Sentence examples for manifold becomes from inspiring English sources

Then, this manifold becomes the Banach space defined by (1.9).

While manifolds like this containing images with sharp edges are not differentiable, manifolds of images containing smooth images are differentiable, and the more one smoothes the images, the smoother the manifold becomes.

When (b=0), the center manifold of system (1.2) is (w=0), and the restriction of system (1.2) in the center manifold becomes dot{x}=y,qquad dot{y}=mx-ny-px^{3}. (2.8) If (n=0), then system (2.8) is a Hamilton system with the Hamiltonian function (H x,y)=frac{1}{2}y^{2}-frac{m}{2}x^{2}+ frac{p}{4}x^{4}x.

Not long after the concept of manifolds became part of the mathematical psyche (and to some extent even earlier), mathematicians began to extract geometric information from the behavior of harmonic functions and differential forms.

The benefits of databases are manifold and become apparent when providing different views on the same data.

One can see that plateau-like bursting takes the place of square-wave bursting after the spiking manifold, M lc, becomes tangent to the saddle branch of in the middle of M eq and further terminates on the upper depolarized branch of M eq through the supercritical Andronov-Hopf bifurcation.

The parameter space is breaking up leading to a multi-manifold, and optimization becomes more difficult to conduct (cf. Section 3.3).

'Analytical thought' intellect, thought in its secondary role may begin with the same experience, but instead of being 'an indivisible unity it becomes a manifold, a network of things with relations between them' (253).

And the opportunities will soon become manifold for willing student mentors.

However, increasingly, with the accelerating power of technology, as opportunities to create have become manifold and magnificent, so the destructive impacts of change have also grown more widespread, deep rooted and precipitous.

The distribution concepts for OC retailing become manifold.