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n. Mathematics
A function that is both one-to-one and onto.

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.


(Mathematics) a mathematical function or mapping that is both an injection and a surjection and therefore has an inverse. See also injection5, surjection
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
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Start Action of PSL(2, Z) on GF([2.sup.9]) [union] {[infinity]} Coset diagram for the action Write the elements of GF*([2.sup.9]) in 16 x 16 matrix, in a specific order determined by the coset diagram Consider h : GF*([2.sup.9]) [right arrow] GF([2.sup.8]) defined by h([[alpha].sup.2n]) = [[omega].sup.n] Apply h on each element of the matrix Consider a bijective map g : GF([2.sup.8]) [right arrow] GF([2.sup.8]) defined by g (z) = [mathematical expression not reproducible] Apply g on each element of the matrix Proposed S-box Step 3.
Hence, we have a bijective map [f.sup.-1] : Y [right arrow] X, which is an isomorphism from K to H.
(A4) u [member of] [C.sup.6] [[OMEGA]], w(x) : [bar.[OMEGA]] [right arrow] [bar.[OMEGA]] is a bijective map in [C.sup.3], with w'(x) > 0, [for all]x [member of] [bar.[OMEGA]], w[-.sup.1] [member of] [C.sup.1] [[OMEGA]],
In fact, if lattice DP(X) is isomorphic to lattice DP(Y) then we obtain a bijective map F: X [right arrow] Y preserving closed nowhere dense sets, which turns out to be a homeomorphism if X and Y are countably compact T3 spaces without isolated points.
Menu M' is a proxy improvement over M if there exists a bijective map h on [R.sub.n] such that [U.sub.h(x)](M') [greater than or equal to] [U.sub.x] (M) for all x [member of] [R.sub.n], and [U.sub.h(x)](M') > [U.sub.x] (M) for at least one x.
A Standard Young tableau is a bijective map T: [D.sub.[lambda]] [right arrow] {1, ..., [absolute value of [D.sub.[lambda]]]} which is increasing along rows and down columns, i.e.
(1) [[phi].sub.1]: [0,c] [right arrow] [0, 1], strictly monotone increasingC'bijective map [[phi].sub.1], [[phi].sup.-1.sub.1] are absolutely continuous
f:X [right arrow] Y is a bijective map defined by: f(x) = y for all x [member of] X satisfying the conditions:
This correspondence defines a bijective map k: [T.sub.2]([OMEGA]) [??] G: [[tau].sub.[alpha],[beta]] [right arrow] [g.sub.[alpha],[beta]] and one verifies easily that k: ([T.sub.2]([OMEGA]), [omicron]) [right arrow] (G, [omicron]) is a group homomorphism (using also the sharp 2-transitivity of [T.sub.2]([OMEGA]) on [OMEGA]).
Let k be a weak isomorphism between the neutrosophic graph G2 and G1 so the relation is anti-symmetric that is k : V2 [left arrow] V1 is a bijective map with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].