Despite agreement that collaborative networks seem to be the best method to address the complexity and fragmentation inherent in health research, the manifold conceptual models and definitions of translational research mean that collaborative networks are difficult to establish and evaluate [ 16].
Something with manifold parts cannot, by definition, be truly singular.
This kind of combined display has been found very useful for the understanding of the mutual dependencies between the variables, as well as of the structures of the data set.' In the context of this definition, a manifold refers to a topological space with well-defined mathematical properties.
Lecture 3 (January 25): Definitions: simplicial complexes; manifolds; triangulations of point sets, polygons, and planar straight-line graphs.
Lecture 3 (January 30): Definitions: simplicial complexes; manifolds; triangulations of point sets, polygons, and planar straight-line graphs.
By the definition of center manifold (C_{0} ), we know that W ( {t,theta} )=W bigl( {z ( t ),bar {z} ( t ),theta} bigr)=W_{20} ( theta )frac{z^{2}}{2}+W_{11} ( theta )z bar{z}+W_{02} ( theta )frac{z^{2}}{2}+cdots (12) from (11), where z and z̄ are local coordinates for the center manifold (C_{0} ) in the directions of q and (bar{q}^{ast}).
We also remark that recently, in [55], Shukla and Rao defined another concept of a semi-slant submanifold of a quaternionic Kähler manifold by analogy with the definition of Papaghiuc, but that class of submanifolds, although generalizes slant submanifolds, does not contain real hypersurfaces as a subclass.
It is well known that sliding mode control is based on the definition of an invariant manifold, where the system dynamics are forced to in a finite time.
The definition of the synchronization manifold is constructed, and the time delay independent criterion of the synchronization of the complex dynamical networks is derived.
See [8] for additional definitions (stable and unstable manifolds, asymptotic stability).
