Sentence examples for manifold in which from inspiring English sources

Poincaré asked if a three-dimensional manifold in which every curve can be shrunk to a point is topologically equivalent to a three-dimensional sphere.

This idea is also taken a step further by making the Stiefel manifold an attracting invariant manifold in which case standard explicit Runge Kutta algorithms can be used.

In the engine with multipoint fuel injection system using electronically controlled fuel injectors has an intake manifold in which only the air flows and, the fuel is injected onto the intake valve.

Dynamical systems theory combines local analytic information, collected in small "neighbourhoods" around points of special interest, with global geometric and topological properties of the shape and structure of the manifold in which all the possible solutions, or paths, reside the qualitative aspect of the theory.

This map was first of all introduced by Duggal in [55] and named by the authors in [56, 57] in the case of a lightlike hypersurface of a Lorentzian manifold in which we know that (S TM)) is Riemannian.

Interestingly, we find that the short-range ferromagnetic Heisenberg chain behaves exactly the same way as the long-range chain does: N + 1 Dicke states form a ground state manifold in which degeneracies can be lifted by magnetic fields, in particular, in favor of | D N / 2, N / 2 〉 by a staggered magnetic field.

Poincaré was led by this work to contemplate mathematical spaces (now called manifolds) in which the position of a point is determined by several coordinates.

By using his extended concept of curvature, he was able to characterize with great elegance the metric manifolds in which all figures can freely move around without changing their size and shape.

In this paper, we study warped product submanifolds of nearly cosymplectic manifolds in which the base manifold is slant and thus we derive a sharp relation for the squared norm of the second fundamental form.

It is possible that between times s and (t_{i+1}), the cell passes through other switching manifolds, in which case, the procedure for identifying switching times and updating the region variable is repeated as many times as necessary.

Sex allows us to explore the manifold ways in which the body may be stimulated.