Sentence examples for extends continuously from inspiring English sources

Then we prove the following result: Suppose that M is compact and U has the property that the action extends continuously to Diff*k(M), the group of Ck diffeomorphisms which are homotopic to the identity, for some finite k.

However, the fact that the cosmic-ray spectrum extends continuously, without steps or peaks, to more than five orders of magnitude in energy beyond the limit of SN shock acceleration appears to be incompatible with this picture, at least without extreme fine-tuning of models.

Let κ ± : ∂ ± S M → B ( ∂ M ) be the orthogonal projection onto the (open) unit ball tangent bundle that extends continuously to the closure of ∂ ± S M. Then κ ± are homeomorphisms, and we set σ = κ + ∘ Σ ∘ κ - - 1 : B ( ∂ M ) ¯ ⟶ B ( ∂ M ) ¯. (104 According to our convention, σ = I d on ∂ ( B ( ∂ M ) ¯ ) = S ( ∂ M ).

We standardized our approach by defining EE as erosion that extends continuously across the entire length of at least one SIJ quadrant of the iliac and/or sacral subchondral bone on the same semicoronal slice.

Let (varphi mathcal{A}rightarrowmathcal{A}) be a continuous identity-preserving Jordan morphism extending continuously to a map (varphi: H^{p, omega}(mathcal{A} rightarrow H^{p, omega }(mathcal{A})), (1leq p

The grasslands extend continuously south of the Ural Mountains on either side of the Ural River.

Euclid's second postulate is: a straight line of finite length can be extended continuously without bounds.

In Riemannian geometry, a straight line of finite length can be extended continuously without bounds, but all straight lines are of the same length.

Thick paludal facies extend continuously up to 60 km landward of the Holocene maximum marine ingression, about 90 km from the modern shoreline.

From the above discussion, we see that can be extended continuously to infinity and.

They extend continuously from upstate New York to Alabama and in patches across Texas and up the Rocky Mountain states to Montana.