'A singular optical phenomenon.'

A singular large deviations phenomenon

A KAM phenomenon for singular holomorphic vector fields

Let X be a germ of holomorphic vector field at the origin of C and vanishing there. We assume that X is a “nondegenerate” good perturbation of a singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals. We show that X admits many invariant analytic subsets in a neighborhood of the ...

Child Soldiers in Africa: A Singular Phenomenon? On the necessity of a historical perspective

In the case of the African conflicts, the issue of children in war was initially the prerogative of humanitarian organizations. Moreover, interest in this issue is relatively recent. In the 1990s, sub-Saharan Africa was marked by a long series of civil conflicts (in Liberia, Sierra Leone, Somalia, Burundi, Rwanda, CongoBrazzaville, the Democratic Republic of the Congo, Sudan, Ivory Coast, etc.)...

A Strange Phenomenon for the Singular Values of Commutators with Rank One Matrices∗

The singular values of XY − Y X are the objects under investigation. Here, X and Y are square matrices with complex entries, and one of them has rank one. Hence, there are at most two non-trivial numbers among the commutator’s singular values, and the pairs of interest can be depicted in the plane. The emphasis will lie on the unexpectedly intriguing case in which both matrices are of rank one ...

Quadratic Forms and Klauder’s Phenomenon: A Remark on Very Singular Perturbations

Recently, Klauder [4] has discussed the following example: Let A be the operator -(d2/A2) + x2 on L2(R, dx) and let B = 1 x 1-s. The eigenvectors and eigenvalues of A are, of course, well known to be the Hermite functions, H,(x), n = 0, l,... and E, = 2n + 1. Klauder then considers the eigenvectors of A + XB (A > 0) by manipulations with the ordinary differential equation (we consider the domai...