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Page "Quaternions and spatial rotation" ¶ 29
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same and way
If I could make myself feel the same way
`` Would you advise us to act the same way??
We are not now afraid of atomic bombs in the same way that people once feared comets.
We talk about national character in the same way that Copernicus talked of the compulsions of celestial bodies to move in circles.
In a certain perfectly definite way, the method and the theme of his stories are one and the same.
Robert Penn Warren puts it this way in `` Brother To Dragons '': `` The recognition of complicity is the beginning of innocence '', where innocence, I think, means about the same thing as redemption.
And it is clearly argued by Lord Percy of Newcastle, in his remarkable long essay, The Heresy Of Democracy, and in a more general way by Voegelin, in his New Science Of Politics, that this same Rousseauan idea, descending through European democracy, is the source of Marx's theory of the dictatorship of the proletariat.
In the same way he coupled Molesworth and Wharton in a letter to Archbishop King, and he had earlier described him as `` the worst of them '' in some `` Observations '' on the Irish Privy Council submitted to Oxford.
In much the same way, we recognize the importance of Shakespeare's familarity with Plutarch and Montaigne, of Shelley's study of Plato's dialogues, and of Coleridge's enthusiastic plundering of the writings of many philosophers and theologians from Plato to Schelling and William Godwin, through which so many abstract ideas were brought to the attention of English men of letters.
In addition to his experiments in reading poetry to jazz, Patchen is beginning to use the figure of the modern jazz musician as a myth hero in the same way he used the figure of the private detective a decade ago.
It could go either way, since the gains for both points of view were about the same.
The evening was not always spent in the same way.
In the past these same Southerners were inclined to look the other way.
if, as often happened, he had to repeat because he had spoken too softly, he would repeat his words in the same way, without emphasis or impatience, only a little louder.
Maybe he felt the same way.
Eileen seemed to feel the same way.
In the same way I like to think we owe our loyalty as legislators to our community, our district, our State.
Mr. Claude is a specialist in torso development and he has long favored the now-famous Weider Push-Pull Super-Set technique in which one exercise of the Super-Set is a pressing or `` pushing '' movement which accents one sector of a muscle group in a specific way, followed by a `` pulling '' exercise which works the opposing sector of the same muscle group.
It would be even more valuable because that same aircraft could immediately destroy any targets it discovered -- no need to wait for a missile to come all the way from the United States with the chance that the target, if it were mobile, would be gone.
Having a boat financed through a local bank is done much the same way as an automobile loan is extended.
Outboard motors, insurance, and boat repairs may also be financed in the same way as boats.
The chines go in the same way except that they are made of two pieces of two-inch wood for strength and easier bending.
We define these values as Af, and define g{t} in the same way for each T.
In a way, we may be witnessing the same thing in the sales of automobiles today as the public no longer is willing to purchase any car coming on the market but is more insistent on compact cars free of the frills which were accepted in the Fifties.
To derive Utopian communism from the Jerusalem Christian community of the apostolic age or from its medieval successors-in-spirit, the monastic communities, is with an appropriate shift of adjectives, misleading in the same way as to derive it from Plato's Republic: in the Republic we have to do with an elite of physical and intellectual athletes, in the apostolic and monastic communities with an elite of spiritual and religious athletes.

same and space
We know that the number of radio and television impulses, sound waves, ultra-violet rays, etc., that may occupy the very same space, each solitary upon its own frequency, is infinite.
Russian tanks and artillery parading through the streets of Havana, Russian intrigue in the Congo, and Russian arms drops in Laos ( using the same Ilyushin transports that were used to carry Communist agents to the Congo ) made it plain once more that the cold war was all of a piece in space and time.
About that same time John Crosby's TV series on the popular arts proved again that giving jazz ample breathing space is one of the most sensible things a producer can do.
There would seem to be some small solace in the prospect that the missile race between nations is at the same time accelerating the study of the space around us, giving us a long-sought ladder from which to peer at alien regions.
The " space " character had to come before graphics to make sorting easier, so it became position 20 < sub > hex </ sub >; for the same reason, many special signs commonly used as separators were placed before digits.
* In linear algebra, an endomorphism of a vector space V is a linear operator V → V. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL ( V ).
( via their ARA / ARA2 / ASR products ) allowed ' Sideways ROM ' capability, that allowed the standard Acorn ROM space to be programmatically mapped out for alternative EPROMs, either physically via ZIF Sockets, or ' virtually ' via ROM-images loaded into ( Battery-backed ) RAM in the same ROM memory space.
Today, Internet forums occupy much of the same social and technological space as BBSes did, and the term BBS is often used to refer to any online forum or message board.
Being politically and geographically inclusive and leaving at the same time space for diversity, this historical vision filled the needs of Dutch nation-building and integration in the 1890-1914 era.
( Technically, the quantum states are rays of vectors in the Hilbert space, as corresponds to the same state for any nonzero complex number c .)
A different basis for the same Hilbert space is:
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.
The key difference between the von Neumann and Harvard architectures is that the latter separates the storage and treatment of CPU instructions and data, while the former uses the same memory space for both.
) Note that the same set of points would not have, as an accumulation point, any point of the open unit interval ; hence that space cannot be compact.
By the same construction, every locally compact Hausdorff space X is a dense subspace of a compact Hausdorff space having at most one point more than X ..
The 1999 game Sid Meier's Alpha Centauri was also created by Meier and is in the same genre, but with a futuristic / space theme.
Gamers that year had a choice between a new game with the Civilization name but no involvement of Sid Meier ; and a " space "- themed civilization game without the name but clearly designed by the same team ( Sid Meier's Alpha Centauri ).
The tangent space and the cotangent space at a point are both real vector spaces of the same dimension and therefore isomorphic to each other via many possible isomorphisms.
A hop consists of jumping over a single adjacent piece, either one's own or an opponent's, to the unoccupied space directly beyond in the same line of direction.
Several space observatories did the same, including the Hubble Space Telescope, the ROSAT X-ray observing satellite, and significantly the Galileo spacecraft, then on its way to a rendezvous with Jupiter scheduled for 1995.
For example, the conservation of energy follows from the time-invariance of physical systems, and the fact that physical systems behave the same regardless of how they are oriented in space gives rise to the conservation of angular momentum.

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