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The other starting points are given by (12).

The points are given by the one-dimensional subspaces of V3 q).

With this activation function the eigenvalues of the fixed points are given by λ = f ′ ( x ) ( N − A ) − f ( x ) − α.

Stationary points are given by the solutions of the trigonometric system in e.g. variables x = φ − α and y = ψ −β as unknowns: ρ a sin x + ρ s sin = 0, ρ b sin y + ρ s sin = 0.

A projective geometry P G 2, q) over a finite field F q  is defined like the following:  The points are given by the one-dimensional subspaces of V3 q).

Consider the system instead with a quadratic activation function: d A d t = ( w N A 2 + h ) ( N − A ) − α A, With this activation function the fixed points are given by g ( A ) = d A d t = − w N + w A 2 − ( h + α ) A + h N = 0, with eigenvalues λ = g ′ ( A ) = − 3 w N A 2 + 2 w A − h − α.

For the infinitesimal neighbourhood of a point on a curved surface there is a local co-ordinate system in which the distance ds between two infinitely near points is given by the equation ds2 = dx2 + dy2 For any arbitrary (Gaussian) co-ordinate-system, however, an expression of the form ds2 = g11dx2 + 2g12dx1dx2 + g22dx22 holds in a finite region of the curved surface.

The set of candidate points is given by the union of access and Steiner points.

The mathematical relation between the two points of selected collocation points is given by a special function, the so-called non-dimensional dynamic influence function.

By the RMD method, the height of a midpoint between two other points is given by: {h_{new} = frac{1}{2}left(h_{left}+h_{right}right)+h_{random}} (2).

Historically, the first outstanding result in this field that guaranteed the existence and uniqueness of fixed points was given by Banach [1].