Sentence examples for extended smoothly from inspiring English sources

Thus, ( v, w ) can be extended smoothly beyond t = T.

Thus, ( u, v, b ) can be extended smoothly beyond t = T.

If one chooses one of the two lobes of the light cone at a point O to be, say, future, that choice can be extended smoothly throughout the whole of the spacetime.

It is proved that if ∫ 0 T ∥ u x 3 ∥ L α β d t < ∞ with 3 α + 2 β ≤ 1 and α ≥ 3, then the solution ( u, v, b ) can be extended smoothly beyond t = T.

We can assume that g is extended smoothly on M 1 ⋑ M. Next, with g extended as above, we extend g ^ 1 so that g ^ 1 = g outside M.

where 3 α + 2 β ≤ 1, α ≥ 3, then the solution ( u, v, b ) can be extended smoothly beyond t = T. Proof Multiplying the first equation of (1.1) by u and integrating with respect to x on R 3, using integration by parts, we obtain 1 2 d d t ∥ u ( t ) ∥ L 2 2 + ∥ ∇ u ( t ) ∥ L 2 2 = ∫ R 3 b ⋅ ∇ b ⋅ u d x + χ ∫ R 3 ( ∇ × v ) ⋅ u d x. (4.1).

I also demonstrate that the luminosity-metallicity relation previously seen in more luminous dSph galaxies (M_V = -13.4 to -8.8) extends smoothly down to an absolute magnitude of M_V = -3.7.

So the result is sort of like the happy ending of one of those screwball romantic comedies that involve mistaken identity and the handsome vagabond turns out to be the prince in disguise; Alice can marry Ted who is really Bob and the bonds of matrimony extend smoothly across the edge of the black hole.

Because of this wormhole connection, Dr. Maldacena explained, "Ted and Bob are the same". So the result is sort of like the happy ending of one of those screwball romantic comedies that involve mistaken identity and the handsome vagabond turns out to be the prince in disguise; Alice can marry Ted who is really Bob and the bonds of matrimony extend smoothly across the edge of the black hole.

The conductive feature extends smoothly to the west; however, there is a sharp resistivity contrast between C1 and resistor R2 in the east.

As ( v ˜ ϵ, β 0, w ˜ ϵ, β 0 ) remains in R p × E, one can extend smoothly F and Σ outside ℰ so that ( F, Σ ) satisfies Assumptions 2.1-2.2 2.1-2.2