We construct a consistent set of monopole equations on eight-manifolds with Spin(7) holonomy. These equations are elliptic and admit nontrivial solutions including all the 4-dimensional… (More)

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and… (More)

Strongly self-dual Yang-Mills fields in even dimensional spaces are characterised by a set of constraints on the eigenvalues of the YangMills fields Fμν . We derive a topological bound on R 8, ∫ M… (More)

The geometry of self-dual 2-forms in 2n dimensional spaces is studied. These 2-forms determine a n 2 − n + 1 dimensional manifold S 2n. We prove that S 2n has only one-dimensional linear submanifolds… (More)

Positively weighted graphs have a natural intrinsic metric. We consider finite, positively weighted graphs with a positive lower bound for their minimal weights and show that any two such graphs,… (More)

The restrictions of a harmonic function on the Sierpinski Gasket (SG) to the segments in SG have been of some interest. We show that the sufficient conditions for the monotonicity of these… (More)