We propose the class of uniformly convex W -hyperbolic spaces with monotone modulus of uniform convexity (UCW -hyperbolic spaces for short) as an appropriate setting for the study of nonexpansive iterations. UCW -hyperbolic spaces are a natural generalization both of uniformly convex normed spaces and CAT (0)-spaces. Furthermore, we apply proof mining techniques to get effective rates of asympt...

Based on the matrix perturbation technique. a fast-fitting algorithm using uniform cubic B-spline curves is presented. Our algorithm entails much less floating-point operations when compared with Gaussian elimination method. In addition, our result can be applied to solve the closed cubic B-spline curve-fitting problem. Experimental results are included for a practical version. These experiment...

We discuss the Sinai method of proving ergodicity of a discontinuous Hamiltonian system with (non-uniform) hyperbolic behavior.

We discuss the Sinai method of proving ergodicity of a discontinuous Hamiltonian system with (non-uniform) hyperbolic behavior.

Suppose G is a hyperbolic group whose boundary ∂∞G has topological dimension k. If ∂∞G is quasi-symmetrically homeomorphic to an Ahlfors kregular metric space, then, modulo a finite normal subgroup, G is isomorphic to a uniform lattice in the isometry group Isom(Hk+1) of hyperbolic (k+1)-space.

We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability are necessarily uniformly expanding. We also present a version of this result for diffeomorphisms with nonuniformly hyperbolic sets.

We consider continuous SL(2, R)-cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove that any cocycle which is not uniformly hyperbolic can be approximated by one which is conjugate to an SO(2, R)-cocycle. Using this, we show that if a cocycle’s homotopy class does not display a certain obstruction to uniform hy...

Chaiken's algorithm is a procedure for inserting new knots into uniform quadratic Bspline curves by doubling the control points and taking two successive averages. Lane and Riesenfeld showed that Chaiken's algorithm extends to uniform B-spline curves of arbitrary degree. By generalizing the notion of successive averaging, we further extend Chaiken's algorithm to B-spline curves of arbitrary deg...

We consider a model for complex networks that was introduced by Krioukov et al. [18], in which conceptually the intrinsic hierarchies of a network are mapped into the hyperbolic plane. This model gives rise to a random graph on the hyperbolic plane, which turns out to behave locally like the well-known Chung-Lu model. The latter is a special case of inhomogeneous random graphs, where two nodes ...

We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimiz...