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求平面上几个点之间的最短连结线的几例方法
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作者 伊亨云 《数学教学通讯》 1981年第4期39-41,共3页
设有甲、乙、丙三地,由甲地向乙丙两地供水,应怎样铺设管道,才能使管道长度最短?(图一) 有甲、乙、丙和丁四村,应如何布置连结四村的输电线路,才能使线路最短?(图二) 上面这些问题都归结于几何上这样一个问题:怎样的连结线是平面上几个... 设有甲、乙、丙三地,由甲地向乙丙两地供水,应怎样铺设管道,才能使管道长度最短?(图一) 有甲、乙、丙和丁四村,应如何布置连结四村的输电线路,才能使线路最短?(图二) 上面这些问题都归结于几何上这样一个问题:怎样的连结线是平面上几个点之间的最短连结线? 当只有两点的时候,显然,连结它们的最短线就是连结这两点的直线段。下面从三点的情况开始讨论。 展开更多
关键词 连结线 铺设管道 输电线路 一个问题 管道长度 丁四 几何方法 已知点 大时 点图
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等腰四面体的一些性质和主要不变量之间的关系
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作者 苏化明 《中学数学教学》 1983年第1期14-16,共3页
三对对棱都相等的四面体称为等腰四面体。等腰四面体具有一些特殊性质。在等腰四面体ABCD中,设BC=AD=a,AC=BD=b,AB=CD=c,且令P=(1/2)(a+b+c),k2=(1/2)(a2+b2+c2),l=ab+bc+ca,n=abc。以BC、BD、CD为棱的侧面间的二面角是α、β、... 三对对棱都相等的四面体称为等腰四面体。等腰四面体具有一些特殊性质。在等腰四面体ABCD中,设BC=AD=a,AC=BD=b,AB=CD=c,且令P=(1/2)(a+b+c),k2=(1/2)(a2+b2+c2),l=ab+bc+ca,n=abc。以BC、BD、CD为棱的侧面间的二面角是α、β、γ,△BCD、△ABC、△ABD、△ACD的面积依次是S、S1、S2、S3,四面体的体积为V,外接球半径为R,内切球半径为r,等腰四面体ABCD性质可以列举如下: 展开更多
关键词 不变量 三角形重心 内切 连结线 锐角三角形 九等 三心 当且仅当 数学通报 半角
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单位质点组重心的性质
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作者 刘宁平 张佳英 《数学教学通讯(教师阅读)》 1990年第1期30-31,共2页
本文证明了:单位质点组的重心是到各质点距离均平方和最小的点。由此确定了到多边形及多面体各顶点距离的平方和最小的点的位置。我们知道:两个质量分别为m<sub>1</sub>和m<sub>2</sub>的质点A和 B,它们的重心... 本文证明了:单位质点组的重心是到各质点距离均平方和最小的点。由此确定了到多边形及多面体各顶点距离的平方和最小的点的位置。我们知道:两个质量分别为m<sub>1</sub>和m<sub>2</sub>的质点A和 B,它们的重心G在线段AB上,重心G的质量为m<sub>1</sub>+m<sub>2</sub>,并且重心G分线段AB的比为m<sub>2</sub>∶m<sub>1</sub>。于是,我们可以得到下面的结论。 [定理1] 设A<sub>1</sub>、A<sub>2</sub>…A<sub>n</sub>是质量相同的n个单位质点,则它们的重心的位置可用下面方法求得:先连结线段A<sub>1</sub>A<sub>n</sub>,并取其中点为B<sub>1</sub>;然后连结线段A<sub>2</sub>B<sub>1</sub>,并在其上取点B<sub>2</sub>,使得A<sub>2</sub>B<sub>2</sub>=2B<sub>2</sub>B<sub>1</sub>;再连线段A<sub>3</sub>B<sub>2</sub>,并在其上取点B<sub>2</sub>,使A<sub>3</sub>B<sub>3</sub>=3B<sub>3</sub>B<sub>2</sub>;再连结线段A<sub>4</sub>B<sub>3</sub>,并在其上取点B<sub>4</sub>,使A<sub>4</sub>B<sub>4</sub>=4B<sub>4</sub>B<sub>3</sub>;…… 展开更多
关键词 连结线 点法 点距 土定 枢心 鸿一 阴中 引趣 线或 理对
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档案絮语
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《档案时空》 1991年第5期1-1,共1页
一片森林烧掉了,过了若干年,新的树木又会生长起来。一座城市破坏了,人们可以在废墟上重建。可是档案损毁了,却不可能再生,也无法重建。
关键词 陈乐民 周小星 页页 彭朋 连结线 江永县 万林 吴锦
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1992年浙江、河南省数学夏令营竞赛试题及参考解答
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《中学教研(数学版)》 1992年第11期35-41,共7页
一、选择题:(本题满分30分,每小题5分) 1.设z是复数,|z-1/z|=1,那么在复平面上点z所描出的曲线是( )。 (A)一个椭圆; (B)一条抛物线; (C)一条双曲线;(D)以上答案都不是。 2.设过空间中的一个平行六面体V的任意三个顶点的平... 一、选择题:(本题满分30分,每小题5分) 1.设z是复数,|z-1/z|=1,那么在复平面上点z所描出的曲线是( )。 (A)一个椭圆; (B)一条抛物线; (C)一条双曲线;(D)以上答案都不是。 2.设过空间中的一个平行六面体V的任意三个顶点的平面(两两不重的)个数为m,其中能平分V的体积的平面个数为n,则n/m等于( )。 (A)1/5;(B)1/4;(C)1/3;(D)3/10。 3.ABCD—A<sub>1</sub>B<sub>1</sub>C<sub>1</sub>D<sub>1</sub>是长方体,A与C<sub>1</sub>是关于中心对称的两个顶点。一个动点从A出发沿长方体的棱移动到C<sub>1</sub>点终止,且每个顶点至多经过一次(不必每条棱都经过),则其可能的不同的路线个数是( )。 展开更多
关键词 竞赛试题 最小距离 抛物线方程 凸六边形 递增函数 补集 大时 时间限制 填空题 连结线
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茶艺的五字真经
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作者 岫岫 《茶(健康天地)》 2011年第2期34-35,共2页
每一位初学泡茶者,最初只是单纯模仿他人的动作,只知其然不知其所以然;经过不断练习,不断思索,渐渐由形似到神似;再进一步成熟,就有了自己的风格和创造,甚至成为一个流派。提高茶艺,最重要的是要掌握"五字真经"。
关键词 单纯模仿 不知其所以然 关公巡城 茶艺表演 敬茶 一杯茶 汤色 连结线 自动氧化 静思
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二元系恒压相图中通过三相点的水平线的命名的讨论
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作者 余世鑫 《武汉工程大学学报》 CAS 1980年第2期24-26,共3页
二元系恒压相图中,如有一个三相点就有一条过此点的水平线(如图1),若有多个三相点就有多条水平线(如图2)。目前有的物理化学教科书称这类水平线为“三相线”或“三相平衡线”,这和有的国外物理化学教科书的名称“line of three-phaseequ... 二元系恒压相图中,如有一个三相点就有一条过此点的水平线(如图1),若有多个三相点就有多条水平线(如图2)。目前有的物理化学教科书称这类水平线为“三相线”或“三相平衡线”,这和有的国外物理化学教科书的名称“line of three-phaseequilibria”或“three—phase line”相吻合;也有的物理化学教科书针对具有低共熔点的恒压图称之为“固相线”或“固液相线”;也有些国内外的物理化学教科书对这类水平线未给以明确的名称。为了体现这类水平线的实质,避免教学过程中学生初学时可能引起的混乱,给这类水平线以确切的命名是必要的,另外,上述的命名是否妥当,值得商榷,理由如下: 展开更多
关键词 化学教科书 三相点 低共熔点 固液相 二元系 相线 杠杆规则 教学过程 连结线 自由度数
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Total Variation and Multisymplectic Structure for CNLS System 被引量:1
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作者 SUN Jian-Qiang QIN Meng-Zhao LIU Ting-Ting 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第1X期28-32,共5页
The relation between the toal variation of classical field theory and the multisymplectic structure is shown. Then the multisymplectic structure and the corresponding multisymplectic conservation of the coupled nonlin... The relation between the toal variation of classical field theory and the multisymplectic structure is shown. Then the multisymplectic structure and the corresponding multisymplectic conservation of the coupled nonlinear Schroedinger system are obtained directly from the variational principle. 展开更多
关键词 coupled nonlinear Schroedinger system total variation multisymplectic structure multisymplectic conservation
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One-dimensional nonlinear consolidation analysis of soil with continuous drainage boundary 被引量:7
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作者 ZONG Meng-fan TIAN Yi +3 位作者 LIANG Rong-zhu WUWen-bing XU Mei-juan MEI Guo-xiong 《Journal of Central South University》 SCIE EI CAS CSCD 2022年第1期270-281,共12页
Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution ... Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution is derived by using finite difference method and its correctness is assessed by comparing with existing analytical and numerical solutions.Based on the present solution,the effects of interface parameters,stress ratios(i.e.,final effective stress over initial effective stress,N_(σ))and the ratio c_(c)/c_(k)of compression index to permeability index on the consolidation behavior of soil are studied in detail.The results show that,the characteristics of one-dimensional nonlinear consolidation of soil are not only related to c_(c)/c_(k)and N_(σ),but also related to boundary conditions.In the engineering practice,the soil drainage rate of consolidation process can be designed by adjusting the values of interface parameters. 展开更多
关键词 one-dimensional nonlinear consolidation continuous drainage boundary finite difference method interface parameter
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Nonlinear identification and characterization of structural joints based on vibration transmissibility 被引量:2
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作者 Liu Xin Sun Beibei +2 位作者 Li Lie Chen Jiandong Xue Fei 《Journal of Southeast University(English Edition)》 EI CAS 2018年第1期36-42,共7页
In order to investigate the nonlinear characteristics of structural joint,the experimental setup with a jointed mass system is established for dynamic characterization analysis and vibration prediction,and a correspon... In order to investigate the nonlinear characteristics of structural joint,the experimental setup with a jointed mass system is established for dynamic characterization analysis and vibration prediction,and a corresponding nonlinearity identification method is studied.First,the sine-sweep vibration test with different baseexcitation levels areapplied to the structural joint system to study the dominant modal of mass rigid motion.Then,based on t e harmonic balance method principle,t e measured vibration transmissibilities a e utilized for nonlinearity identification using different excitation levels.Experimental results show that nonlinear spring and damping force can be represented by a polynomial order approximation.The identified nonlinear stiffness and damping force can predict the system’s response,and they can reveal t e shifts of resonant frequency or damping due to discontinuity of contact mechanisms within a certain range. 展开更多
关键词 structural joint vibration transmissibility nonlinear identification harmonic balance method
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Fatigue Strength Evaluation of Resin-Injected Bolted Connections Using Statistical Analysis 被引量:1
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作者 Jose Antonio Fonseca de Oliveira Correia Bruno Alexandre Silva Pedrosa +6 位作者 Patricia Cordeiro Raposo Abilio Manuel Pinho De Jesus Helena Maria dos Santos Gervisio Grzegorz Stanislaw Lesiukc Carlos Alberto da Silva Rebelo Rui Artur Bartolo Calcada Luis Alberto Proenca Simoes da Silva 《Engineering》 SCIE EI 2017年第6期795-805,共11页
Different strategies can be used to perform reparations and reinforcements of ancient bolted and riveted metallic bridges. As the riveting process is not currently a common practice, it requires proper equipment and s... Different strategies can be used to perform reparations and reinforcements of ancient bolted and riveted metallic bridges. As the riveting process is not currently a common practice, it requires proper equipment and skilled workers. Another solution is the use of welding. However, the weldability of old steels is poor. Bolts are very attractive alternative solutions, and are most commonly used to repair old metallic bridges. Fitted bolts are expensive solutions; the alternative is the use of resin-injected bolts. The behavior of bolted joints with preloaded resin-injected bolts has been studied using quasi-static and creep tests; however, few studies on the slip and fatigue behavior of these joints can be found in the literature. This paper presents an overview of a few experimental programs that were carried out by several authors aiming at evaluating the fatigue behavior of single and double shear resin-injected bolted connections. A comparison between the experimental data of joints with preloaded standard bolts and preloaded resin- injected bolts shows a fatigue strength reduction in the latter. Since Eurocode 3 (EC3) suggests the same fatigue strength curve for joints made of resin-injected bolts and standard bolts, this may raise some con- cerns. Furthermore, research on the feasibility of using both bonded and bolted connections is shown. This last study was performed with high-strength low-alloy structural steel plates and an acrylic struc- tural adhesive for metal bonding. For both case studies, a statistical analysis is performed on fatigue experimental data using linearized boundaries and the Castillo and Fernandez-Canteli model. Fatigue design curves are proposed and compared with the design suggestions of several European and North American standards, 展开更多
关键词 FATIGUE CONNECTIONS Structural reinforcements Structural adhesives S-N curves Resin-injected bolts
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Progressive collapse resisting capacity of reinforced concrete load bearing wall structures 被引量:1
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作者 Alireza Rahai Alireza Shahin Farzad Hatami 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第7期2730-2738,共9页
Reinforced concrete(RC) load bearing wall is widely used in high-rise and mid-rise buildings. Due to the number of walls in plan and reduction in lateral force portion, this system is not only stronger against earthqu... Reinforced concrete(RC) load bearing wall is widely used in high-rise and mid-rise buildings. Due to the number of walls in plan and reduction in lateral force portion, this system is not only stronger against earthquakes, but also more economical. The effect of progressive collapse caused by removal of load bearing elements, in various positions in plan and stories of the RC load bearing wall system was evaluated by nonlinear dynamic and static analyses. For this purpose, three-dimensional model of 10-story structure was selected. The analysis results indicated stability, strength and stiffness of the RC load-bearing wall system against progressive collapse. It was observed that the most critical condition for removal of load bearing walls was the instantaneous removal of the surrounding walls located at the corners of the building where the sections of the load bearing elements were changed. In this case, the maximum vertical displacement was limited to 6.3 mm and the structure failed after applying the load of 10 times the axial load bored by removed elements. Comparison between the results of the nonlinear dynamic and static analyses demonstrated that the "load factor" parameter was a reasonable criterion to evaluate the progressive collapse potential of the structure. 展开更多
关键词 reinforced concrete(RC) load bearing wall structure progressive collapse fiber sections nonlinear analysis load factor method
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Analysis and Modeling of k-regular and k-connected Protection Structure in Ultra-High Capacity Optical Networks
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作者 LI Xin HUANG Shanguo +3 位作者 ZHANG Jie ZHAO Yongli GU Wanyi WANG Yang 《China Communications》 SCIE CSCD 2015年第3期106-119,共14页
This paper proposes k-regular and k-connected(k&k) structure against multifaults in ultra-high capacity optical networks.Theoretical results show that pre-configured k&k structure can reach the lower bound on ... This paper proposes k-regular and k-connected(k&k) structure against multifaults in ultra-high capacity optical networks.Theoretical results show that pre-configured k&k structure can reach the lower bound on logical redundancy.The switching time of k&k protection structure is as quickly as ringbased protection in SDH network.It is the optimal protection structure in ultra-high capacity optical networks against multi-faults.We develop the linear programming model for k&k structure and propose a construction method for k&k structure design.Simulations are conducted for spare spectrum resources effi ciency of the pre-confi gured k&k structure under multi-faults on representative COST239 and NSFnet topologies.Numerical results show that the spare spectrum resources efficiency of k&k structure can reach the lower bound on logical redundancy in static networks.And it can largely improve spare spectrum resources effi ciency compared with p-cycles based protection structure without reducing protection effi ciency under dynamic traffi cs. 展开更多
关键词 multi-faults k-regular and k-connected structure ultra-high capacity optical networks
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Analysis of nonlinear settlement for an unsaturated soil under stage continuous loading 被引量:1
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作者 陈伟志 蒋关鲁 +2 位作者 赵慧爽 吴丽君 李安洪 《Journal of Central South University》 SCIE EI CAS 2014年第12期4690-4697,共8页
A new approach was proposed to describe settlement behavior of an unsaturated soil with subgrade filling for high-speed railway. Firstly, based on Terzaghi consolidation theory, equations considering the variation coe... A new approach was proposed to describe settlement behavior of an unsaturated soil with subgrade filling for high-speed railway. Firstly, based on Terzaghi consolidation theory, equations considering the variation coefficient of consolidation with void ratio and saturation for consolidation of an unsaturated soil under stage continuous loading were derived, and according to analytical solutions of equations, a formula for settlement computation under stage continuous loading was obtained. Then, combined with the width-to-height ratio of subgrade to compute ground reaction, and by means of in-situ plate loading curves, a correctional approach was presented for the analysis of nonlinear settlement of foundation. Also, the comparison between calculated and measured loadsettlement behavior for an unsaturated soil in Qingdao-Ji'nan high-speed railway was given to demonstrate the effectiveness and accuracy of the proposed approach. It can be noted that the presented solution can be used to predict the settlement of an unsaturated soil foundation under stage continuous loading in engineering design. 展开更多
关键词 settlement unsaturated soil consolidation stage continuous loading high-speed railway
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生物材料中重金属测定试样予处理
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作者 沈文 《环境科学研究》 EI CAS 1979年第6期1-41,共41页
金属是长周期表中硼和砹连结线左侧,除氢之外,其他元素的总称,通常所谓重金属是指那些比重大于5的金属元素,例如:镉、汞、铅、铬都是重金属;而非金属硒和砷等,我们常称其为准金属(metalloid),因此往往将砷、硒等元素也视为重金属。依金... 金属是长周期表中硼和砹连结线左侧,除氢之外,其他元素的总称,通常所谓重金属是指那些比重大于5的金属元素,例如:镉、汞、铅、铬都是重金属;而非金属硒和砷等,我们常称其为准金属(metalloid),因此往往将砷、硒等元素也视为重金属。依金属元素对人体的生理作用来看,可以将它们分为三大类:(1)人体必须的金属元素;(2)对人体有害的金属元素;(3)跟人体关系尚不明确的金属元素. 展开更多
关键词 生物材料 重金属污染 氧瓶燃烧法 甲基汞 有机汞化合物 连结线 炭粒 萃取率 比色法 四甲基
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只用直尺 所以精彩 被引量:1
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作者 邢成云 《中小学数学(初中版)》 2015年第9期33-36,共4页
只用无刻度的直尺,就决定了这把尺子的功能只能是作直线或连结线段,不能用以度量,这仅有的直尺,失去圆规的助力,该如何作图,确实需要学生大动一番脑筋,这就需要深入挖掘现有条件,用好直接的或潜在的固有功能,发挥“转化”的威力,这类作... 只用无刻度的直尺,就决定了这把尺子的功能只能是作直线或连结线段,不能用以度量,这仅有的直尺,失去圆规的助力,该如何作图,确实需要学生大动一番脑筋,这就需要深入挖掘现有条件,用好直接的或潜在的固有功能,发挥“转化”的威力,这类作图有着荡人神思、开人心智的曼妙之趣,劲透数学的奇异之美! 展开更多
关键词 连结线 固有功能 到角 圆心位置 圆心坐标 网格线 平分线 灵活调度 可由 等腰梯形
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大爱无疆——记远在新疆博州的湖北省第四批援疆干部
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作者 谭兵 王凌云 《民族大家庭》 2009年第6期24-26,共3页
有这样一群人,他们远离温暖的家,将亲人的叮咛放在心中,奔赴边关,一走经年;有这样一群人,他们置身大漠戈壁、西部草原,与边疆各族人民共同奋斗,如沙漠胡杨。
关键词 大爱无疆 西部边陲 内陆腹地 规划专家 水产养殖基地 连结线 平在 打乒乓球 水产养殖品种 派出单位
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从一道中考最值问题说起 被引量:2
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作者 杨雪华 《初中数学教与学》 2016年第7期31-33,共3页
本文以一道中考题为例,与各位共同探讨最值问题的解题思路与策略.一、注重分析,讲究方法最值问题是初中数学中的难点之一.我们在分析解答时要特别注重分析已知条件,紧扣已有的知识经验,力求做到思路清晰,水到渠成.[试题呈现](2013年无... 本文以一道中考题为例,与各位共同探讨最值问题的解题思路与策略.一、注重分析,讲究方法最值问题是初中数学中的难点之一.我们在分析解答时要特别注重分析已知条件,紧扣已有的知识经验,力求做到思路清晰,水到渠成.[试题呈现](2013年无锡中考题)已知点D与点A(8,0),B(0,6),C(a,-a)是一平行四边形的四个顶点,则CD长的最小值为____. 展开更多
关键词 最值问题 已知条件 已知点 解题思路 中位线定理 解题能力 最大距离 最短路径问题 连结线 最短距离
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学习圆的知识应注意五个要点
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作者 夏凤仙 金友良 《数理化学习(初中版)》 2008年第1X期23-25,共3页
掌握好圆的知识,应注意以下的五个方面.一、弄清知识要点圆的基本概念有:弦,弧,圆心角,圆周角,圆的确定,点与圆的位置关系,直线与圆的位置关系,圆与圆的位置关系,弧长的计算和扇形面积的计算.主要性质定理是垂径定理及逆定理,
关键词 性质定理 辅助线 一元二次方程 实数根 阴影部分 弧长 数形结合 连结线 圆相 浙江省兰溪市
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Geometry of the Second-Order Tangent Bundles of Riemannian Manifolds
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作者 Aydin GEZER Abdullah MAGDEN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2017年第4期985-998,共14页
Let (M, g) be an n-dimensional Riemannian manifold and T2M be its second- order tangent bundle equipped with a lift metric g. In this paper, first, the authors con- struct some Riemannian almost product structures ... Let (M, g) be an n-dimensional Riemannian manifold and T2M be its second- order tangent bundle equipped with a lift metric g. In this paper, first, the authors con- struct some Riemannian almost product structures on (T2M, g) and present some results concerning these structures. Then, they investigate the curvature properties of (T2M, g). Finally, they study the properties of two metric connections with nonvanishing torsion on (T2M, g: The//-lift of the Levi-Civita connection of g to TaM, and the product conjugate connection defined by the Levi-Civita connection of g and an almost product structure. 展开更多
关键词 Almost product structure Killing vector field Metric connection Rie-mannian metric Second-order tangent bundle
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