SINGULAR

Singular constrained linear systems

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

Explicit multiple singular periodic solutions and singular soliton solutions to KdV equation

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...

Generalized Helices and Singular Points

In this paper, we define X-slant helix in Euclidean 3-space and we obtain helix, slant helix, clad and g-clad helix as special case of the X-slant helix. Then we study Darboux, tangential darboux developable surfaces and their singular points. Especially we show that the striction lines of these surfaces are singular locus of the surfaces.

Singular and Totally Singular Generalised Quadratic Forms

In this paper we present a decomposition theorem for generalised quadratic forms over a division algebra with involution in characteristic 2. This is a generalisation of a decomposition result on quadratic forms in characteristic 2 from [3] and extends a generalisation of the Witt decomposition theorem for nonsingular forms to cover forms that may be singular.

Evaluating Singular and Nearly Singular Integrals Numerically