The phrase "a sum of a solution" is not commonly used in written English and may be unclear in meaning.
It could be used in contexts discussing mathematical or analytical results, but it may require additional clarification for the reader to understand its intent.
Example: "After analyzing the data, we found a sum of a solution that addressed the problem effectively."
Alternatives: "total of a solution" or "aggregate of a solution".
The standard PSO algorithm is designed for optimization problems in the continuous domain; therefore, a new solution can be easily obtained by a sum of the three solution vectors multiplied by some random weights.
As a solution of a constant coefficient equation, is a sum of characteristic solutions.
A candidate is in this case an interval, for which the optimal solution cannot be written as a sum of optimal solutions of sub-intervals.
The general solution of the linear system F Y k + 1 = G Y k + V. is the sum of a partial solution and the solution of the homogeneous system (3).
Let us look for a solution to (16) in the form of the sum of a transient solution and a steady-state solution, p ( x,t ) =U ( x,t ) +V x,t).
The solutions that have been obtained are presented as a sum of steady-state and transient solutions and can be easily reduced to the similar solutions corresponding to Newtonian or Maxwell fluids.
A superposition technique is used to represent the interfacial stresses as a sum of Smith and Teng's solution and an additional part due to shear deformation effect, with the latter being expressed by Fourier series with linear supplementary terms.
Moreover, since ∑ m = 0 ∞ c m x m is a solution of (6), it can be expressed as a sum of both y 0 ( x ) and a solution of the homogeneous equation (1) with p ( x ) ≡ 1.
New exact solutions for the same problem, but presented as a sum of steady-state and transient solutions, have also been established by Corina Fetecau et al. [6].
Then, we use energy arguments coupled with dispersive estimates to show that the solution approaches this family in the energy norm, in the non-characteristic case, and to a finite decoupled sum of such a solution in the characteristic case.
