In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

Two single parameter families of polyhedra P (ψ) are constructed in three dimensional spaces of constant curvature C(ψ). Identification of the faces of the polyhedra via isometries results in cone manifolds M(ψ) which are topologically S × S, S or singular S . The singular set of M(ψ) can have self intersections for some values of ψ and can also be the Whitehead link or form other configuration...

This paper presents a general necessary condition for singular time optimal control of robotic manipulation moving along specified paths. Early work [l], [7] ignored the issue of singular control, assuming bang-bang acceleration along the path. Recent work [6] has shown that the time optimal control can be singular if one of the equations of motion reduces to a velocity constraint. This paper d...

In this paper, we consider the problem of the existence of non-negative weak solution u of A u + u P = O i n ~ u = 0 on Of~ n n + 2 ~ / n 1 having a given closed set S as its singular set. We prove that when < p < _ _ and n 2 n 4 + 2 nv/'n-L--1 S is a closed subset of f2, then there are infinite many positive weak solutions with S as their singular set. Applying this method to the conformal sca...

The implicit function theorem implies that the zero set of a smooth function, the set where the function vanishes, is a smooth hypersurface away from the critical zero set. Hence to study zero sets it is important to understand the structure of the critical zero sets. For solutions of the second order elliptic equations the critical zero sets represent the singular parts of zero sets. They have...

A singular hyperbolic attractor for flows is a partially hyperbolic at-tractor with singularities (hyperbolic ones) and volume expanding central direction [MPP1]. The geometric Lorenz attractor [GW] is an example of a singular hyperbolic attractor. In this paper we study the perturbations of singular hyperbolic attractors for three-dimensional flows. It is proved that any attractor obtained fro...