Sentence examples for defined a sequence of from inspiring English sources

For a real-valued bounded function f on ([0,1]), Bernstein [2] defined a sequence of polynomials given by begin{aligned} B_{n}(f;x)=sum_{r=0}^{n}f biggl( frac{r}{n} biggr) {binom{n}{r}}x^{r} 1-x ^{n-r}, quad forall xin [0,1]mbox{ and } 1-x ^{n-r}{N} 1-x ^{n-r}ed} to provide a very simple and elegant proof of the Weierstrass approximation theorem.

Using the specification described above, we defined a sequence of models and evaluated the performance of each model, using cross-validation.

A flow defines a sequence of steps and a set of design tools for a specific type of design style.

Let us define a sequence of credibilistic stopping times.

We define a sequence of radii by setting and.

For and, define a sequence of as follows: (3.47).

This transformation defines a sequence of conditional uniform random variables.

Given a sequence in, we define a sequence of self-mappings on by (1.4).

A specification in Rapide defines a sequence of events, and one in Wright describes an abstract process.

A quasi-linearization procedure defines a sequence of linear problems whose solutions converge to that of the given nonlinear problems.

We can define a sequence of elementary collapses of K ≤ n to obtain a complex K ≤ n ′.   □.