The phrase "a smooth extension of" is correct and usable in written English.
It can be used to describe something that seamlessly continues or builds upon a previous idea, concept, or action.
Example: "The new policy is a smooth extension of our previous efforts to improve employee satisfaction."
Alternatives: "a natural progression of" or "a seamless continuation of".
This ghost state is a smooth extension of the solution at the exceptional point from the other side of the interface.
The two ideas are combined by constructing a smooth extension of the normal velocity off the moving boundary, in a way suggested by the physics of the problem.
Democrats and their allies are now trying to brand a McCain presidency as "Bush's third term," but the McCain campaign has not exactly been running like a smooth extension of the Bush machine.
Olin Partnership, the landscape architect, has suggested that the same effect could be accomplished with a more gradual slope -- a significant improvement -- but the key will be to create a balance in which the gardens feel like a smooth extension of the public realm.
In both cases, there is a smooth extension of the results in Jackson and Wolinsky's connections model in these regions.
It is a lower bound for the number of fixed points in S n − 1 of a smooth extension of a smooth and transversally fixed map ϕ.
Hence by hypothesis, it is a section of C T c (S ) along M. Consider, now, any smooth extension of L to a section of T 1, 0 (S ) over a neighborhood of 0 in S, which we denote by L ˜.
In Section 3, we prove that a smooth extension f : R 2 → R 2 of a power map ϕ d : S 1 → S 1 for d ≥ 2 must have at least one interior fixed point.
The approach suggested for the solution of this problem is based on the search for the solution with minimal Sobolev's norm (the most smooth solution), which provides, in particular, smooth extension of the solution to the area where no input data is available.
The (bar{partial }) data, (alpha ), associated to the smooth extension of (f), is large as (epsilon rightarrow 0): (|alpha |^2 =|bar{partial }chi |^2, |f|^2 approx frac{1}{epsilon ^2}) on the support of (bar{partial }chi ).
On the other hand, the reason for the presence of fixed points in int ( B n ) for smooth extensions of certain maps of S n − 1 demonstrated in [3] is considerably more subtle.
