The phrase "a double sum" is correct and usable in written English.
It can be used in mathematical or statistical contexts to refer to the summation of two separate sums or to indicate a summation that involves two variables.
Example: "To calculate the total revenue, we need to compute a double sum of the sales from both regions."
Alternatives: "twofold sum" or "dual sum".
Throughout the paper, we assume W ( 0 ) = 0. 〈 x, y 〉 is the scalar product between two vectors x, y ∈ R n. ∥ u ( t ) ∥ p for p = 1, 2 is the L p norm of u ( t ) ∈ R n, i.e., ∥ u ( t ) ∥ p = ( ∑ i = 1 n | u i ( t ) | p ) 1 p. And similarly for the connectivity matrices of R n × n with a double sum.
The minimisation following (9) is an optimisation problem of the least squares type featuring a double sum of experiments e = 1,…, E and time points k = 1,…, T e, i.
The rate expression reduces to a double sum if the proton states involved in the process are again restricted to a single pair, such as the ground diabatic proton states whose linear combinations give the adiabatic states with split levels, as in Figure 46.
Given a pair of sites that are matched to a corresponding pair in another protein, if d is the distance difference between the two pairs, Dali's individual score is, where is the average distance, and a and b are defined constant values; and the total score is the sum (a double sum, in fact) over all possible pairs.
It reads (11 with (12)where δ denotes Dirac's delta function, e r, e ϑ and e φ are unit vectors of the spherical coordinate system, and is a short expression for the double sum in Eq. (9).
Note that the arc ((k,j)) is a part of the unique cycle CQ of Q, and that the same unicyclic graph Q can be formed when each arc of CQ is added to a corresponding rooted tree T. Therefore, the double sum in (G_{2}) can be reorganized as a sum over all unicyclic subgraphs Q containing vertices ({1,2,ldots,m}).
Here, ({Y_{k}^{l}}(theta,phi)) is the spherical harmonic of degree k and order l, μ 0 is the magnetic permeability of free space, ({vec r} = a, theta, phi)) with θ and ϕ designating geographic colatitude; and longitude, (sum limits _{l,k}) is a short-hand expression for the double sum over k and l, and ω p is the angular frequency.
One may be interested in a quicker but approximate computation by only taking the double sum of the earthquake pairs closer than a certain distance, such as 4 times of the Utsu Spatial Distance 3.33 × 100.5M−2 km (cf., Section 3).
Each term of the double sum of Eq. 10 corresponds to a different degree n k, where n k is a real number.
Reversing the double sum of (A.11) and using [10, equation (8.352.4 ], we obtain (A.2).
When the number of earthquakes is very large, the computing takes substantially long time due to the double sum in the first term of the log likelihood (8).
