Sentence examples for iterated sums from inspiring English sources

Theorem 2 shows that the calculation of iterated sums plays an important role in solving equation (23).

Remark 2. As one can see, the established results above mainly deal with Volterra-Fredholm type discrete inequalities with four iterated sums and infinite sum upper limit, and they are different from the results presented in [3].

Some new generalized Volterra-Fredholm type nonlinear discrete inequalities involving four iterated infinite sums are established in this paper.

Motivated by the works in [22 24], in this paper, we establish some new generalized Volterra-Fredholm type discrete inequalities involving four iterated infinite sums with the right-hand side denoted by an arbitrary function ϕ ( u ), which are of more general forms.

The behavior of the iterated Fejér partial sums, Fejér and Riesz means is investigated in order to improve the convergence, observing that the Riesz means have better convergence properties than those of the original partial sums of Fourier series.

In sum, iterated admissibility is an eliminative approach: starting from the set of all (truth-abiding) strategies, some strategies are weeded out at every step until we remain with a stable set of strategies from which nothing can be eliminated anymore.

On a first stage, the Iterated Cumulative Sums of Squares algorithm (ICSS) of [27] is applied to detect the presence of structural breaks in deaths number relevant to the studied countries.

In case of the V-type graphs with five massive propagators, new types of nested sums and iterated integrals emerge.

In [3], Lai studied the analogues of the law of the iterated logarithim for delayed sums of independent random variables.

We used the reverse iterator of thrust::device_vector to iterate and compute sum of suffixes transparently.

This procedure is iterated independently with various weighted sum objective functions.