试从极坐标系中的柯西-黎曼方程消去[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]或[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]
解：柯西-黎曼方程的极坐标表示为：[tex=7.429x5.786]fnpmC2J6JmQBLyo5NmGAzwWskHkYW3pO4L9W/DfMamEcTajn0dQ/EvlHrLZ4tGxindE5riPFrdWhIOACP+yfnr3Eos+j7c2myuvvO/IbVxf0yGZuBrOTqwsUY9DYxHgJGYHdSMqiPMitJRW7PqOq+8epqRP5lcuO887k2J9rzXDTq/kqhXZmd5SBCSWj/oU+weep6xJthgF30kDAenZojsZFuuxtbuzuu+7SYm61XoFmxnhDUevRTihuQxizlKEsOagobBVAoHa8WS1tbXgf9k7rD2P0W8pWhl/RIwfpFIs=[/tex] ①首先消去[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]，将柯西-黎曼方程变形为[tex=7.643x5.786]fnpmC2J6JmQBLyo5NmGAz6tcWOCSCsa/OEGgWn0dljFNKHuEnjBKCYV9f4aDnVqiVW5WYkYwbL05/qDjwNSoLaVAXS9eR6iRTVu9S6kcq0lSiyK/ArjP33rReagoloQrSpkrs3PtQcvGyTS5DG5o5HPzqtnRiNyYbx8Wr/DpMGk+ZC76TGzW11uFrITp0uYXJ/lzul2dBar+Wn6UWTNG5GtV/Y9RvRpprGalwu+TEbA9rQkcVMN/CkgWDhs3MSKWmTx9L8lfJOkfd9cmetLF9g==[/tex] ②②中分别对[tex=0.571x1.0]BMX8X5xI0h1MuijqrEhCyw==[/tex]和[tex=0.714x1.0]y9ABqRCnjQW6yIa1BUBRPA==[/tex]求微分[tex=8.571x2.786]gCY/iAehrLEDrnZW89qHhWXhnPQgIV3fwDwrIed/aFVtjM3lcyG9fEAofLqYN1n+knMSPKUiuwIqe+VXkA0Vmvilqon/B6j2r6Qa9tvmu3oHSEEd1S/NT8GVS59hTohfuRJrf/zFUQ44JNGa3s4lecveUC/G0KAjMDLYOTbRLzvU4obPO+KRdMUf3LBeG4Bh[/tex]，[tex=7.286x2.714]883meqBGMwcVgA7tTpuh+/CzKSuq9wF8uokGPyyZmVxXhDS/5H2962VA6CCgyAMEicLq0a17fpyT8uRA8DgdWfRb6r2xHQVfnu78UBn2x7vzgvH5pEf6MzGJDsadpbZcxQZt4zchJdghhqnTP50D/lz9mG8CD8JKOXmnDnWT8us=[/tex]由于[tex=6.071x2.714]Hvc3DRViYQYrFC7OWnSXU8PDf8wtv8wIPMdzrZ3idy5OKJX8DKtAvyYSI7CKF4gCp0Lk63aDe9qrTsA4qVUIYSLWpv7X8p1aPFww/4UmmDg8r3dt1/JI50RD0+lWS0A5b4d/j8tAZrYl7Y9Wis4MxA==[/tex]，有[tex=8.143x2.714]gCY/iAehrLEDrnZW89qHhcKtVCh0FxJ8vLqoWl7D+V0tCs42lrGYGbkRQTbSJ3QhyWfZywbrJXk8PfxBc7vpB03qIhcpXSu9myix+vSnQPxDohV4pDOAHMPeBUmpCXBpl2udO9DzaUq+clC6oky2nXQoBU941S1I5NlHFJOq0eIFcFHt8rpU70pwVvUXdfmd[/tex]，即[tex=8.786x2.714]gCY/iAehrLEDrnZW89qHhcKtVCh0FxJ8vLqoWl7D+V0tCs42lrGYGbkRQTbSJ3Qhs/nDPN0BObsIGWyNEkjoHQN3D83HL0OMa9DYIlaYBEFlovZGdbFn4gnSAUVetW9kOCvx+4JS9JdNx+VkRIP+d56udKHKk5Xnklc8CP2iCpc=[/tex]为消去[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]的结果再将[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]从柯西-黎曼方程中消去，变形为[tex=7.071x5.786]fnpmC2J6JmQBLyo5NmGAzwWskHkYW3pO4L9W/DfMamEcTajn0dQ/EvlHrLZ4tGxindE5riPFrdWhIOACP+yfnr3Eos+j7c2myuvvO/IbVxf0yGZuBrOTqwsUY9DYxHgJGYHdSMqiPMitJRW7PqOq+wJLjGuQB7kklZ4WNI6R9/EfzGwxuNtFjgYEFv66oJl0T+9l2wLZ1l98iXUQiFcCOdBrOfrJUthMOIlB9DFc2Y/RR0/8x+EH6QlTQBAbtuxAzsc2yUuckbSFE7RXa0/5bw==[/tex]将其对[tex=0.571x1.0]BMX8X5xI0h1MuijqrEhCyw==[/tex]和[tex=0.714x1.0]y9ABqRCnjQW6yIa1BUBRPA==[/tex]求微分[tex=12.857x2.786]Hvc3DRViYQYrFC7OWnSXU55bZRv9jRqn0lnxpN+ya7kwpWXIZvX0tHNQobo2QJ+h74cHFQoyg0H06eSnCif2vp97jSydTMfruNGrCcFpnoDEIBfDXVKaA51K+dMecVn5IqZU0J5qtq5W2pnyvyB9IK8x4IlmbZVpXrQ3Z9WMUIRRh0KelGv4PhH8HmTqOiPz4lcbWGIErgFl6QZsoLJoTl4ggLWwx9uNd+shZcwzwmH2OUMOggYKtR7IUY/eoIq9nymeDeMeuX2uPzO3yJSJ3bc08hcNDwuDSSUATKquvI8=[/tex]，[tex=16.071x2.786]Hvc3DRViYQYrFC7OWnSXU55bZRv9jRqn0lnxpN+ya7kJGuVQPmDxEjLYbm/mpFrQKMvYp9In6zw8wlFRgNii6LEKDzmp8IEWvdBu8LUGg10wob37q3rdPSpYATLSMdPjIqFxriX7CRp4QXyRQVX6Be6YUIBw9vz+XfbKbOQPe+guNzkDJj6qvpNAeuWYXQ6/MfcP0Z9bFn6O0Fbi9z0XWtW03JLJ2zJ7qefzMA57SiHqi4pPxSu3NYilWR6VrwuSxqC/HFWngcpWRvmXmjr7V23HDI9ZEfnqVzgL/9oanlg=[/tex]由于[tex=6.071x2.714]Hvc3DRViYQYrFC7OWnSXU55bZRv9jRqn0lnxpN+ya7kwpWXIZvX0tHNQobo2QJ+h74cHFQoyg0H06eSnCif2vsDSb4Y9ClgYPjMzk3ABBjuLGKc3I2PomKSxzpvhbmxF6gxptybhk/l8K+yvHNrSZA==[/tex]，所以[tex=9.571x2.786]heL+mNT2qwXO4jrz6kuap7XbgG0zji9rcBTm2379D1OJoniqEASAlaUrJ/2WyOeyOwmh1awJucO5G5UYWzxIPAMdLsHj6cWNaDN+hKNvJBmXQyCf9ixTbAHcWhzaxYz+RCUH6VNhU7oDLeMfSx/XWqdhfdxe0qf+OHoPhf49xflIICUygJyvUvnemGamuVH+[/tex]即[tex=10.214x2.786]gCY/iAehrLEDrnZW89qHhWXhnPQgIV3fwDwrIed/aFVtjM3lcyG9fEAofLqYN1n+vvYzeTK35yKw9GpKR+PAZ3gEQtMKaejRJcz/tmvTwrP90dBsGOifhbSoj7+vfdde/izuVsL84vkDbMZcpZBhmfd8I89G0oPreMGzOur7PabYJbg97b+f9kRdB94e8u4f[/tex]为消去[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]的结果[tex=12.143x6.071]fnpmC2J6JmQBLyo5NmGAzwWskHkYW3pO4L9W/DfMamFac2iRTZxQzx7kTCc0gDavpEa3+Dw5LG+cGAn9yZfA2HqvopJjbR5XozrK8ZH4WMcHXgyMeGUmmxmHt7yv12rUZjTwUDCgT+YmBVramWUnXOdVDcGd3nhkHBWZQbwz3QZGDkpHvuv/eDm05XA5oiy9t1KzRafROoBrt0LqIzHlNons5DhoBkAuIG5QPjAefJeS9Izc8rp+1dfF7FgiIRnfvZ6hVL+njmhNcm7nu4w4amCbviLQlkUcWnCkuhmzp31UErPuoMbIqpjtd4zAKEdN9xXVYINXje8+M9l9wJSkpFVGWhu5p/Fje63zZ8qZcqSGre8uitq1M2vvpUW21R1Tj9eFA9o+KTMI9XyRL6WmaWLrv/+RtKF40r4aCmQG7Gzjpwf4BK2Hkg8SoL01kDJI[/tex]为极坐标系中拉普拉斯方程的b'd's
举一反三
- 设[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]、[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]和[tex=0.786x0.786]44SGfA2gQ2VZlXa1QKZD0Q==[/tex]是一个简单图的3个顶点，简单图[tex=0.786x1.0]JTRtgqQ00R3dUQzwS4iwbg==[/tex]的簇系数[tex=2.286x1.357]LwqQzNryA4iLraKFpWGw+w==[/tex]是当[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]和[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]是邻居且[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]和[tex=0.786x0.786]44SGfA2gQ2VZlXa1QKZD0Q==[/tex]是邻居时，[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]和[tex=0.786x0.786]44SGfA2gQ2VZlXa1QKZD0Q==[/tex]是邻居的概率。设[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]、[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]和[tex=0.786x0.786]44SGfA2gQ2VZlXa1QKZD0Q==[/tex]是一个简单图的3个顶点，当这些顶点构成的所有3对顶点之间都有边相连时，这3个顶点构成一个三角形。求用图中三角形个数以及图中长度为2的通路的条数表示的[tex=2.286x1.357]LwqQzNryA4iLraKFpWGw+w==[/tex]的公式。
- 设[tex=6.286x2.786]sSXBpxJWudVpH1R35o4LnNqtHlH5UjfBVTOmTW8BesmxYz2MP+BvmFQJfMZJeNPcy4ThYyieay+fljxIl6phFA==[/tex]，[tex=6.286x2.786]tAg4kjefm91yBdigy4ffjNhyLpgIixV0MMu+888/BDqJfwPkdMwWQN9lGtA6Squ0YnkROEim0IrVlMdpcAiuFw==[/tex]，[tex=7.0x2.786]XbmfowmH+x2njRlGmJod4kR6X4UWu06xrikpHrm1d19lRAZYRfxYgm0nIma48KGN5KhG6FqEHRJLu4V9BK8mbw==[/tex]，且[tex=6.286x1.143]ECHz4HQK/40982jrlVGfFw==[/tex]，试求[tex=0.571x0.786]c5VsltFnl9nO0qB/vNKOWA==[/tex]，[tex=0.5x1.0]iwXm0SwS+lfupyC0IyH8yQ==[/tex]，[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]，[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]的值．
- 假设图[tex=0.786x1.0]JTRtgqQ00R3dUQzwS4iwbg==[/tex]采用邻接表存储,设计一个算法,输出图[tex=0.786x1.0]JTRtgqQ00R3dUQzwS4iwbg==[/tex]中从顶点[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]到[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]的所有简单路径。
- 证明:若[tex=4.0x1.357]THnRwu1934YXhnQhFyLmxw==[/tex]是有向图，则[tex=0.643x1.0]SW0o8G0GHsmLXldwnq7xKg==[/tex]中的两个顶点[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]和[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]所在的强连通分支要么相同，要么不相交。
- 设[tex=4.0x1.357]1SDnUjdWVQFV4kZw1rzrtQ==[/tex]是无向完全图（无自环），[tex=2.571x1.357]ZjkiTZGSyNGoWWOwHFZ7+A==[/tex]（3）设[tex=5.286x1.214]zT0mhj7jlVF1+aul86Anth5+vlcPdIPg/QAH+wZLLSo=[/tex]，求由[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]到[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]有几条初级路？
内容
- 0
设[tex=1.0x1.214]fxP5NKfuaC23W5waarA1ZQ==[/tex]和[tex=1.0x1.214]oSv4U8R1pGloBPK+RYGtWA==[/tex]是简单图[tex=0.786x1.0]JTRtgqQ00R3dUQzwS4iwbg==[/tex]中顶点[tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex]和[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]之间的没有相同边集的两条简单通路。证明:在[tex=0.786x1.0]JTRtgqQ00R3dUQzwS4iwbg==[/tex]中存在简单回路。
- 1
试从方程 [tex=9.143x1.214]j6esVvrKhRBH+Kgq291g1HeQEJjuvft7uj+b3NhCT4kNjuD3ny2uZ8N/M/w3MzfU[/tex] ([tex=0.643x0.786]W9TCskxkagdDgWMvasdFzg==[/tex] 为固定常数)消去参数使之成为微分方程.
- 2
设函数 [tex=4.0x1.357]AcsG/g4yU933TGrJs0qkCQ==[/tex] 由方程组[tex=5.071x3.929]7EJHVCtO2IWq3KpdB+jQspq+JO+uwPH8Ux91tyN71vTdDKBfwgk8MiTF21OOk6PAeXolIsQy49irgUqeQ2Fx9WEUFro6j/PYBuWYZFoBw0w=[/tex],([tex=0.643x0.786]cnVwa8IjZzNSEmAUXJ8VCQ==[/tex] 及 [tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex] 为参数 ) 定义,求当 [tex=2.429x1.0]jLFeTkQ9+gF8zZ0Q+HAm6g==[/tex] 及 [tex=1.786x1.0]fzjjdGRcIzXvIiuaRk9mgA==[/tex]时的 [tex=1.0x1.0]GuSsJw9EJz841iz2HGPwOQ==[/tex] 及 [tex=1.429x1.214]DruUkpmNsOeolYelbImbJw==[/tex]
- 3
已知解析函数的实部[tex=0.643x0.786]2LwQJcArGuAsQ0k00CwMFw==[/tex]（虚部[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]），求其虚部[tex=0.5x0.786]WThQ8iw4nU0wcEP44SeqUw==[/tex]（实部[tex=0.643x0.786]2LwQJcArGuAsQ0k00CwMFw==[/tex]），并求此解析函数：[tex=5.143x2.357]VBHNDNmvV1994URrJ1CE7QVnAFXgeamWgYGmRgvonyo=[/tex].
- 4
已知解析函数的实部[tex=0.643x0.786]2LwQJcArGuAsQ0k00CwMFw==[/tex]（虚部[tex=0.5x0.786]GWrvJtODhYOBa2bpkSPSFQ==[/tex]），求其虚部[tex=0.5x0.786]WThQ8iw4nU0wcEP44SeqUw==[/tex]（实部[tex=0.643x0.786]2LwQJcArGuAsQ0k00CwMFw==[/tex]），并求此解析函数：[tex=5.0x1.143]xK30dwm0qZ4c2ZELwVkBhIwMka1ZX/qgOzAmQjEZusI=[/tex].