Sentence examples for in the singular case from inspiring English sources

We recently characterized the spectral flow of such paths in the singular case.

It is possible to become a legend and be forgotten, or, as in the singular case of Gloria Swanson, to become a legend for having been forgotten.

In the singular case we show that the second derivatives uxixj of a solution of the Cauchy problem belong to L2.

Because of the principal applications of generalized inverses is to the solution of linear systems and matrix equations in the singular case, we use the generalized inverse of matrices to demonstration that the transform function of the neural synaptic matrix is trapdoor one-way function.

The paper studies the existence problem of periodic solutions of the nonlinear dynamical systems in the singular case.

But in the singular case, we establish the existence of a positive solution for any (a > 0).

Then we proceed to prove that under certain assumptions, the spectral flow of paths along these operators is the same in both the smooth and the singular case.

In Section 4, we discuss the singular case, that is, maybe singular at the end points or, or at.

In this paper, we consider the singular case and always assume that (operatorname{rank}(B =r< m) and that the singular nonsymmetric saddle-point problem (1.1) is consistent, that is, (bin operatorname{range}(mathcal{A})).

and got -estimates of the degenerate parabolic equation with -growth conditions for, where is a constant, then in [16] the authors established the Hölder continuity of the equation for the singular case, and in [17] the authors discussed Harnack estimates for the bounded solutions of the above parabolic equation for.

For the singular case, the conditions in the paper are not enough.