• 2022-06-12
    设[tex=21.0x1.571]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+hVTIREG04nfnohj3+3XWYMMsCLvUXp2+4cOBBgWP4LysvMw8iTR+PUn0KqP3gq9fOSmalmrjAy2TbvgAD1nFVfy1Oinz9c4/I96aiIxT2k5p5PcIIeMmPdkqaO9G7zrfx95yC2bgGpuwxci2BKvZXOb6bpcPPkfUF3dzpZaymYmgAHn/C/dpEdouePYl46kffeblAoFYNzuvoFeevlKyz0[/tex]其中范数定义为[tex=11.214x4.214]C2Z1okXIB9N6IXD+I3AE30V4KRCMUuCW1s0jlSfvlLWZz/YRFbiOS71BkBeBKBXSDcPweigVYRGZIv3NEorLT+ad2ji6SOyIH7ItbIYfkqYWKZxBxhMaDNv+T1bbrZv6yO1iXIipHBmyfznTq3mrTw==[/tex]又对 [tex=5.929x1.357]IYH/UBb8Awi/yk8qRDzRLeVx3pYuN3TFsZqQrUGoRw/P5J4ReCDovIXN/JqN2sb2ErDA6pQpKcPl9LStH4iw+Q==[/tex]定义[tex=23.929x3.0]WIrYU0rKhL/zpyMF9weCsaT+cNX3DFRVwwrhJk4Ig0pf2BYG9jEnxYL28N2rZKbelVMZWrmYdevd2BzFWmOlQbfgcFRI+gbe4aelp/qhVLdT0WEj+0jaTOu67HCV5qmjKO9DKza8wQy2Fsd+eRSpvbPcVPXHIGqmopVl8Eya5EpeHrPFv5gFvfckpiW6rtKz3hs7dYqyoZM1Ew96fxSLy7srOg2nptL090SOGzbN988hGlEAH24sl4a+8ebX8zTVRi4DmEIph5Cp+kgekoNjNQ==[/tex]求证:(1) [tex=4.143x1.429]WIrYU0rKhL/zpyMF9weCsXVUVnoIJViv50bDvDsbw3U=[/tex](2) [tex=2.429x1.286]TcPYtqbLyx9HEJHO4uMSi/jOa0fUSR2ermpAS6B3lSc=[/tex] 是 [tex=3.714x1.357]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+h4tmA9IpCQLFRdf10cJgMQ[/tex]的等价模;(3) [tex=3.714x1.357]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+h4tmA9IpCQLFRdf10cJgMQ[/tex]完备.
  • 证 首先[tex=2.286x1.286]Ueo2H3dg9WG5pdnvB+FK1Apk4tSoTAhYBizhdebfLps=[/tex][tex=6.143x2.929]j6iiTp6Zfl2/HijLp9Bhks1BGyTsMt58iQhDPT6cJNgaTojf0RdqfvpdAwsTDFMu2knmavEiGNYF+GdaDepXujTh2+u5otu2lNBFLJ+VeAc=[/tex]   [tex=5.929x1.571]ofntoEmLfn0XUIs11G/x5qGONow33ioN7C/KuYDkJ8RAYcdVCHlVX8Odl04cxrlsGe7C6PNx3oPaC1D2Yb5ypzbW+mmQ7yLy9oPoWyA12HU=[/tex]  [tex=14.357x3.357]5rgjoiab4YVq0pqOIxaa2texaULAZw2WiAep65Clyz4OrUfZqPOQkMlhKYgMbnzkhgAKzqqc++QfgLorKwrwdTI1sCOGak4LtCD/5+vYns0KZ/qUY7bELFtYOQM8pVzJ43obHmHdZNzIzP34YohnRMIleM/hwZTjMmp76QFwhwh4CqKC93I3erqBoArsGPrlzL2+ZA2W0MPvChnywx6G/Pg2maKtUB3X+5kIToQnURxwXWBiPUDi8tSQNNJlpoJz[/tex][tex=10.429x3.143]j6iiTp6Zfl2/HijLp9Bhksgoh81LMAOmdd3uJNGiAQLMr1QmR0kvc3z64nUcED1YGQHcNqDKMtRROKqKT4zxH5xND7Lv6pC6G0dh6fL9LMpC1U/MdOuGWcUu1D4xvOeqH74zp8ESPxWyrJ/58/9mUg==[/tex]从此等式可知[tex=12.357x3.143]PIHr+dQvshhaTLGTNxgKwYB9bQdghqto5PN7+pqsASXRif9jOwQsKIYc5JRUNeTaTxi16VuXVc4qNg1kuCotLXhXBrJb23wG+XUhH6WmvtkQX455SYFdbPjyqcsVaJEVmdtrz3416BefkkNuRsnqIw==[/tex]又[tex=11.071x2.357]LD2LcxjkLEIh3n9PsE60rZiSIE/IU45ytFgpuNWKvN3xDnnXWN/SClYVHWPH/b0udouuxfuA/tyGhdpMPM1OlT2TNCPMVJMfO7EOy0s9f1HpFjEeKC3faw/h1C+RjQHzSCb+SSJZcJ/GITDeFYB7OA==[/tex]再根据一个常用不等式:[tex=15.929x2.929]+h2oulxmEIkABM8sHZYksqbB2EjfN0bV/+/WqRFEnqtZB69iSCFS4y1OQO2sQN1agAOkNj5fcxDlqqjjGfOGpLTFd/AkbT1dM8i+ll6ZwNUMYBiTyAyPmnGrvp8FwQFqCalc1e6VBVVyx2+NlfqFFLVEVdB89c49jCXHOrJ+GwgvrvZ1HkYF5KXx+RErA9oH[/tex]便有[tex=11.071x1.286]K6v732qefe6rnW4pbx1lvIdKGOetbx+VBP4Y8v0JqpO1PHuVYrnm9IAgFtM1I8WiWXrLWtW6jcs3bPuKItu7xK3E1qhE+Ww5xQxVu544y1R32dizViGqmGDJI9CZD+p9[/tex]到 此 (1),(2) 结论已证. 下证 3. 由 2 只需证[tex=6.714x1.429]b7CNbXPN/pM0Vd0jvRhUGCU8Tgjp8v1c2Bhvirk7+OP0upHArHy/uMgk5Oyv+GQIZ+qewc/sCZzVyCI+JUJcjzropmqs2o2GiG1gyVmyjDc=[/tex] 完备.事实上,设 [tex=2.0x1.357]/aFyWAjC8I1XGTGuEP56a+Ud8G6l11fs1abAWu2WtLQ=[/tex] 是基本列,既[tex=6.571x1.571]2lUdcijS+tCaIfgoF9RdWo4/g64nZkrnY+OpU5GvudgrZ9WS4SCH9e4jX9N00cW7j3Be5fPpJndXcNpJfbEd3A==[/tex]也就是[tex=18.143x2.643]y4MOK3K2X+ETzz8rQ6/f7jazItabb7ahXdJwqq7PDWVad5uJXAoheAPGxu8tk7ddxsCC5H+j8E9N+LHzVj+jSKAnORgnBmTS5p7Xl08K+RvaEWnINVutb8Q1qCfm1HhgdNJ4UHJn/GxD58CM7O90KUClp4xB5HWzO/dbj9WajOUhg3xmBJyfeV7WFLKtpbotMmSr5Qm5Y7AwJJWOA9X1Aw==[/tex]对 [tex=1.071x1.214]e4yzJ/N73x9Uopfd4k63hQ==[/tex] 一致成立.由此可见[tex=8.214x2.214]CAWRIK/pjEKzlWCXKfNzRnA7P+iaFQDdGqbktBCRG/TN55BCV9k/NnDiLdkfVrAI3jx7c8Zse2MPZ9H49m19Ne6sLk3UweF967Fr9GePvjk=[/tex]是 [tex=3.214x1.5]dYjbSlxCGKLmbXD54HadeAwy++ColRJWAXOoab+n9XsJe4rzJCxoKxitcAPNogmX[/tex] 的基本列,从而 [tex=3.357x1.357]oBqqs1w+5UI3pT0eiRV8eMfzWsd/VP+bEuLHNPfXw7A=[/tex]也为 [tex=3.214x1.5]dYjbSlxCGKLmbXD54HadeAwy++ColRJWAXOoab+n9XsJe4rzJCxoKxitcAPNogmX[/tex]的基本列. 因为 [tex=3.214x1.5]dYjbSlxCGKLmbXD54HadeAwy++ColRJWAXOoab+n9XsJe4rzJCxoKxitcAPNogmX[/tex]完备,所以设[tex=11.071x3.929]7EJHVCtO2IWq3KpdB+jQslR4UhPCBwmD8qJ7D4H6l1qzGmPz/jj1Ky1fvCI/CktlV/v9tD/MoJV4hz8wPz4HxVSk3TMjtzO6FQpzQakoce5m7Sns8vCoCZIdtZOSJ7PHDm+ayzZ2MO1rc0KtNZoHNrCq/1CXWzXLd4N9/GdYsm6r5WjLvL0MdWBx5VeNYiDUtLUHkc2zBai5A+YyjnoLJ4ul1NS9fviJu/kvh77G1qzWdHCX7QWHZnYGmTxAApmL[/tex]则存在 [tex=1.571x0.786]e5kU0z6j5RCa3ZWHIzfXjQ==[/tex] 收敛子列[tex=12.571x2.214]BrODlBfQmeKIA/BJyxzMdJaHk3ZFLyjgGFAKYlnFQIDHgbQq3wm+z4i+EKWpzg9b8DiSbvICDqg7JHFzZrXHDZHclpt1U6wof9Oj7+wIerpTdJFPBQOCy1jtHgOKMRToiQ77Fx3itbO6e3zamVCu07g6R1HAVk2m95IJuZTPwAE=[/tex]使得[tex=20.143x2.0]Q7tExsev4oklTN28FsHouIb9+wQJkiwRA7/ZJONDDn2vOG2hqdl3+Bm9qS4sBObQJZPisVnu+S67oSYITk5QfIy+Sup9XSLC6boWGLtmJ3lMkDb/2ytIka9XofFdfXd/VyeC5LuM+0qG4K1i32P/ZW7VnK1M2w22+4RVKLDNQiblRgtHAa2RKqaQpdIaOUCt/epeDTBzInPXxTskdcACXRQZ8DP+BsypzXqaZIYTJfKqlnCVY6ZGkReS9+qgICXpWiFYvGKyuOltXtqTYozR5RIT2rzKXicNs972yGsuwEs=[/tex]故有[tex=14.357x1.786]brZyx2i/j66yGbiFdRMAZ3CdLy5ovQ5TF7JiFzTnYuSBoQLXSNnJazObozaP8T2ZOBSKG/6UT+GZjSxkyDn47v/+Q/Rn9kSkabo7HaYRNztu9AqKMoHtmCa8csnRAiVWF6pHujFUWPleA35VKNU3Z6CN1CAhsH3wjrewVxxmB9jIgtAT9FYl1yPtyp1OVc1A[/tex]由此即知[tex=8.857x1.786]brZyx2i/j66yGbiFdRMAZ3CdLy5ovQ5TF7JiFzTnYuShkcaoPSe2h2bg04QLL+6rk5hay/A/r9o3F5CK+Vmd9vAcyUCtQxztLqlZZHjVCmikS6isc2rw2Nm8EruwEZ4J[/tex][tex=14.429x1.786]kFRo/7XpTTDTqLHuaXq8JFI5GeWpcW748rmwLUMnhzNeBFwQ5fpNdvz2unaqHjR0v3yYBTZ1w9wAeLh0IG6xR9sX2t2oB7pu3c9UHiXWa/lsA4T0qt51pThzy4liZjl9dN6nyopg5DyAcRwrdCYdwOaUbBwIBdoaK/x5pxT92eQNUxzckZ81jMySqPdo0BOD[/tex]其中 [tex=2.143x1.0]Ht2GnvB6m0ly/iA+5p2f/Q==[/tex]故有[tex=8.929x1.5]RnJVxApC31u56zY6C8Mw8gzxiKaVjQ2Zm9xmxzjHqycmj8p6I4rWb6rDGdaDt3dxadgXpPlrTAmvSXguh3nhiJMvpYkfiMqCCSflLoAeGcA=[/tex] 于是  [tex=6.714x1.429]b7CNbXPN/pM0Vd0jvRhUGCU8Tgjp8v1c2Bhvirk7+OP0upHArHy/uMgk5Oyv+GQIZ+qewc/sCZzVyCI+JUJcjzropmqs2o2GiG1gyVmyjDc=[/tex]完备.

    举一反三

    内容

    • 0

      设[tex=21.0x1.571]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+hVTIREG04nfnohj3+3XWYMMsCLvUXp2+4cOBBgWP4LysvMw8iTR+PUn0KqP3gq9fOSmalmrjAy2TbvgAD1nFVfy1Oinz9c4/I96aiIxT2k5p5PcIIeMmPdkqaO9G7zrfx95yC2bgGpuwxci2BKvZXOb6bpcPPkfUF3dzpZaymYmgAHn/C/dpEdouePYl46kffeblAoFYNzuvoFeevlKyz0[/tex]其中范数定义为[tex=11.214x4.214]C2Z1okXIB9N6IXD+I3AE30V4KRCMUuCW1s0jlSfvlLWZz/YRFbiOS71BkBeBKBXSDcPweigVYRGZIv3NEorLT+ad2ji6SOyIH7ItbIYfkqYWKZxBxhMaDNv+T1bbrZv6yO1iXIipHBmyfznTq3mrTw==[/tex]又对 [tex=5.929x1.357]IYH/UBb8Awi/yk8qRDzRLeVx3pYuN3TFsZqQrUGoRw/P5J4ReCDovIXN/JqN2sb2ErDA6pQpKcPl9LStH4iw+Q==[/tex]定义[tex=23.929x3.0]WIrYU0rKhL/zpyMF9weCsaT+cNX3DFRVwwrhJk4Ig0pf2BYG9jEnxYL28N2rZKbelVMZWrmYdevd2BzFWmOlQbfgcFRI+gbe4aelp/qhVLdT0WEj+0jaTOu67HCV5qmjKO9DKza8wQy2Fsd+eRSpvbPcVPXHIGqmopVl8Eya5EpeHrPFv5gFvfckpiW6rtKz3hs7dYqyoZM1Ew96fxSLy7srOg2nptL090SOGzbN988hGlEAH24sl4a+8ebX8zTVRi4DmEIph5Cp+kgekoNjNQ==[/tex]求证:(1) [tex=4.143x1.429]WIrYU0rKhL/zpyMF9weCsXVUVnoIJViv50bDvDsbw3U=[/tex](2) [tex=2.429x1.286]TcPYtqbLyx9HEJHO4uMSi/jOa0fUSR2ermpAS6B3lSc=[/tex] 是 [tex=3.714x1.357]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+h4tmA9IpCQLFRdf10cJgMQ[/tex]的等价模;(3) [tex=3.714x1.357]/78IfboECKECUUMdsLuwCqHTL8QoTRwdM16/eOf81+h4tmA9IpCQLFRdf10cJgMQ[/tex]完备.

    • 1

      输出九九乘法表。 1*1=1 2*1=2 2*2=4 3*1=3 3*2=6 3*3=9 4*1=4 4*2=8 4*3=12 4*4=16 5*1=5 5*2=10 5*3=15 5*4=20 5*5=25 6*1=6 6*2=12 6*3=18 6*4=24 6*5=30 6*6=36 7*1=7 7*2=14 7*3=21 7*4=28 7*5=35 7*6=42 7*7=49 8*1=8 8*2=16 8*3=24 8*4=32 8*5=40 8*6=48 8*7=56 8*8=64 9*1=9

    • 2

      当执行下面的语句定义一维数组a后,此数组的所有元素为 ( ) inta[10]; A.a[1],a[2],a[3],a[4],a[5],a[6],a[8],a[9],a[10],a[10] B.a[0],a[1],a[2],a[3],a[4],a[5],a[6],a[7],a[8],a[9] C.a[0],a[2],a[3],a[4],a[5],a[6],a[7],a[8],a[9],a[10] D.a[1],a[2],a [3],a[4],a [5],a [9],a [7],a [8],a [9],a [10],a [11]

    • 3

      下面语句的输出结果是?range(len('HelloWorld')) A: [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11] B: 11 C: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] D: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]

    • 4

      设DES加密算法中的一个S盒为: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0 15 12 8 2 4 9 1 7 5 11 A: 1010 B: 0001 C: 1011 D: 0111