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角在平面内的射影
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作者 张留杰 《中学数学教学参考(上半月高中)》 北大核心 2006年第5期55-55,共1页
如果角所确定的平面与射影平面平行,则任意角等于射影角。如果角平面垂直于射影平面,则射影角为180°或O°或不存在(当角的一边垂直于射影平面时)。因此,只考虑角所在平面β与射影平面α斜交(二面角小于90°)的情形。
关键词 “角在平面内射影 高中 数学 立体几何 证明
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谈射影点的确定法
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作者 申建睿 《中学数学(江苏)》 1995年第1期27-29,50,共4页
立体几何计算与证明中,涉及点在直线或平面内的射影问题非常多。确定射影点的位置成为学生最为头痛的问题之一。本文想谈谈怎样才能准确找出点在直线或平面内的射影。
关键词 射影 平面内 内射影 二面角的平面角 几何计算 高考题 钝角三角形 逆定理 两平面 线面垂直
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向量的夹角概念在高维欧氏空间E ̄n中的推广 被引量:1
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作者 李桃生 《数学杂志》 CSCD 北大核心 1995年第3期287-290,共4页
本文给出了E ̄n中不同维数平面之间多维角、单维角的定义,它们是向量的夹角概念的推广,其几何意义非常明显,在此基础上还给出了Q_(AB)P ̄(-1)A的特征多项式各项系数的几何意义,这些结论对于研究各类曲率非常有用.
关键词 多维角 单维角 内射影 欧氏空间 向量 夹角
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有限维欧氏空间中内积问题的矩阵研究
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作者 王爱青 《山东农业大学学报(自然科学版)》 CSCD 北大核心 2008年第2期318-320,共3页
利用向量组的Gram矩阵和向量的坐标矩阵对有限维欧氏空间中子空间的正交性给出了矩阵判定条件,对子空间的正交补及向量在子空间上的内射影给出了矩阵表示.获得了一些简捷有用的结果。
关键词 内积 正交 子空间 内射影 矩阵
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空间等角直线系的存在条件
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作者 杨炼 《中学数学月刊》 1999年第11期18-20,共3页
本文旨在解决空间n条直线两两成等角矽,数对n,矽的存在条件先给出定理:
关键词 直线系 存在条件 角平分线 等角 共点 对称直线 内射影 点直线 任意角 可安置
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数学接力
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作者 程厚旺 《数学教学》 北大核心 1996年第3期22-23,共2页
在体育运动中,有个接力赛;在娱乐活动中,有一种接力游戏;……;如此种种,人们都是如此地迷恋它。设想,把这种手段引入数学教学,将会怎样呢?笔者进行了一些尝试,效果理想。 我们把数学教学中的接力活动称数学接力,它的主要形式和种类有:... 在体育运动中,有个接力赛;在娱乐活动中,有一种接力游戏;……;如此种种,人们都是如此地迷恋它。设想,把这种手段引入数学教学,将会怎样呢?笔者进行了一些尝试,效果理想。 我们把数学教学中的接力活动称数学接力,它的主要形式和种类有:一、组题接力;二、解题接力;三、系统接力。以下分别叙述: 展开更多
关键词 数学教学 组题 梯形 活动称 面接 引入数 二面角 分面 接力赛 内射影
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三垂线定理的教学设计
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作者 蒋先松 《中学数学教学》 1995年第S1期186-186,共1页
教学目的:掌握三垂线定理,从复习旧知到渗透新知识,使学生处新而不惊,于不知不觉中理解和掌握三垂线定理及其证明。 模式:观察实践——发现——证明——应用。采用师生共同问答式教学(下文中T代表教师,S代表学生) T:我们已学过平面... 教学目的:掌握三垂线定理,从复习旧知到渗透新知识,使学生处新而不惊,于不知不觉中理解和掌握三垂线定理及其证明。 模式:观察实践——发现——证明——应用。采用师生共同问答式教学(下文中T代表教师,S代表学生) T:我们已学过平面的垂线、平面的斜线及斜线在平面内射影等知识,再来回忆一下: 什么叫平面的垂线?(先画一平面,再提问) S:与平面内所有直线垂直的直线叫平面的垂线。 展开更多
关键词 三垂线定理 教学设计 平面内 斜线 问答式教学 教学目的 观察实践 内射影 空间直线 条件与结论
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也谈挖掘教材——浅论四面体
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作者 张光幸 《中学数学教学》 1995年第S1期50-52,共3页
在立体几何教学中,对四面体的适当探讨,颇有效益。本文以课本中最简的问题着手,由浅至深适当加以探究。 问题1 已知:E、F、G、H分别是空间四边形的四条边AB、BC、CD、DA的中点,求证:四边形EFGH是平行四边形。(现行教材立几必修本第16... 在立体几何教学中,对四面体的适当探讨,颇有效益。本文以课本中最简的问题着手,由浅至深适当加以探究。 问题1 已知:E、F、G、H分别是空间四边形的四条边AB、BC、CD、DA的中点,求证:四边形EFGH是平行四边形。(现行教材立几必修本第16页6题) 思索1:由平行四边形EFGH深入易知,空间四边形对边中点的连线交于中点;对角线中点连线也相交于该点且被其平分。从而得: 结论1:空间四边形中,对边中点及对角线中点的连线相交于一点且被该点平分。 展开更多
关键词 四面体 对棱 内射影 平行四边形 垂心 立体几何教学 锐角三角形 充要条 现行教材 线相交
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高中数学会考模拟试卷(B)
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作者 傅启凤 《中学数学月刊》 1998年第Z1期91-93,共3页
(1)∵A<sub>1</sub>B<sub>1</sub>∥AB,AB⊥BC,∴A<sub>1</sub>B<sub>1</sub>⊥BC,又∵直棱柱,∴BB<sub>1</sub>⊥平面A<sub>1</sub>B<sub>1</sub... (1)∵A<sub>1</sub>B<sub>1</sub>∥AB,AB⊥BC,∴A<sub>1</sub>B<sub>1</sub>⊥BC,又∵直棱柱,∴BB<sub>1</sub>⊥平面A<sub>1</sub>B<sub>1</sub>C<sub>1</sub>。∴BB<sub>1</sub>⊥A<sub>1</sub>B<sub>1</sub>,∴A<sub>1</sub>B<sub>1</sub>⊥平面BB<sub>1</sub>C<sub>1</sub>C.(2)∵A<sub>1</sub>C在平面BC<sub>1</sub>内射影为B<sub>1</sub>C,由三垂线定理得A<sub>1</sub>C⊥BC<sub>1</sub>.(3)取BB<sub>1</sub>中点F,连EF,DF,∵DE∥A<sub>1</sub>B<sub>1</sub>,∴BE⊥平面BB<sub>1</sub>C<sub>1</sub>C,∴∠DFE为二面角D-BB<sub>1</sub>。 展开更多
关键词 高中数学 模拟试卷 会考 等差数列 内射影 直棱柱 双曲线方程 侧面积 通项公式 全面积
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Endoscopic retrograde cholangiopancreatography during pregnancy without radiation 被引量:17
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作者 Adem Akcakaya Orhan Veli Ozkan +2 位作者 Ismail Okan Orhan Kocaman Mustafa Sahin 《World Journal of Gastroenterology》 SCIE CAS CSCD 2009年第29期3649-3652,共4页
AIM: To present our experience with pregnant patients who underwent endoscopic retrograde cholangiopancreatography (ERCP) without using radiation, and to evaluate the acceptability of this alternative therapeutic p... AIM: To present our experience with pregnant patients who underwent endoscopic retrograde cholangiopancreatography (ERCP) without using radiation, and to evaluate the acceptability of this alternative therapeutic pathway for ERCP during pregnancy. METHODS: Between 2000 and 2008, six pregnant women underwent seven ERCP procedures. ERCP was performed under mild sedoanalgesia induced with pethidine HCI and midazolam. The bile duct was cannulated with a guidewire through the papilla. A catheter was slid over the guidewire and bile aspiration and/or visualization of the bile oozing around the guidewire was used to confirm correct cannulation. Following sphincterotomy, the bile duct was cleared by balloon sweeping. When indicated, stents were placed. Confirmation of successful biliary cannulation and stone extraction was made by laboratory, radiological and clinical improvement. Neither fluoroscopy nor spot radiography was used during the procedure. RESULTS: The mean age of the patients was 28 years (range, 21-33 years). The mean gestational age for the fetus was 23 wk (range, 14-34 wk). Five patients underwent ERCP because of choledocholithiasis and/or choledocholithiasis-induced acute cholangitis. In one case, a stone was extracted after precut papillotomy with a needle-knife, since the stone was impacted. One patient had ERCP because of persistent biliary fistula after hepatic hydatid disease surgery. Following sphincterotomy, scoleces were removed from the common bile duct. Two weeks later, because of the absence of fistula closure, repeat ERCP was performed and a stent was placed. The fistula was closed after stent placement. Neither post-ERCP complications nor premature birth or abortion was seen. CONCLUSION: Non-radiation ERCP in experienced hands can be performed during pregnancy. Stent placement should be considered in cases for which complete common bile duct clearance is dubious because of a lack of visualization of the biliary tree. 展开更多
关键词 CHOLANGITIS CHOLEDOCHOLITHIASIS Endoscopic retrograde cholangiopancreatography JAUNDICE PREGNANCY
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Topological inverse semigroups 被引量:6
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作者 ZHUYongwen 《Journal of Chongqing University》 CAS 2004年第1期82-85,共4页
That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and... That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups. 展开更多
关键词 topological inverse semigroup COMPACT projective limit injective limit
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Characterization of Hereditary Rings ViaInjectivity and Projectivity Classes
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作者 于增海 段海生 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第2期27-30, ,共4页
In this note,some characterizations of hereditary rings using injectivity classes and projectivity classes are given.These results unify many well known results.
关键词 hereditary ring injectivity classes projectivity classes
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从立体几何中的“动”谈思维能力的培养
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作者 樊文联 魏国民 《石油教育》 1997年第4期52-52,共1页
关键词 立体几何 思维能力 “动” 异面直线 内射影 思维的灵活性 河南油田 思维定势 性质定理 平行直线
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Radiographic verification of pedicle screw pilot hole placement in thoracic spine using Kirschner wires versus spiral wires 被引量:3
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作者 刘一 张绍昆 +5 位作者 苗巍巍 单玉兴 孙大辉 王柏 李印良 黄晓刚 《Chinese Journal of Traumatology》 CAS 2003年第5期288-291,共4页
Objective: To evaluate the feasibility of the pedicle screw pilot holes placement in thoracic spine using the spiral wires as the guide pin. Methods: The pedicle screw pilot holes were drilled within the center of the... Objective: To evaluate the feasibility of the pedicle screw pilot holes placement in thoracic spine using the spiral wires as the guide pin. Methods: The pedicle screw pilot holes were drilled within the center of the pedicle and the lateral and medial pedicle walls were violated in 9 human dried thoracic vertebrae. Kirschner wires or spiral wires were separately placed in the holes, and then the posteroanterior and lateral radiographs were taken. The radiographs were evaluated by 3 experienced spine surgeons and 3 young orthopedists. After radiographs were shown to these observers, they combined the posteroanterior and lateral radiographs in each place and determined whether the pedicle screw pilot hole violated the pedicle cortex or not. The results were analyzed by a statistical software. Results: Sensitivity, specificity and accuracy of the method using spiral wires to detect pedicle pilot hole placement were significantly higher than those of using Kirschner wires. With a true posteroanterior radiograph, the sensitivity, specificity and accuracy of the method using spiral wires approximated or attained 100%. Conclusions: The method of intrapedicular pilot hole placement verification using spiral wires is effective for guiding the accurate placement of pedicle screws. 展开更多
关键词 Thoracic vertebrae Bone screws Kirschner wires
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