Sentence examples for multiple sums from inspiring English sources

In some papers the multiple sums (2) appear explicitly; see for example [1 4] or [5].

OpenMP has been used with the reduction clause, that allows to organize the operation to be done in a loop (in this case it acts on multiple sums).

However, Mathematica 8 gives no response to the same question for multiple sums more than triple one as in (3.2) and (3.4).

In fact, we find that this question for multiple sums more than triple one has already been generally solved as follows (see, e.g., [19, 20], [[1], pp.85-86] and [[2], pp.151-153]): The n-ple (or, simply, the multiple) Hurwitz zeta function ζ n ( s, a ) is defined by ζ n ( s, a ) : = ∑ k 1, …, k n = 0 ∞ ( a + k 1 + ⋯ + k n ) − s ( ℜ ( s ) > n ; n ∈ N ; a ∈ C ∖ Z 0 − ).

The calculations required to break down the multiple sums to interpretable expressions are lengthy but straightforward and detailed in File S1.

Prior to the field work, multiple SUMS were attached to both stove types using heat-resistant tape and sampled every 10 sec during three independent cooking events.

Reversing the multiple sum in (B.2), we can rewrite as.

Our methods have applications to inclusion theorems for multiple summing multilinear mappings and to the product of p-Sidon sets.

We invent the new notion of coordinatewise multiple summing operators in Banach spaces, and use it to study various vector valued extensions of the well-know Bohnenblust Hille inequality (which originally extended Littlewood's 4/3-inequality).

Those participants who indicated smoking and harmful alcohol drinking were categorised as simultaneous SUM (multiple SUM).

The reasons why this happens are multiple, summed up by the Virchow triad [ 29].