Sentence examples for representations for this from inspiring English sources

We also present a differential equation, several recurrence relations, and integral representations for this k-Struve function.

In Section 2, we obtain two representations for this fractional derivative operator in terms of the classical Riemann-Liouville fractional operator.

There are two possible minimal arrow diagram representations for this case (Figure 4A).

An unconventional representer theorem is established to provide a finite dimensional representation for this class of covariance estimators based on data, although the solutions are searched over infinite dimensional functional spaces.

Except that serious constitutional people should indeed regard it as a crisis when a state is denied its rightful representation for this long a period.

It contained a warning that false representation for this purpose was a crime for which one could be imprisoned for up to twenty years and fined up to two hundred and fifty thousand dollars.

Observe that the Wigner distribution provides an ideal representation for this signal.

Sketching and drawing with paper and pencil provide an ideal representation for this process.

Our goal is to derive a stochastic representation for this problem, similar to the Feynman-Kac formula.

All kinds of statistical analysis and graphical representation for this study were done in R statistical program of 3.2.0 and MS excel 2007 version.

Also it is proved that the ANN simulation can be used instead of analytical computations because of ensuring a simplified representation for this method and time saving.