电大离散数学作业5答案(图论部分)

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1、 形成性考核作业 专业好文档姓 名： 学 号： 得 分： 教师签名： 离散数学作业5离散数学图论部分形成性考核书面作业本课程形成性考核书面作业共3次，内容主要分别是集合论部分、图论部分、数理逻辑部分的综合练习，基本上是按照考试的题型（除单项选择题外）安排练习题目，目的是通过综合性书面作业，使同学自己检验学习成果，找出掌握的薄弱知识点，重点复习，争取尽快掌握。本次形考书面作业是第二次作业，大家要认真及时地完成图论部分的综合练习作业。要求：将此作业用A4纸打印出来，手工书写答题，字迹工整，解答题要有解答过程，要求2010年12月5日前完成并上交任课教师（不收电子稿）。并在05任务界面下方点击“保存

2、”和“交卷”按钮，以便教师评分。一、填空题1已知图G中有1个1度结点，2个2度结点，3个3度结点，4个4度结点，则G的边数是 15 2设给定图G(如右由图所示)，则图G的点割集是 f 3设G是一个图，结点集合为V，边集合为E，则G的结点 度数之和 等于边数的两倍4无向图G存在欧拉回路，当且仅当G连通且 等于出度 5设G=是具有n个结点的简单图，若在G中每一对结点度数之和大于等于 n-1 ，则在G中存在一条汉密尔顿路 6若图G=中具有一条汉密尔顿回路，则对于结点集V的每个非空子集S，在G中删除S中的所有结点得到的连通分支数为W，则S中结点数|S|与W满足的关系式为 W(G-V1) V1 7设完全

3、图K有n个结点(n2)，m条边，当 n为奇数 时，K中存在欧拉回路8结点数v与边数e满足 e=v-1 关系的无向连通图就是树9设图G是有6个结点的连通图，结点的总度数为18，则可从G中删去 4 条边后使之变成树10设正则5叉树的树叶数为17，则分支数为i = 5 二、判断说明题（判断下列各题，并说明理由）1如果图G是无向图，且其结点度数均为偶数，则图G存在一条欧拉回路(1) 不正确，缺了一个条件，图G应该是连通图，可以找出一个反例，比如图G是一个有孤立结点的图。2如下图所示的图G存在一条欧拉回路(2) 不正确，图中有奇数度结点，所以不存在是欧拉回路。3如下图所示的图G不是欧拉图而是汉密尔顿图

4、G 解：正确因为图中结点a，b，d，f的度数都为奇数，所以不是欧拉图。如果我们沿着(a,d,g,f,e,b,c,a)，这样除起点和终点是a外，我们经过每个点一次仅一次，所以存在一条汉密尔顿回路，是汉密尔顿图4设G是一个有7个结点16条边的连通图，则G为平面图解：(1) 错误假设图G是连通的平面图，根据定理，结点数v，边数为e，应满足e小于等于3v-6，但现在16小于等于3*7-6，显示不成立。所以假设错误。 5设G是一个连通平面图，且有6个结点11条边，则G有7个面(2) 正确根据欧拉定理，有v-e+r=2，边数v=11，结点数e=6，代入公式求出面数r=7三、计算题1设G=，V= v1，v2

5、，v3，v4，v5，E= (v1,v3)，(v2,v3)，(v2,v4)，(v3,v4)，(v3,v5)，(v4,v5) ，试(1) 给出G的图形表示； (2) 写出其邻接矩阵；(3) 求出每个结点的度数； (4) 画出其补图的图形解：(1)oooov1ov5v2v3v4(2) 邻接矩阵为(3) v1结点度数为1，v2结点度数为2，v3结点度数为3，v4结点度数为2，v5结点度数为2(4) 补图图形为oooov1ov5v2v3v42图G=，其中V= a, b, c, d, e，E= (a, b), (a, c), (a, e), (b, d), (b, e), (c, e), (c, d),

6、(d, e) ，对应边的权值依次为2、1、2、3、6、1、4及5，试（1）画出G的图形； （2）写出G的邻接矩阵；（3）求出G权最小的生成树及其权值（1）G的图形如下：（2）写出G的邻接矩阵（3）G权最小的生成树及其权值3已知带权图G如右图所示 (1) 求图G的最小生成树； (2)计算该生成树的权值解：(1) 最小生成树为12357(2) 该生成树的权值为(1+2+3+5+7)=184设有一组权为2, 3, 5, 7, 17, 31，试画出相应的最优二叉树，计算该最优二叉树的权35251071731173465权为 2*5+3*5+5*4+7*3+17*2+31=131四、证明题1设G是一个n

7、阶无向简单图，n是大于等于3的奇数证明图G与它的补图中的奇数度顶点个数相等证明：设，则是由n阶无向完全图的边删去E所得到的所以对于任意结点，u在G和中的度数之和等于u在中的度数由于n是大于等于3的奇数，从而的每个结点都是偶数度的（度），于是若在G中是奇数度结点，则它在中也是奇数度结点故图G与它的补图中的奇数度结点个数相等2设连通图G有k个奇数度的结点，证明在图G中至少要添加条边才能使其成为欧拉图证明：由定理3.1.2，任何图中度数为奇数的结点必是偶数，可知k是偶数又根据定理4.1.1的推论，图G是欧拉图的充分必要条件是图G不含奇数度结点因此只要在每对奇数度结点之间各加一条边，使图G的所有结点的

8、度数变为偶数，成为欧拉图故最少要加条边到图G才能使其成为欧拉图If we dont do that it will go on and go on. We have to stop it; we need the courage to do it.His comments came hours after Fifa vice-president Jeffrey Webb - also in London for the FAs celebrations - said he wanted to meet Ivory Coast international Toure to discuss his

9、 complaint.CSKA general director Roman Babaev says the matter has been exaggerated by the Ivorian and the British media.Blatter, 77, said: It has been decided by the Fifa congress that it is a nonsense for racism to be dealt with with fines. You can always find money from somebody to pay them.It is

10、a nonsense to have matches played without spectators because it is against the spirit of football and against the visiting team. It is all nonsense.We can do something better to fight racism and discrimination.This is one of the villains we have today in our game. But it is only with harsh sanctions

11、 that racism and discrimination can be washed out of football.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunda

12、y.I am going to be at the match tomorrow and I have asked to meet Yaya Toure, he told BBC Sport.For me its about how he felt and I would like to speak to him first to find out what his experience was.Uefa hasopened disciplinary proceedings against CSKAfor the racist behaviour of their fans duringCit

13、ys 2-1 win.Michel Platini, president of European footballs governing body, has also ordered an immediate investigation into the referees actions.CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We found no racist insults from fans of CSKA.Bau

14、mgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunda.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The

15、balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles

16、/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platfo

17、rm.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big

18、jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins

19、 out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will

20、have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed t

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25、蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节

26、袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂

27、羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆 羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁

28、莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀

29、芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀

30、薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁

31、肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇

32、螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂

33、肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇

34、薃 肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁

35、蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇

36、螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅

37、莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃

38、艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇膆蚀蚆 螃艿蒃薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆莇螆羃荿薃蚂羂肈莅薈羂膀薁薄羁莃蒄袂羀肂虿螈罿膅蒂蚄羈芇蚇薀羇荿蒀衿肆聿芃螅肆膁葿蚁肅莄芁蚇肄肃薇薃肃膆莀袁肂芈薅螇肁莀莈蚃肀肀薃蕿膀膂莆袈腿芄薂螄膈蒇莅螀膇 膆蚀蚆螃艿蒃 薂螃莁蚈袁螂肁蒁螇螁膃蚇蚃袀芅葿蕿衿莈节袇袈肇蒈袃袈芀芁蝿袇莂薆蚅袆肂荿薁袅膄薄袀袄芆9