Let G be a finitely generated group which is hyperbolic relative to a finite family fH1; . . . ;Hng of subgroups. We prove that G is uniformly embeddable in a Hilbert space if and only if each subgroup Hi is uniformly embeddable in a Hilbert space.

The singularly perturbed parabolic boundary value problem is considered. Difference scheme is obtained by using cubic spline difference scheme on Shishkin’s mesh in space and classical discretization on uniform mesh in time. To obtain better stability and simpler matrix the fitting factor in polynomial form is used. The uniform convergence is achieved. Numerical results are presented. AMS Mathe...

A domain G in a Banach space is said to be δ-hyperbolic if it is a Gromov δ-hyperbolic space in the quasihyperbolic metric. Then G has the Gromov boundary ∂∗G and the norm boundary ∂G. We show that the following properties are quantitatively equivalent: (1) G is C-uniform. (2) G is δ-hyperbolic and there is a natural bijective map G ∪ ∂∗G → G ∪ ∂G, which is η-quasimöbius rel ∂∗G. (3) G is δ-hyp...

We investigate mutually orthogonal spline wavelet spaces on non-uniform partitions of a bounded interval, addressing the existence, uniqueness and construction of bases of minimally supported spline wavelets. The relevant algorithms for decomposition and reconstruction are considered as well as some stability-related questions. In addition, we briefly review the bivariate case for tensor produc...

We consider a spline difference scheme on a piecewise uniform Shishkin mesh for a singularly perturbed boundary value problem with two parameters. We show that the discrete minimum principle holds for a suitably chosen collocation points. Furthermore, bounds on the discrete counterparts of the layer functions are given. Numerical results indicate uniform convergence. AMS Mathematics Subject Cla...

Let X be a 2-dimensional right-angled hyperbolic building. We characterise the set of covolumes of uniform lattices in Aut(X). We also show that the group Aut(X) admits an infinite ascending tower of uniform lattices.

This chapter introduces the concepts, theories and algorithms of discrete curvature flows for surfaces with arbitrary topologies. Discrete curvature flow for hyperbolic 3-manifolds with geodesic boundaries is also presented. Curvature flow method can be used to design Riemannian metrics by prescribed curvatures, and applied for parameterization in graphics, shape registration in computer vision...

PH curves; B-spline curves; Nodal points; CNC interpolators; Variable feedrate control; Contour error. Abstract This paper presents a C2 Pythagorean-Hodograph (PH) spline curve interpolator for high speed contouring applications. With the knot vector and control points given, the C2 PH quintic spline curve is a ‘‘good’’ interpolant to the nodal points of the cubic B-spline curve, with the same ...

We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph product of finite groups, a uniform lattice is commensurable with the graph product provided all of its quasiconvex subgroups are separable. W...