Sentence examples for manifold of such from inspiring English sources

For example, one might hold that it is part of the essence of a spacetime point that it be part of a manifold of such points, whereas it is no part of the essence of an electron (or electron-time-slice, if you prefer) that it coexist with any other electrons.

In general, on Dretske's view, an organism can be said to represent P just in case that organism contains a subsystem whose function it is to enter state A only if P holds, and that subsystem is in state A. To have beliefs, Dretske suggests, is to have an integrated manifold of such representational systems, acquired in part through associative learning, poised to guide behavior.

Threshold phenomena are closely related to folded critical manifolds of such singularly perturbed neural problems.

The critical manifolds of such systems are typically two-dimensional folded surfaces.

Certain construction methods, such as harmonic frames and spectral tetris, are known in the special case of unit norm tight frames, but even these provide but a few examples from the manifold of all such frames, the dimension of which is known and nontrivial.

Invariant manifold is one of such structures and, in particular, invariant curve is the main object for 2-dimensional systems and easier to be discussed deeply.

Further, ∇ is a Levi-Citvita connection of the induced Riemannian manifold M. The approach of such type inequalities for warped products in almost Hermitian and almost contact metric manifolds has been an important field for a few decades.

It is a work of such manifold characterisation and knotty scenarios that it could surely not have been written shorter or more quickly.

The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices.

A typical Hodgkin-Huxley model possesses a pair of such manifolds [4]: quiescent and tonic spiking.

We present a novel method for computing approximations of such manifolds using trajectory-based optimization.