A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found thatâ€¦ (More)

Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a â€˜reductionâ€™ of the â€˜universalâ€¦ (More)

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-, rightand bicovariance. A corresponding frameworkâ€¦ (More)

We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes'â€¦ (More)

A well-known ansatz ('trace method') for soliton solutions turns the equations of the (noncom-mutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. Weâ€¦ (More)

Umbral calculusâ€™ 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 and toâ€¦ (More)

The existence of an infinite set of conserved currents in completely integrable classical models, including chiral and Toda models as well as the KP and self-dual Yang-Mills equations, is traced backâ€¦ (More)

A discrete differential manifold we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with aâ€¦ (More)

We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed inâ€¦ (More)

Conference Record of the Thirty-Eighth Asilomarâ€¦

2004

We assume a large-scale wireless sensor network of n nodes, measuring a physical quantity of interest (e.g. temperature). Most of the sensors are used as storage devices and relays while only aâ€¦ (More)