The numerical treatment of a single nonlinear equation by Alston Scott Householder

By Alston Scott Householder

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18) where cijk stand for the G2 -invariant tensor made of octonionic structure coefficients, and ϕ is a Higgs field. The BRST quantization of this topological term yields a twisted version of the dimensional reduction to seven dimensions of the D=8 super Yang–Mills action on a manifold with Spin(7) or SU (4) holonomy. Basically, the topological gauge functions are the generalization of Bogolmony equations in 7 dimensions, as shown in [4]. G2 manifolds of the kind Σ6 × S1 , where Σ6 is a Calabi–Yau 3-fold, are of special interest both for mathematical [15] and physical [12] applications.

Math. Phys. 125 (1989) 417; C. G. Torre, “Perturbations Of Gravitational Instantons,” Phys. Rev. D 41 (1990) 3620; M. Abe, A. Nakamichi and T. Ueno, “Gravitational instantons and moduli QUANTIZATION OF HOLOMORPHIC FORMS 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 39 spaces in topological two form gravity,” Phys. Rev. D 50, 7323 (1994), hep-th/9408178. work in progress. E. Witten, “(2+1)-Dimensional Gravity As An Exactly Soluble System,” Nucl. Phys. B 311 (1988) 46.

Plebanski, “On the separation of Einsteinian substructures,” J. Math. Phys. 18 (1977), 2511; G. T. Horowitz, “Exactly Soluble Diffeomorphism Invariant Theories,” Commun. Math. Phys. 125 (1989) 417; C. G. Torre, “Perturbations Of Gravitational Instantons,” Phys. Rev. D 41 (1990) 3620; M. Abe, A. Nakamichi and T. Ueno, “Gravitational instantons and moduli QUANTIZATION OF HOLOMORPHIC FORMS 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 39 spaces in topological two form gravity,” Phys.

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