Sentence examples for is bounded so that from inspiring English sources

Note that, and is bounded, so that.

Thus from (24), the error is bounded so that.

If is compact, then it is bounded so that conditions (3.30) and (3.31) hold.

Since K is bounded, so that { x n } and { y m } are all bounded, and hence (3.17).

For any bounded set (Dsubset P), (A(D)) is bounded, so that the functions in (A(D)) are uniformly bounded.

There is a canonical choice of eigenvalues for the Dirac operator D which ensures that [D,u] is bounded, so that it extends to a spectral triple on the crossed product.

They are bounded so that (x 2 + y 2) ≤ 1, while the shape's structure contributes through the orthogonal complex Zernike polynomials[44] S ( m, n ) = [ V mn ( r, θ ) ] ∗ (3).

Moreover, it is known via the regularity for PDEs that, when the initial data ψ and φ are properly smooth, it can be ensured that (|nablaboldsymbol{u}^{n-1}|_{0,infty}) of the sequence of solutions for Problem III are bounded so that the assumptions (|nablaboldsymbol{u}^{n-1}|_{0,infty}lealpha) are reasonable.

In addition, by the regularity, we know that, when the original value pair ((boldsymbol {sigma}^{0}, boldsymbol {u}^{0})) is suitably smooth, the solutions to Problem III are bounded so that the conditions (Vert nablaboldsymbol {u}^{i-1} Vert _{0,infty}lealpha) are rational.

Since, and is bounded, so it follows that.

which shows that is bounded, so is.