Ω(R) d −→ Ω(R) d −→ Ω(R) d −→ Ω(R), where Ωi(R) is the space of differential forms of degree i = 0, 1, 2, 3 on the space R over the ring of functions A = {f : R → R | f ∈ C(R)}. In the consideration, which follows, we give definitions of the first-order differential operations. Let us notice that one-dimensional spaces Ω0(R) and Ω3(R) are isomorphic to A and let φ0 : Ω (R) → A, φ3 : Ω (R) → A b...

We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincaré duality in the transversally orientable case. We use this twisted basic cohomology to show relationships between curvature, tautness, and vanishing of the basic Euler characteristic and basic signature.

We numerically test the correspondence between the scaling limit of self-avoiding walks (SAW) in the plane and Schramm-Loewner evolution (SLE) with κ = 8/3. We introduce a discrete-time process approximating SLE in the exterior of the unit disc and compare the distribution functions for an internal point in the SAW and a point at a fixed fractal variation on the SLE, finding good agreement. Thi...

A tting system for multidimensional printer gamut data was produced The re sultant B Spline hyper volume provides a functional de nition of a printer s output capabilities Additional system features determine the closest point on a tted hyper surface to a point on its exterior This permits optimal reproduction of all colours including those not precisely obtainable by an output device Visualiza...

The result of simulation of an idealized thin wet film connecting fixed points in the Euclidean plane is a length-minimizing curve. Gradually increasing the exterior pressure we are able to achieve the film configuration near to the Steiner minimal tree. This film evolution may be an interesting tool for solving the Euclidean Steiner problem, but several dead-point situations may occur for a ce...

This article treats connections on ber bundles B = P G F that are induced by a connection 1-form on the associated principal bundle P. Using horizontal lifts of vector elds it is shown which combinations of diierential forms on the ber F and on P canonically deene diierential forms on B. Local representations for these forms involving the gauge potentials and elds of the connection are given an...

Bryant and Salamon constructed metrics with holonomy G2 and Spin(7) on spin bundles of 3-dimensional space forms, and spin bundles and bundles of anti-self-dual 2-forms on self-dual Einstein 4-manifolds [BrS]. Since, apart from holonomy, the construction of integrable G2(respectively Spin(7)) structures amounts to finding differential 3(4)forms of generic type on 7(8) manifolds satisfying appro...

Exterior tomographic data are taken over lines outside a central region, and such data occur in the industrial nondestructive evaluation of large objects such as rockets. We explain, using microlocal analysis, which singularities are well reconstructed from exterior data, and we explain how this phenomenon is reflected in the singular value decomposition for the exterior transform [E.T. Quinto,...