In other words, the set of phylogenetic trees forms a manifold in the linear cone R + 2 n − 1.
For every formal power series B of closed two-forms on a manifold Q and every value of an ordering parameter κ∈[0,1] we construct a concrete star product ★κB on the cotangent bundle T∗Q.
composite: a collection of d-dimensional primitives that form a d-manifold, which is a topological space that is locally like a d-dimensional Euclidean space ((mathbb {R}^{d})).
The geodesics determined by all linear combinations of v and w form a 2-manifold about P, with a definite Gaussian curvature KP v,w) at P. The real number KP v,w) measures the curvature of M at P in the "surface direction" (Riemann 1854, p. 145) fixed by v and w.
The critical manifold S in Figure 4 forms a single manifold, containing four fold curves, and can be divided into six different sheets depending on the stability type of the equilibria; the stable sheets are coloured black and the unstable ones red.
The critical manifold S, when considered in the full five-dimensional phase space of system (1), is a two-dimensional surface, or collection of surfaces, and the associated families of periodic orbits form a three-dimensional manifold, or collection of manifolds, that we denote by P. Together, these collections of manifolds organise the behaviour of solutions of (1).
They include the designs of the scalar parameter in a one dimensional cubic polynomial function with two unidentifiable parameters forming a linear manifold, and the boundary source locations for impedance tomography in a square domain, where the unknown parameter is the conductivity, which is represented as a random field.
The covariance matrix, which is symmetric positive definite matrix, forms a Riemannian manifold.
Also, a pressure capsule was formed by creating a manifold at a distance from the orifice tip.
In specifying that events form a four dimensional manifold, there is still a lot we have not said about the events.
