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.
We recently characterized the spectral flow of such paths in the singular case.
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).
The small oscillations have zero amplitude in the singular case, which grows as C m for C m sufficiently small [23].
In the singular case we show that the second derivatives uxixj of a solution of the Cauchy problem belong to L2.
By means of variational arguments and a version of the concentration-compactness principle in the singular case, they proved the existence of solutions for positive values of the parameter under the principal eigenvalue of the associated singular eigenvalue problem.
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.
In the singular case we find the solution in the step function limit by putting y* = θ and solve for m*, getting m* = λθ/ κ, Z* = 1 + r/ α - g, where g = γλθ/.
We extend the concept here by showing that differential cancer stem cell proliferation vs. committed cell proliferation is merely advanced further by directed migration (except in the singular case where the point of attraction is in the tumor itself) in the same general manner as was seen with undirected migration without imposition of spatial heterogeneity.
