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The following discussion is a summary based on the introduction to Appel and Haken's book Every Planar Map is Four Colorable.
Some Related Sentences
following and discussion
Since I have already discussed his moral position, that discussion is incorporated by reference into the following pages, which will focus on the empirical and analytic side of Fromm's treatment.
The following discussion of this subject has been adapted from the book Causes Of Catastrophe by L. Don Leet.
It will be recalled from the discussion in Section 7 that the position of the `` right '', as represented by Barth, rests on the following thesis: The only tenable alternative to Bultmann's position is a theology that ( 1 ) rejects or at least qualifies his unconditioned demand for demythologization and existential interpretation ; ;
Melville devotes the following chapter to a discussion of ambergris, with special attention to the irony that " fine ladies and gentlemen should regale themselves with an essence found in the inglorious bowels of a sick whale.
Reaction to the withdrawal by both the Russian Federation and the People's Republic of China was much milder than many had predicted, following months of discussion with both Russia and China aimed at convincing both that development of a National Missile Defense was not directed at them.
In 2011, the UK version controversially adapted the discussion of nominations, before changing this rule back following a poll by Big Brother broadcaster Channel 5, which revealed that 90 % of voters believed that housemates should not discuss nominations.
In the following discussion the terms " sequence " and " vector " will be considered interchangeable.
Note: In the following discussion, only one or two common pronunciations of American and British English varieties are used in this article for each word cited.
The following discussion and resources give an indication of the breadth of law that falls within the " environmental " metric.
In the following discussion, we will use a binary operation on the subsets of G: if two subsets S and T of G are given, we define their product as
Some shock sites display a single picture, animation, video clip or a small gallery, and are often passed around via e-mail or disguised in posts to discussion sites as a hoax in an attempt to trick users into following the link to the website ( a bait and switch ).
He draws on Maimonides ' work but also offers Talmudical material ( in effect a summary of the Talmudic discussion ) largely following the commentary of Rashi.
In the climate of English thought in the period following Isaac Newton's major contributions to physics, there was much discussion of a distinction between primary qualities and secondary qualities.
For simplicity's sake, the following discussion assumes the validity of the Altaic language family, although for linguists who do not accept Altaic a relation of Altaic to Uralic is obviously a non-starter, though some part of " Altaic " ( e. g. Turkic ) might be related to Uralic, in theory.
He disingenuously claimed that he would have been out handled the ball if he had removed it and, following a discussion, it was agreed that three runs should be awarded.
The two men met for the first time the following year, and Jung recalled the discussion between himself and Freud as interminable.
On December 13, 1884, following much research and discussion among the group, Whitehouse submitted his designs.
The following exampless provide an overview for various business model types that have been in discussion since the invention of term business model:
The increasingly free discussion generated from the surfacing of new and accurate data following the coup revealed that the military situation was far worse than what was reported by Diệm.
The following discussion is mostly presented in terms of linear functions but the use of least-squares is valid and practical for more general families of functions.
The following discussion has been reported in the German media: 42 spectators left the audience without a word and later distributed leaflets to the audience.
following and is
When I try to work out my reasons for feeling that this passage is of critical significance, I come up with the following ideas, which I shall express very briefly here and revert to in a later essay.
Such a comparison reminds us that in employing low characters in his works Faulkner is recording actuality in the South and moreover is following a long-established literary precedent.
If `` Jack the Courtier '' is really to be taken as Swift, the following remark is obviously Steele's comment on Swift's change of parties and its effect on their friendship: `` I assure you, dear Jack, when I first found out such an Allay in you, as makes you of so malleable a Constitution, that you may be worked into any Form an Artificer pleases, I foresaw I should not enjoy your Favour much longer ''.
Khrushchev himself is reported to be concerned by the surge of animosity he has aroused, yet our own nuclear statesmen seem intent on following compulsively in his footsteps.
Really there is no reason why this fine exercise should not find its way into your leg program at all times, for the following suggestions show why it is so effective: 1.
Currently, marina is used to indicate a municipal or commercially operated facility where a pleasure boat may dock and find some or all of the following available: gasoline, fresh water, electricity, telephone service, ice, repair facilities, restaurants, sleeping accommodations, a general store, and a grocery store.
It is this subject matter that has brought Mason a large and enthusiastic following among sportsmen, but it is his exceptional performance with this motif that commends him to artists and discerning collectors.
In following this general principle, Mason provides the observer with a natural eye progression from foreground to background, and the illusion of depth is instantly created.
`` It is as though '', I said on the historic three-hour, coast-to-coast radio broadcast which I bought ( following Father Coughlin and pre-empting the Eddie Cantor, Manhattan Merry-go-round and Major Bowes shows ) `` That Man in the White House, like some despot of yore, insisted on reading my diary, raiding my larder and ransacking my lingerie!!
The mean temperature of the surface was then computed according to the following relation: Af where x is the fraction of the plug area covered by the hot spot.
The following information on snakes varying greatly in size ( but all with less than a 10-foot maximum ) shows, when considered with the foregoing, that there is probably no correlation between the length of a snake and the time required for it to mature.
The following summary, based on Figures 5 and 6, is an example of one way of interpreting the 42 figures constructed from onset ages and completion ages of individual children with respect to the appropriate mean age for each growth center.
In the following paper it is shown that in a certain definite sense, exactly an odd number of squares can be inscribed in every such curve which does not contain an infinite number of inscribed squares.
A final class of exceptional lines is identifiable from the following considerations: Since no two generators of Af can intersect, it follows that their image curves can have no free intersections.
Autosuggestibility, the reaction of the subject in such a way as to conform to his own expectations of the outcome ( i.e., that the arm-rise is a reaction to the pressure exerted in the voluntary contraction, because of his knowledge that `` to every reaction there is an equal and opposite reaction '' ) also seems inadequate as an explanation for the following reasons: ( 1 ) the subjects' apparently genuine experience of surprise when their arms rose, and ( 2 ) manifestations of the phenomenon despite anticipations of something else happening ( e.g., of becoming dizzy and maybe falling, an expectation spontaneously volunteered by one of the subjects ).
In the primary grades, reading permeates almost every aspect of school progress, and the children's early experiences of success or failure in learning to read often set a pattern of total achievement that is relatively enduring throughout the following years.
For example, property `` used in the trade or business '' of a transferor corporation, as defined in section 1231, presumably would not retain its special status following a non-taxable reorganization if it is not so used in the business of the acquiring corporation.