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Non-commutative geometry of finite groups
A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A correspondingExpand
Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice
`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models andExpand
Teleparallelism-A viable theory of gravity?
The teleparallelism theory of gravity is presented as a constrained Poincare gauge theory. Arguments are given in favor of a two-parameter family of field Lagrangians quadratic in torsion. TheExpand
KP line solitons and Tamari lattices
The KP-II equation possesses a class of line soliton solutions which can be qualitatively described via a tropical approximation as a chain of rooted binary trees, except at "critical" events where aExpand
Integrable Discretizations of Chiral Models
A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprisesExpand
Bidifferential calculus approach to AKNS hierarchies and their solutions
We express AKNS hierarchies, admitting reductions to matrix NLS and matrix mKdV hierarchies, in terms of a bidifferential graded algebra. Application of a universal result in this framework quicklyExpand
KP Solitons, Higher Bruhat and Tamari Orders
In a tropical approximation, any tree-shaped line soliton solution, a member of the simplest class of soliton solutions of the Kadomtsev-Petviashvili (KP-II) equation, determines a chain of planarExpand
KdV soliton interactions: a tropical view
Via a tropical limit (Maslov dequantization), Korteweg-deVries (KdV) solitons correspond to piecewise linear graphs in two-dimensional space-time. We explore this limit.
Familiar nonlinear and in particular soliton equations arise as zero curvature conditions for connections with noncommutative differential calculi. The Burgers equation is formulated in this way andExpand