We discuss the algebraic way of solving the descent equations corresponding to the BRST consistency condition for the gauge anomalies and the Chern–Simons terms on a nontrivial bundle. The method of decomposing the exterior derivative as a BRST commutator is extended to the present case.

We show how the high order finite element spaces of differential forms due to Raviart-Thomas-Nédelec-Hiptmair fit into the framework of finite element systems, in an elaboration of the finite element exterior calculus of Arnold-Falk-Winther. Based on observations by Bossavit, we provide new low order degrees of freedom. As an alternative to existing choices of bases, we provide canonical resolu...

Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing the discrete analogue of the Atiyah sequence, with a connection corresponding to the choice of a splitting of the short exact sequence. Equivalent represent...

We show asymptotic completeness for the charged Klein–Gordon equation in exterior De Sitter–Reissner–Nordström spacetime when product of charge black with Klein-Gordon field is small enough. then interpret scattering as transports along principal null geodesics a Kaluza–Klein extension original spacetime.

Abstract We give a pedagogical account of noncommutative gauge and gravity theories, where the exterior product between forms is deformed into $$\star$$ ⋆ -product via an abelian twist (e.g. Groenewold–Moyal twist). The Seiberg–Witten map commutative theories introduced. It allows to express action Einstein c...

Contamination of the external surface of anticancer drug vials supplied to hospital pharmacies has been recognized as a potential health hazard. The aim of this study was to investigate the levels of contamination on the exterior surface of vials containing platinum anticancer drugs in Japan. Platinum contamination on the exterior surface of vials containing cisplatin or carboplatin was examine...

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 perform error analyses explaining some previously mysterious phenomena arising in numerical computation of the Evans function, in particular (i) the advantage of centered coordinates for exterior product and related methods, and (ii) the unexpected stability of the (notoriously unstable) continuous orthogonalization method of Drury in the context of Evans function applications. The analysis ...

We study solutions of Einstein’s equations corresponding codimension n > 2 global topological defects with de Sitter slices. We analyze a class of solutions that are cylindrically symmetric and admit positive, negative or zero Bulk cosmological constant. We derive the relevant graviton equations. For an extended brane, the properties of the solution depend on appropriate boundary conditions tha...