Sentence examples for smooth forms from inspiring English sources

History, of course, came to treat the latter as classics and consigned most of the smooth forms to oblivion, but Melody Maker was nonetheless a symbolic arrival, confirming jazz music's now unshakeable presence on the map.

Since the smooth forms are dense, the result holds for all (beta ) in the domain of (T^*_{psi }).

Here we investigate the ¯∂-Neumann Laplacian □ on M. We show that it is essentially self-adjoint on its restriction to compactly supported smooth forms.

(Graph norm density of smooth forms) The smooth forms in the domain of (bar{partial }^*_{varphi }) are dense in the space (mathrm{Domain}(bar{partial }) cap mathrm{Domain}(bar{partial }^*_{varphi })) with respect to the graph norm begin{aligned} |||alpha |||_{varphi } := ||alpha ||_{varphi } + ||bar{partial }alpha ||_{varphi } +||bar{partial }^*_{varphi }alpha ||_{varphi }. end{aligned}.

It is densely defined: indeed, (mathrm{Domain}(bar{partial })) is a dense subset of (L^2_{ p,q)}(Omega, e^{-varphi })) since it contains all the smooth forms on a neighborhood of (Omega ).

For smooth forms satisfying the (bar{partial } -Neumann boundary condition, the identity (3) generalizes as the following theorem, proved by C.B. Morrey for ((0,1))-forms, and generalized to ((p,q))-forms by J.J. Kohn.

Silicon substrates are often used since they are readily available in atomically smooth form.

The inherited factor that proved to be DNA was transferred from the virulent (or smooth) form of the bacteria to the nonvirulent (rough) form, not the reverse.

It is round like the sun, like the spheres of perfection: it is "all calm", a smooth form without snags or breaks, and it circles back like the year, from light to darkness and back again.

Let,,, be a smooth form in a domain.

Let be a smooth form and let be Green's operator,, and.