Sentence examples for trivial solution and from inspiring English sources

Here it is demonstrated that those conclusions were drawn from incomplete evidence, in one case because the experimental designs leads only to a trivial solution and in a second case because of an incomplete search of the literature.

has only the trivial solution and Green's function is (3.2).

The above equation has only the trivial solution and hence has only one critical point.

Here, we note that the associated homogeneous problem has only the trivial solution and on.

The stability of the trivial solution and the existence of periodic solutions are investigated.

The stability of the trivial solution and the existence of periodic solutions are discussed.

Here, three modifications are proposed in a GP technique available in the literature for Innovization problems: (i) a method to ensure the consistency of the units of the principles using protected operations that ignore invalid terms, (ii) a strategy to avoid trivial solutions, and (iii) the use of an external archive to store the solutions of interest found during the search.

In order to avoid such trivial solutions and to regularize the minimization problem, the authors in [21] propose to restrict all columns of transform matrices to have unit norm.

But (3.8) is equivalent to { ∂ ∂ α [ q − ( − T − − q + ( T + ] α = 0 w = 0, T − ′ ( 0 ) w = 0, and hence (3.8) has the trivial solution if and only if the non-degenerateness condition (1.4) holds.

Clearly, system (4) admits a trivial solution (u t,0 equiv0) and (v t,0 equiv0) corresponding to the initial data (xi=0) and (tilde{xi}=0), respectively.

On the one hand, Lyapunov exponent as a measure is used to estimate the local stability with probability one for the trivial solution of uncontrolled and controlled systems.