Sentence examples for space of points from inspiring English sources

Riemann argued that the fundamental ingredients for geometry are a space of points (called today a manifold) and a way of measuring distances along curves in the space.

It was assumed, with anticipation that there is frequently such a thing in nature, that a transformation T relates members of the series by successively transforming an underlying space of points ω according to a rule.

The term X denotes an abstract mathematical space of points.

Let X be a space of points with generic elements of X denoted by x and I = [ 0, 1 ].

Much of the modeling of physical systems takes place in what is called state space, an abstract mathematical space of points where each point represents a possible state of the system.

Some general methods for deriving such equations are the master equation approach and an approach that relies upon coarse-graining the phase space of points representing the micro-states of the system into finite cells and assuming fixed transition probabilities from cell to cell (Markov assumption).

In this model, the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures in order to take the time since detection into account.

With the frequency being restricted to close to the natural frequency of the "perturbed" mode, an analytic modeling of the distortions in the spacing of points in the resonance region caused by the presence of a closely spaced "perturbing" mode is carried out.

The space of data points is partitioned by finding a hyperplane that places as many of the points as possible into their pre-defined class.

In this whole process, storage space of data points is not increased with new obtained overlapping scans, and none of the overlapping points are discarded which increases the representation accuracy.

Exploring the properties of a balanced weighted Laplacian matrix of the reaction network and the Laplacian of the simplicial complex, we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points.