# diffeomorphism

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## diffeomorphism

[‚dif·ē·ə′mȯr·fiz·əm]
(mathematics)
A bijective function, with domain and range in the same or different Euclidean spaces, such that both the function and its inverse have continuous mixed partial derivatives of all orders in neighborhoods of each point of their respective domains.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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To calculate the optimality conditions of the following problem [mathematical expression not reproducible], where C ([[OMEGA].sub.0]) is the set of admissible forms obtained by diffeomorphism, the cost function J([OMEGA]) is the compliance defined by
An optimized framework with nonrigid registration and the diffeomorphism strategy was used, a similarity energy function based on grey value was designed, and termination conditions were set to stop iterations adaptively.
Further, we assume that there exists a diffeomorphism h from [K.sub.1] to [K.sub.2] = h([K.sub.1]), defined by
And this turns out to be true, since black hole entropy can be shown to be the Noether charge of the diffeomorphism symmetry .
Then there is a diffeomorphism h : [[summation].sub.s] [right arrow] M, having the form h(0, y) = (a(y),y), where [alpha]'(u) > 0 at u = a(y), that maps the flow of the sliding vector field [Z.sub.s] to the flow of the reduced problem on M.
It is clear that det D[phi](u, v, [tau]) = (1/q)(a + [K.sup.2][u.sup.2]) > 0, and [phi] is a diffeomorphism .
A solution to the Ricci flow is called Ricci soliton if it moves only by a one parameter group of diffeomorphism and scaling.
Technically, the Smale's construction involves a planar diffeomorphism, acting on a square, whose image has the shape of a horseshoe that crosses the square in a suitable manner (see [43, 54, 55] for the mathematical details).
Lim, "Feedback linearisation of time-varying nonlinear systems via time-varying diffeomorphism," IEE Proceedings: Control Theory and Applications, vol.
If the map is a diffeomorphism on R, the sets [W.sup.s]([bar.x]) and [W.sup.u]([bar.x]) are the stable and unstable manifolds of [bar.x].
If [rho] < n, then a diffeomorphism restricted to a neighborhood N can be built as

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