Sentence examples for continuous and discrete settings from inspiring English sources

For the one-dimensional fractional Hardy Littlewood maximal operator, we prove by means of counterexamples that the corresponding continuity statements do not hold, both in the continuous and discrete settings, and for the centered and uncentered versions.

We study general dynamical and topological behaviors of minimal sets in skew-product circle flows in both continuous and discrete settings, with particular attentions paying to almost periodically forced circle flows.

Both continuous and discrete time settings are considered for systems subject to polytopic parameter uncertainty.

This work investigates the construction, characterizations, and applications of tight framelets on such a manifold M. Characterizations of the tightness of a sequence of framelet systems for L2(M) in both the continuous and semi-discrete settings are provided.

The proposed algorithm is applied to find the settings of continuous and discrete control variables such as tap positions of tap changing transformers, generator voltages, and the amount of reactive compensation devices to optimize three conflicting and non-commensurable objective functions: voltage deviation, the total voltage stability and real power loss.

The control variables consist of both continuous and discrete variables, including generator voltage magnitudes, discrete tap settings of transformers and outputs of reactive compensation devices.

We present a general introduction to the topic followed by overviews of how to calculate tolerance intervals for some continuous and discrete distributions, nonparametric tolerance limits, tolerance intervals for regression settings, and multivariate normal tolerance regions.

Both continuous and discrete systems are considered.

Following Aristotle's division of quantities into continuous and discrete quantities (Cat. 6), medieval philosophers divide the integral whole into continuous integral wholes and discrete integral wholes.

The continuous and discrete cases are investigated.

The methodology can handle both continuous and discrete variables.