BOUNDARY ALGEBRA Jeffrey

A Boundary Notation for Visual Mathematics

Instead of traditional mathematical notation, we can describe formal mathematical systems in visual form. While traditional notation uses a linear sequence of symbols, visual mathematics uses boundary notation, which is comprised of objects and boundaries to enclose objects. Boundary notation is abstract, decoupling the underlying mathematics of a system from its visual representation. Once a s...

Tameness on the boundary and Ahlfors’ measure conjecture

Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: 1. N has non-empty conformal boundary, 2. N is not homotopy equivalent to a compression body, or 3. N is a strong limit of geometrically finite manifolds. The fir...

Algebraic limits of geometrically finite manifolds are tame

In his 1986 article [Th2], W. Thurston proposed that one might approachMarden’s conjecture from a dynamical point of view via a study of limits in the natural deformation space: its interior consists of geometrically finite manifolds, and promoting their tameness to algebraic limits on the boundary has proven to be a successful strategy to address Marden’s conjecture in special cases. In this p...

Error estimation for nonlinear pseudoparabolic equations with nonlocal boundary conditions in reproducing kernel space

In this paper we discuss about nonlinear pseudoparabolic equations with nonlocal boundary conditions and their results. An effective error estimation for this method altough has not yet been discussed. The aim of this paper is to fill this gap.

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow