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Journals and Conferences
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 Seiberg-Witten solutions as a special case.
The well-known classification of the Clifford algebrasCl(r, s) leads to canonical forms of complex and real representations which are essentially unique by virtue of the Wedderburn theorem. For s ≥ 1 representations of Cl(r, s) on R are obtained from representations on R by adding two new generators while in passing from a representation of Cl(p, 0) on R to… (More)
We show that there are no nontrivial solutions of the Seiberg-Witten equations on R 8 with constant standard spin c structure.
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 (F,F ) 2 ≥ k ∫ M p 2 1 where p1 is the first Pontrjagin class of the SO(n) Yang-Mills bundle and k is a constant. Strongly self-dual Yang-Mills fields realise the… (More)
Abstract We define the “shift-match number” for a binary string and we compute the probability of occurrence of a given string as a subsequence in longer strings in terms of its shift-match number. We thus prove that the string matching probabilities depend not only on the length of shorter strings, but also on the equivalence class of the shorter string… (More)
Einstein’s field equations for a spherically symmetric metric coupled to a massless scalar field are reduced to a system for the metric functions only, decoupled from the scalar field φ. In suitable logarithmic coordinates, these equations involving μ = m/r and y = (α/ra), where a, α, r and m are as in [W.M. Choptuik, “Universality and Scaling in… (More)
In this study the following Cauchy problem is considered: utt − uxx − Luxx = (g(u))xx, x ∈ R, t > 0, u(x, 0) = φ(x), ut(x, 0) = ψ(x), where g is a sufficiently smooth nonlinear function and L is the linear operator defined by F (Lv) (ξ) = l (ξ)Fv (ξ) . Here F denotes the Fourier transform with respect to variable x and l(ξ) is the Fourier transform of the… (More)
Einstein’s field equations for a spherically symmetric metric coupled to a massless scalar field are reduced to a system effectively of second order in time, in terms of the variables μ = m/r and y = (α/ra), where a, α, r and m are as in [W.M. Choptuik, “Universality and Scaling in Gravitational Collapse of Massless Scalar Field”, Physical Review Letters 70… (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 for n odd. In eight dimensions the self-dual forms of Corrigan et al constitute a seven dimensional linear subspace of S 8 among many other equally interesting… (More)