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TRANSFINITENESS - FOR
GRAPHS, ELECTRICAL NETWORKS AND RANDOM WALKS |
| ERRATA ((In the following, one symbol does not appear properly on this web-page display. When this occurs, I explain what the proper symbol is by a statement in double parentheses. Also, upon request, I will send by regular mail a hard copy with that symbol correctly displayed.)) Page 3, line 8 down: Replace the symbol n by mPage 4, line 12 up: After ``on'' insert the following phrase: ``- with however certain designated exclusions from or additions to the embracings.''Page 23: After the definition of a subgraph, insert the following sentence: ``A graph or subgraph is said to embrace itself, all the branches and nodes of its elements, all tips of its embraced nodes, and all subgraphs of itself.''Page 31, line 8 down: After ``ranks.'' insert the sentence, ``Finally, by this definition ntm does not embrace anything else, such as the representatives of its embraced tips.''Page 32: After the definition of a subgraph, insert the following sentence: ``A graph or subgraph is said to embrace itself, all the branches and nodes of its elements, all tips of its embraced nodes, and all subgraphs of itself.''Page 37, line 14 up: The words ``nodes and'' are superfluous. Remove them.Page 37, last line: Add the parenthetical statement: ``(As before, n[(w)\vec] does not embrace anything else, by definition.)'' (([(w)\vec] should be an ``omega with an arrow over it''.))Page 40, line 16 up: After ``we define'' insert the phrase ``embraced elements,''Page 42, line 5 up: Remove the arrow over the omegaPage 43, line 4 up: After the colon, insert the phrase ``embraced elements,''Page 49, line 17 down: Just before the period, insert the phrase, ``augmented by the nodes of ranks larger than r that contain tips traversed by that component''Page 49, line 9 up: In the first line of Lemma 3.1-2, insert the following phrase just before the comma: ``and if r-sections partition Gn (i.e., if different r-sections do not share branches)''Page 50, line 4 down: Remove the phrase ``definition of a r-section'' and replace it by the phrase ``assumed partitioning''Page 54, line 11 down: Just after the comma, insert the phrase ``under Conditions 3.2-1,''Page 55, line 18 up: Replace nb by ncPage 60, line 16 up: At the end of that paragraph, add the following sentence: ``Moreover, it is understood that no node appears more than once in the lowest level of this hierarchy of sequences. We assert this by stating that every sequence (of any rank) is node-distinct.''Page 60, line 12 up: Replace ``sequence'' by ``node-distinct sequence''Page 61, line 15 down: Replace ``0-sequence of 0-sequences'' by ``node-distinct 0-sequence of 0-sequences''Page 63, line 7 up: Replace `` 0-sequence'' by ``node-distinct 0-sequence''Page 68, line 2 down: Replace ``0-sequence'' by ``node-distinct 0-sequence''Page 69, line 11 down: Replace ``0-sequence'' by ``node-distinct 0-sequence''Page 87, last line: Add the phrase ``and every 0-node is of finite degree''Page 89, line 10 down: Replace ``two-ended'' by ``endless''Page 90, line 4 down: Replace ``4.1-2'' by ``4.2-1''Page 92, line 10 down: Replace ``k'' by ``1'' Page 89, line 7 up: Just before the period, insert a comma and then inequality, ``((nu not equal to omega with an arrow over it))'' Page 97, line 3 down: Replace m0 by m00 Page 129, line 9 down: Delete the first ``of'' Page 129, line 2 up: Delete ``of'' Page 151, line 11 up: Replace vk by -vk Page 151, line 10 up: Replace vk by -vk Page 151, line 3 up: Replace P0 by P1 Page 153: In the caption of Fig. 5.11, replace ``5.5-2'' by ``5.5-3'' Page 179, line 18 down: Replace ``Properties 6.3-1 hold for Ns'' by ``the node voltages for Ns are bounded above and below by the maximum and minimum of the node voltages at the nk'' Page 182: line 16 up: Insert ``P'' after the word ``path'' Page 193, line 16 up: Replace ``elements'' by ``branches, nodes, tips, and walks'' Page 198, line 12 down: Make ``T'' boldface Page 203, line 6 up: Replace ``and'' by ``an'' Page 206, line 12 up: Replace the superscript 0 by delta Page 209, line 4 down: Replace Mp by M and replace Mpa by Mp Page 214, line 15 up: Replace ``alternative'' by``alternatively'' Page 217, line 7 down: Replace ``Theorem 7.6-1'' by ``Theorems 7.4-2 and 7.6-1'' Page 218, line 1 down: Replace ``that'' by ``such a'' Page 218, line 12 down: Replace ``Theorem 7.6-1'' by ``Theorems 7.4-2 and 7.6-1'' Page 221, line 7 down: Just before the period insert ``containing all the v-nodes and possibly other nodes as well.'' Page 221, last line: Just after n0 insert ,ns Page 241, line 5 down: Replace 75 by 74 Page 245: Replace ``surrogate network, 219'' by ``surrogate network, 215, 220''
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