• 2022-06-12
    用等价范数定理证明 [tex=5.286x1.357]sp1SAX4MS5ouBpfi45MH+21QERCYroOnhQaJvmzlWa4gJDJq05unaaoXX3779WLB[/tex] 不是 [tex=3.429x1.0]hRlWsjFqxdxSbRSyuIRayg==[/tex] 空间,其中[tex=12.214x2.786]dLGGLAPL0xFCxvU9J3KDZEvPA/f7moSAbePCXJ55WH1kkhn29x2849//5t5YbUxwjdQB28UP6tQ0Zu/ssmjqD07ys+bcwv62RJN9BBACoG0=[/tex]
  • 证   用反 证 法. 假如 [tex=5.286x1.357]sp1SAX4MS5ouBpfi45MH+21QERCYroOnhQaJvmzlWa4gJDJq05unaaoXX3779WLB[/tex] 是 $B$ 空间,注 意 到 空 间[tex=2.714x1.357]cMf/ATOuKTCQQx3cKnaH4Q==[/tex] 的范数是[tex=7.357x1.929]D4uJQVuywBZPESM8zIIJyiv2TM1SPzlaubh5gSIgqKLYWoI91F6yyUE8KfBL+ACob7EPspqmF6m+xWbrF0kBAg==[/tex]现在[tex=16.214x2.786]dLGGLAPL0xFCxvU9J3KDZEvPA/f7moSAbePCXJ55WH2PWetraiZQIo7ujAGKw4uHEiBdcPsjhnYnSvns7UNHJPfjEpU+e5hVCskmzPd0Wdhz9Dv86FBnpNcd4Eptp+jb0Prvd+kYT4k78BKN3Fe2cA==[/tex][tex=1.786x1.357]xBtKqCHl8kKAq4P2HzdKTA==[/tex] 是比 [tex=1.643x1.357]WYfx5d3rmuEzi1iGnsDJZw==[/tex]强的范数,用等价范数定理,[tex=1.786x1.357]xBtKqCHl8kKAq4P2HzdKTA==[/tex] 与 [tex=1.643x1.357]WYfx5d3rmuEzi1iGnsDJZw==[/tex]等 价 ,  即 [tex=3.143x1.214]1p7/6/aMfoyWT964y4FWCA==[/tex]使得 [tex=11.5x1.357]RGFpX0rumLlc7HXdPx401sYx7mpzrOo3TPHF3h4Eg36B7ikS3Ffn249zkfAGwNuVBJJM6E7EPs3DNTCyXUuLfg==[/tex] 今取[tex=15.143x3.357]eWobf/mlJkHLDWun+f29Wz9vbYcVnSRHPLaTtSzrGZfwJAO6pf4NpXlTQD2o2nqlXJZL3jMuKLI+D3JALjvq8YnFY7HCB1l/mI2Lg+8hgu7W/0g76mgKzV9XF5qb3tPdFNqnhcS6EsIFTuxEyyHXM+A9sRPLINIvfDxf6u2YcFKxMyLXhLdlhHGqG3KNNreDUWc0ba6PebQcfKkYI6OdTg==[/tex]则有 [tex=4.357x1.357]sfEKAwb2Gpzq0IRcUY416puNJLJck/ZMxqQqYCIl2WI=[/tex] 且 [tex=10.643x1.357]tsdVU46qUGiZLAR6e6ukyKUDyVwuI7qxShd2oZi7AibTWDUkOPcVPH9ngF7eWufCuFlye71OpExjEEPAa+yFfw==[/tex](参见图 2.5 ). 于是出现[tex=13.714x2.357]QJsUA2hmNaPBQGbZY7ZgUF8eC1EfkE1sfzmYhT5+jX92hApRwjjFN6YTFiGb5bylAe6T/1S784V0PZGcNM6rIfQXRBxfZL1C4gHTdYIK6EDzDPSuPQfXtM30FaGGTTFp[/tex]矛盾[img=292x364]178555f26e5cd47.png[/img]

    内容

    • 0

      set1 = {x for x in range(10)} print(set1) 以上代码的运行结果为? A: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} B: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10} C: {1, 2, 3, 4, 5, 6, 7, 8, 9} D: {1, 2, 3, 4, 5, 6, 7, 8, 9,10}

    • 1

      设f(x)具有性质:[tex=8.571x1.357]8gPeznjMnng12qtkk9Vgczii1Sh4d1qJxc9iHYT5+YI=[/tex]证明:必有f(0)=0,[tex=5.5x1.357]rt5qCY7TXHcsFUQrD44nPA==[/tex](p为任意正整数)

    • 2

      >>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']

    • 3

      设函数f(x)在[tex=3.286x1.357]64m0xE4nFlaKGIakApV0PA==[/tex]上连续,且有f(0)=0及f'(x)单调增,证明:在[tex=3.5x1.357]vgrW1/jK/GZ1TOWaPFIQWA==[/tex]上函数[tex=5.071x2.429]KmCvFjqAEA9O51+9erVGP+KtDDqVtXZQWqxj1eiTO5k=[/tex]是单调增的。

    • 4

      以下创建数组的方式错误的是() A: shortx[];x={1,2,3,4,5,6}; B: shortx[]=newshort[6];x[0]=9;x[1]=8;x[2]=7;x[3]=6;x[4]=5;x[5]=4; C: shortx[]=newshort[6];intlen=x.length;for(inti=0;i