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Page "Exponential decay" ¶ 42
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We and see
We hear equally fervent concern over the belief that we have not enough generalists who can see the over-all picture and combine our national skills and knowledge for useful purposes.
We see at once what Victor Hugo means when he calls Macbeth a northern scion of the house of Atreus.
`` We would see it that way, but it was glorious then.
Referring to Britain, he says, `` We see a nation that traditionally values sovereignty above all else willing to give up its economy, placing this authority in Continental hands ''.
We out here don't see enough of the conference to know he is being abused.
We fail to see how such procedure resulted in any prejudice to petitioner's contention, which was considered by the appeal board and denied by it.
We can see others more clearly than we can see ourselves, and others can see us better than we see ourselves.
The same editorial continued that `` We expected to democratize Japan and Korea and to see a new China pattern itself easily on our institutions.
We can see the general characteristics of the earlier decade if we look at two poems of very different qualities: `` Revulsion '' ( 1866 ) and `` Neutral Tones '' ( 1867 ).
We first see him shaking Mrs. Joe's hand on discovering the sizable amount of the premium paid to her husband for Pip's indenture as an apprentice and later pumping Pip's hands `` for the hundredth time at least '' ( `` May I -- may I -- ''??
We also see how the results may be presented, although if n, the number of state variables, is large any tabulation will become cumbersome.
We could see maggots moving.
He provoked outraged editorials when, after a post-Inaugural inspection of the White House with Mrs. Kennedy, he remarked to reporters, `` We just cased the joint to see what was there ''.
We shall not make a decisive advance in the ecumenical movement until such a church begins to see itself not merely as a haven of comfort and peace but as a base of Christian witness and mission to the world.
Said he: `` We will see whether whites and Negroes are treated the same around here ''.
We have not the leisure, or the patience, or the skill, to comprehend what was working in the mind and heart of a then recent graduate from the Harvard Divinity School who would muster the audacity to contradict his most formidable instructor, the majesterial Andrews Norton, by saying that, while he believed Jesus `` like other religious teachers '', worked miracles, `` I see not how a miracle proves a doctrine ''.
We seem to see things coming into being and passing from it ; but reflection tells us that decease and growth only mean a new aggregation ( synkrisis ) and disruption ( diakrisis ).
We only know of Andrew through references in other writers: see especially William of Rubruck's in Recueil de voyages, iv.
We entered a small, narrow doorway, and went down two steps, but beyond those one could see nothing.
" Jagger also praised the late star as a one of a kind musician, adding, " We will never see his like again.
We say we want to see put on the statute book something which will make our people citizens of the world before they are citizens of this country ".
Attlee responded the next day in the debate on increased air estimates that Hitler's speech contained unfavourable references to the Soviet Union but that " We see here a chance to call a halt in the armaments race ... We do not think that our answer to Herr Hitler should be just rearmament.

We and exponential
We can solve both problems using a more abstract definition of the exponential map that works for all Lie groups, as follows.
We have explicitly extracted the exponential phase factors exp (- iE < sub > n </ sub > t /< strike > h </ strike >) on the right hand side.
We endow this space with the usual topology of a linear order, and then it can be shown that for each the exponential maps are well defined order preserving / reversing, topological group isomorphisms.
We see that the Theta functions can also be defined in terms of w and q, without a direct reference to the exponential function.
We know that the exponential function satisfies e < sup > x + y </ sup >
We have the following formula for the matrix exponential which is useful in the numerical evaluation of certain continuous-time Markov processes,
We could go through each possible parenthesization ( brute force ), but this would require time exponential in the number of matrices, which is very slow and impractical for large n. The solution, as we will see, is to break up the problem into a set of related subproblems.
We have on one hand the exponential speed that technology has grown and is growing and on the other hand we have the practical use of the personal computer in our everyday life.

We and decay
" We created a setting that reflects the moral decay of the people in it ", says Max.
For example, the society of We is in no scientific or technological decay, featuring X-rays, airplanes, microphones, and so on.
We therefore conclude that the transmitted wave must be a non-vanishing solution to Maxwell's equations that is not a traveling wave, and the only such solutions in a dielectric are those that decay exponentially: evanescent waves.
We could be seeing a period of foreign movement at a time of internal decay ".
We cannot here do more than enumerate the leading troubadours and briefly indicate in what conditions their poetry was developed and through what circumstances it fell into decay and finally disappeared: Peire d ' Alvernha, who in certain respects must be classed with Marcabru ; Arnaut Daniel, remarkable for his complicated versification, the inventor of the sestina, a poetic form for which Dante and Petrarch express an admiration difficult for us to understand ; Arnaut de Mareuil, who, while less famous than Arnaut Daniel, certainly surpasses him in elegant simplicity of form and delicacy of sentiment ; Bertran de Born, now the most generally known of all the troubadours on account of the part he is said to have played both by his sword and his sirveniescs in the struggle between Henry II of England and his rebel sons, though the importance of his part in the events of the time seems to have been greatly exaggerated ; Peire Vidal of Toulouse, a poet of varied inspiration who grew rich with gifts bestowed on him by the greatest nobles of his time ; Guiraut de Borneil, lo macsire dels trobadors, and at any rate master in the art of the so-called close style ( trebar clus ), though he has also left us some songs of charming simplicity ; Gaucelm Faidit, from whom we have a touching lament ( plaint ) on the death of Richard Cœur de Lion ; Folquet of Marseille, the most powerful thinker among the poets of the south, who from being a merchant and troubadour became an abbot, and finally bishop of Toulouse ( d. 1231 ).
He quotes Holger Bech Nielsen ’ s formulation: “ We do not even know if there should exist some extremely dangerous decay of say the proton which caused eradication of the earth, because if it happens we would no longer be there to observe it and if it does not happen there is nothing to observe .” ( From: Random dynamics and relations between the number of fermion generations and the fine structure constants, Acta Pysica Polonica B, May 1989 ).
We decay

We and is
We are desperately in the need of such invention, for man is still very much at the mercy of man.
We consider a rural community as an assemblage of inhabited dwellings whose configuration is determined by the location and size of the arable land sites necessary for family subsistence.
We assume for this illustration that the size of the land plots is so great that the distance between dwellings is greater than the voice can carry and that most of the communication is between nearest neighbors only, as shown in Figure 2.
We have proved so able to solve technological problems that to contend we cannot realize a universal goal in the immediate future is to be extremely shortsighted, if nothing else.
We are reminded, however, that freedom of thought and discussion, the unfettered exchange of ideas, is basic under our form of government.
We know that much is made of the multiplicity and ambiguity of the identities that cluster around the key symbol of the Jew.
We saw it frequently afterward, but our suggestion for the very first encounter is near sunset.
In the rhyming catechism this doctrine is worded thus: `` In Adam's fall We sin-ned all ''.
We may further grant to those of her ( Poetry's ) defenders who are lovers of poetry and yet not poets, the permission to speak in prose on her behalf: let them show not only that she is pleasant but also useful to States and to human life, and we will listen in a kindly spirit ; ;
We find, in the first place, that the students overwhelmingly approve of higher education, positively evaluate the job their own institution is doing, do not accept most of the criticisms levelled against higher education in the public prints, and, on the whole, approve of the way their university deals with value-problems and value inculcation.
There is, of course, nothing new about dystopias, for they belong to a literary tradition which, including also the closely related satiric utopias, stretches from at least as far back as the eighteenth century and Swift's Gulliver's Travels to the twentieth century and Zamiatin's We, Capek's War With The Newts, Huxley's Brave New World, E. M. Forster's `` The Machine Stops '', C. S. Lewis's That Hideous Strength, and Orwell's Nineteen Eighty-Four, and which in science fiction is represented before the present deluge as early as Wells's trilogy, The Time Machine, `` A Story Of The Days To Come '', and When The Sleeper Wakes, and as recently as Jack Williamson's `` With Folded Hands '' ( 1947 ), the classic story of men replaced by their own robots.
We saw Giuseppe Berto at a party once in a while, tall, lean, nervous and handsome, and, in our opinion, the best novelist of them all except Pavese, and Pavese is dead.
We submit that this is a most desirable effect of the law -- and one of its principal aims.
We believe that autism, like so many other conditions of defect and deviation, is to a large extent inborn.
`` Dear Doctors: We learned this year that our older son, Daniel, is autistic.
We feel that The Detroit News is to be complimented upon arranging for articles on these subjects and we hope that it will continue to provide material along wholesome lines.
We will know, and He will know, to whom it is rendered, what the birds would ask:
If it is not enough that all of our internationalist One Worlders are advocating that we join this market, I refer you to an article in the New York Times' magazine section ( Nov. 12, 1961 ), by Mr. Eric Johnston, entitled `` We Must Join The Common Market ''.
We repeat, that the test of a violation of 7 is whether, at the time of suit, there is a reasonable probability that the acquisition is likely to result in the condemned restraints.

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