transposition

Definitions

  • WordNet 3.6
    • n transposition (music) playing in a different key from the key intended; moving the pitch of a piece of music upwards or downwards
    • n transposition the act of reversing the order or place of
    • n transposition (electricity) a rearrangement of the relative positions of power lines in order to minimize the effects of mutual capacitance and inductance "he wrote a textbook on the electrical effects of transposition"
    • n transposition (mathematics) the transfer of a quantity from one side of an equation to the other along with a change of sign
    • n transposition (genetics) a kind of mutation in which a chromosomal segment is transfered to a new position on the same or another chromosome
    • n transposition an event in which one thing is substituted for another "the replacement of lost blood by a transfusion of donor blood"
    • n transposition any abnormal position of the organs of the body
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Webster's Revised Unabridged Dictionary
    • n Transposition (Alg) The act of transposing, or the state of being transposed.
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Century Dictionary and Cyclopedia
    • n transposition In geometry, any motion other than revolution.
    • n transposition In electricity, arrangement of the wires of a power-transmission, telegraph-, or telephone-line so that after a certain distance the wires change places with each other, for the purpose of reducing the disturbing effect of the line on other lines or of other lines on the former, which may occur by induction, electromagnetic or electrostatic.
    • n transposition The act of transposing; a putting of each of two things in the place before occupied by the other; less frequently, a change in the order of more than two things; also, the state of being transposed, or reciprocally changed in place.
    • n transposition In algebra, the bringing over of any term or terms of an equation from one side to the other side. This is done by changing the sign of every term so transposed, the operation being in effect the adding of the term with its sign reversed to both sides of the equation. If a + x =b + c, then by transposition we get x =b + c—a, or x—b =c—a, or x + a—c =b, etc.
    • n transposition In rhetoric and grammar, a change of the usual order of words in a sentence; words changed from their ordinary arrangement for the sake of effect.
    • n transposition In music, the act, process, or result of altering the tonality of a piece or passage from a given tonality, either in performance or in transcription. Transposition in itself involves only a change of key-note and a uniform shift of pitch upward or downward; but such a change may also involve more or less serious collateral changes. In purely vocal music slight transpositions are practically immaterial, and considerable ones are only noticeable because they change the ease or the method in which given tones are produced. Transposition in instrumental music, however, usually involves somewhat radical changes in the mechanism of performance, as in fingering, stopping, etc.; and these changes often involve also extensive changes in the ordinary staff-notation. Musically such mechanical or graphic changes are merely nominal and fictitious, though they often appear to have considerable importance.
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Chambers's Twentieth Century Dictionary
    • Transposition act of putting one thing in place of another: state of being transposed; a change of the order of words:
    • Transposition (mus.) a change of key into a higher or lower scale
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Etymology

Webster's Revised Unabridged Dictionary
F. transposition, from L. transponere, transpositum, to set over, remove, transfer; trans, across, over + ponere, to place. See Position
Chambers's Twentieth Century Dictionary
Fr.,—L. transponĕretrans, across, ponĕre, to place.

Usage

In literature:

Occult transposition of letters, 69.
"Notes and Queries, Index of Volume 3, January-June, 1851" by Various
The sudden transposition of affairs made me sensitive.
"A Romantic Young Lady" by Robert Grant
The transposition of the McArdles, like most charitable enterprises, had not been entirely a success.
"Money Magic" by Hamlin Garland
Here, then, are above a dozen striking coincidences in this one example; and they are given with but slight dislocation or transposition.
"Notes and Queries, Number 232, April 8, 1854" by Various
This really amounts to an almost absolute transposition of the classes.
"Violence and the Labor Movement" by Robert Hunter
In the cab between stops he tried the mechanical transposition of himself into the mountains, according to Bob's suggestion.
"The Dual Alliance" by Marjorie Benton Cooke
But neither pole circuit differs in transposition from any other regular scheme except in the frequency of transposition.
"Cyclopedia of Telephony and Telegraphy, Vol. 2" by Kempster Miller
A transposition has since taken place.
"The English Language" by Robert Gordon Latham
When Paul was persecuted for righteousness' sake, how easily might "the offence of the cross" have been made to cease, by a mere transposition!
"Speeches, Addresses, and Occasional Sermons, Volume 3 (of 3)" by Theodore Parker
The transposition was due to the Foolah maid.
"The Maroon" by Mayne Reid
Perhaps the copyist may have committed here an error of transposition.
"A Philosophical Dictionary, Volume 5 (of 10)" by François-Marie Arouet (AKA Voltaire)
The different dramatizations she had indulged in with Peavey, Sassoon and Blainey had aroused her craving for sudden transpositions.
"The Salamander" by Owen Johnson
Then there are certain words with regard to which transposition is likely to take place.
"Psychotherapy" by James J. Walsh
The other package is now treated in the same manner, after which the supposed transposition of the balls will be easily understood.
"Magic" by Ellis Stanyon
A difficulty about the carving was the more immediate cause of the transposition.
"My Lord Duke" by E. W. Hornung
No increase of value, he contends, can occur in the process of exchange, for an exchange is a mere transposition of things of equal value.
"Contemporary Socialism" by John Rae
The reader will pardon this anticipation and transposition of years.
"Memoirs of Mrs. Rebecca Steward" by T. G. Steward
The necessity for this insertion shows that Westphal's transposition is not in itself an easy one.
"The Modes of Ancient Greek Music" by David Binning Monro
However, he is more fond of Transposition.
"Musical Myths and Facts, Volume II (of 2)" by Carl Engel
The language is transpositive.
"The Indian in his Wigwam" by Henry R. Schoolcraft
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In news:

Congenitally corrected transposition of the great vessels.
A transposition of usually initial sounds of two or more words.
She was diagnosed with transposition of the great arteries and had open heart surgery at 5 days old.
Transposition of the great arteries &mdash.
The University of South Dakota Department of Art presents the exhibition, "In Transposition ," featuring the work of USD students Johnne Law McMahan, Zechariah Blasy, Paige Reinders, Jaymee Harvey and Anna Ayotte.
Columnar transposition ciphers and permutations, oh my.
Denis's sensational transposition of "Billy Budd" to a French Foreign Legion post on the horn of Africa is a mosaic of pulverized shards.
Oropharyngeal reconstruction using a myomucosal uvular transposition flap following transoral resection of oropharyngeal carcinoma.
The University of South Dakota Department of Art presents the exhibition, "In Transposition," featuring the work of USD students Johnne Law McMahan, Zechariah Blasy, Paige Reinders, Jaymee Harvey and Anna Ayotte.
The Toronto Raptors' injury woes continued as the team announced Thursday that swingman Landry Fields has undergone ulnar nerve transposition surgery in his right elbow.
""We feel that Reyes would benefit from a transposition of the nerve," head trainer Lonnie Soloff said.
Jaxon Keeney was born with transposition of the great arteries, which was diagnosed four months before his birth and was corrected through surgery.
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In science:

We shall refer to this procedure as a random transposition of n cards.
Random walks on wreath products of groups
This procedure is denoted by (~v ; τ ), where τ ∈ Sn is the transposition (p q ) and the only possible non-identity entries of ~v ∈ Gn = S n m are in positions p and q .
Random walks on wreath products of groups
Gn , and where if τ ∈ Sn is the transposition (p q ) then the only possible non-identity entries of ~v ∈ Gn are in positions p and q .
Random walks on wreath products of groups
In the special case of the hyperoctahedral group Z2 ≀ Sn , the calculation of the type matrix splits the signed transpositions into two sets.
Random walks on wreath products of groups
We will refer to one which flips either, but not both, of the cards as an odd transposition and designate it as (~v ; τ − ).
Random walks on wreath products of groups
G and χ[λj ] is the character of the irreducible representation ρ[λj ] of Snj , where r(λj ) := χ[λj ] (τ )/d[λj ] with transposition τ ∈ Snj , and where gk is any element of the conjugacy class Ck of G.
Random walks on wreath products of groups
In the special case of the hyperoctahedral group Z2 ≀ Sn , the conjugacy class C (~v ;τ ) is the even transpositions.
Random walks on wreath products of groups
Generating a random permutation with random transpositions. Z.
Random walks on wreath products of groups
It suffices to check that IU (X ) is invariant under a transposition of two adjacent xi ’s.
Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials
E (ρ) = TrH [(11K ⊗ ρT ) S ] , where T is the transposition.
Characterising a universal cloning machine by maximum-likelihood estimation
Now if τ ∗i,j is the automorphism induced by the (i, j )-transposition, we have : τ ∗i,j xk = xk , and τ ∗i,j Vn = Vn , so that τ ∗i,j [xk , aj ] = [xk , ai ] ∈ Vn , thus ai ∈ Vn , and this is true for all n.
Number Operator Algebras
Then the permutation induced by w should be I d if k is even or a transposition of exactly two strings if k is odd.
Identifying Half-Twists Using Randomized Algorithm Methods
For any category C we have the transposition functor τ : C × C −→ C × C defined by τ (X, Y ) = (Y , X ) and τ (f , g ) = (g , f ). A symmetry for a monoidal category is expressed using the functor τ .
The categorical theory of relations and quantizations
Let τ : C × C −→ C × C be the transposition bifunctor.
The categorical theory of relations and quantizations
It is thus evident that for relations the simple transposition (x, y ) −→ (y , x) is not the right notion for a symmetry.
The categorical theory of relations and quantizations
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