillars by molecular dynamics study 被引量:7
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作者 TANG QiHeng 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2012年第6期1111-1117,共7页
The influence of specimen size on the mechanical behavior of Au pillars is studied by means of molecular dynamics (MD) simulations with the EAM potential.Under compression at 300 K,as the deformation of pillars is in ... The influence of specimen size on the mechanical behavior of Au pillars is studied by means of molecular dynamics (MD) simulations with the EAM potential.Under compression at 300 K,as the deformation of pillars is in the plastic stage,nucleation of partial dislocations is observed.The coupling effect of surface stress and thermal activation is considered when analyzing the size effect on the yield property of the Au pillars.It appears that both the tensile stress component and the temperature in the surface layer impart significant effect on the mechanical behaviors of the nano-sized Au pillars. 展开更多
关键词 molecular dynamics simulation size effect DISLOCATION compression
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Theoretical and experimental researches of size effect in micro-indentation test 被引量:9
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作者 魏悦广 白以龙 +1 位作者 王学峥 武晓雷 《Science China Mathematics》 SCIE 2001年第1期74-82,共9页
Micro-indentation tests at scales on the order of sub-micron have shown that the measured hardness increases strongly with the indent depth or indent size decreasing, which is frequently referred to as the size effect... Micro-indentation tests at scales on the order of sub-micron have shown that the measured hardness increases strongly with the indent depth or indent size decreasing, which is frequently referred to as the size effect. However, the trend is at odds with the size-independence implied by conventional elastic-plastic theory. In this paper, strain gradient plasticity theory is used to model the size effect for materials undergoing the micro-indenting. Meanwhile, the micro-indentation experiments for single crystal copper and single crystal aluminum are carried out. By the comparison of the theoretical predictions with experimental measurements, the micro-scale parameter of strain gradient plasticity theory is predicted, which is fallen into the region of 0.8—1.5 micron for the conventional metals such as copper (Cu), aluminum (Al) and silver (Ag). Moreover, the phenomena of the pile-up and sink-in near micro-indent boundary are investigated and analyzed in detail. 展开更多
关键词 micro-indentation test size effect strain gradient plasticity MICRO-SCALE
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Recent understanding on the subgrid-scale modeling of large-eddy simulation in physical space 被引量:4
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作者 FANG Le SHAO Liang BERTOGLIO J.-P. 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2014年第12期2188-2193,共6页
In the last 50 years,the methodology of large-eddy simulation(LES)has been greatly developed,while lots of different subgridscale(SGS)models have appeared.However,the understanding of the procedure of SGS modeling is ... In the last 50 years,the methodology of large-eddy simulation(LES)has been greatly developed,while lots of different subgridscale(SGS)models have appeared.However,the understanding of the procedure of SGS modeling is still not clear.The present contribution aims at reviewing the recent SGS models and,more importantly,expressing our recent understanding on the SGS modeling of LES in physical space.Taking the Kolmogorov equation for filtered quantities(KEF)as an example,it is argued that the KEF alone is not enough to be a closure method.Three physical laws are then introduced to complete this closure procedure and are expected to inspire the future researches of SGS modeling. 展开更多
关键词 large-eddy simulation subgrid-scale modeling Koimogorov equation
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