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Full-Text Articles in Applied Mathematics
The Möbius Geometry Of Hypersurfaces, Ii, Michael Bolt
The Möbius Geometry Of Hypersurfaces, Ii, Michael Bolt
University Faculty Publications and Creative Works
No abstract provided.
The Möbius Geometry Of Hypersurfaces, Ii, Michael Bolt
The Möbius Geometry Of Hypersurfaces, Ii, Michael Bolt
University Faculty Publications and Creative Works
No abstract provided.
A Generalised Kummer's Conjecture, M. J.R. Myers
A Generalised Kummer's Conjecture, M. J.R. Myers
University Faculty Publications and Creative Works
Kummer's conjecture predicts the rate of growth of the relative class numbers of cyclotomic fields of prime conductor. We extend Kummer's conjecture to cyclotomic fields of conductor n, where n is any natural number. We show that the Elliott-Halberstam conjecture implies that this generalised Kummer's conjecture is true for almost all n but is false for infinitely many n.
A Generalised Kummer's Conjecture, M. J.R. Myers
A Generalised Kummer's Conjecture, M. J.R. Myers
University Faculty Publications and Creative Works
Kummer's conjecture predicts the rate of growth of the relative class numbers of cyclotomic fields of prime conductor. We extend Kummer's conjecture to cyclotomic fields of conductor n, where n is any natural number. We show that the Elliott-Halberstam conjecture implies that this generalised Kummer's conjecture is true for almost all n but is false for infinitely many n. Copyright © 2010 Glasgow Mathematical Journal Trust.
A Global Characterization Of Tubed Surfaces In ℂ2, Michael Bolt
A Global Characterization Of Tubed Surfaces In ℂ2, Michael Bolt
University Faculty Publications and Creative Works
Let M3 S C2 be a three times differentiable real hypersurface. The Levi form of M transforms under biholomorphism, and when restricted to the complex tangent space, the skew-Hermitian part of the second fundamental form transforms under Möbius transformations. The surfaces for which these forms are constant multiples of each other were identified in previous work, provided the constant is not unimodular. Here it is proved that if the surface is assumed to be complete and if the constant is unimodular, then the surface is tubed over a strongly convex curve. The converse statement is true, too, and is easily …
A Global Characterization Of Tubed Surfaces In ℂ2, Michael Bolt
A Global Characterization Of Tubed Surfaces In ℂ2, Michael Bolt
University Faculty Publications and Creative Works
Let M3 S C2 be a three times differentiable real hypersurface. The Levi form of M transforms under biholomorphism, and when restricted to the complex tangent space, the skew-Hermitian part of the second fundamental form transforms under Möbius transformations. The surfaces for which these forms are constant multiples of each other were identified in previous work, provided the constant is not unimodular. Here it is proved that if the surface is assumed to be complete and if the constant is unimodular, then the surface is tubed over a strongly convex curve. The converse statement is true, too, and is easily …
Higher Homotopy Operations And Cohomology, David Blanc, Mark W. Johnson, James M. Turner
Higher Homotopy Operations And Cohomology, David Blanc, Mark W. Johnson, James M. Turner
University Faculty Publications and Creative Works
We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams. © 2010 ISOPP.
Interaction Of Excited States In Two-Species Bose-Einstein Condensates: A Case Study, Todd Kapitula, Kody J. H. Law, Panayotis G. Kevrekidis
Interaction Of Excited States In Two-Species Bose-Einstein Condensates: A Case Study, Todd Kapitula, Kody J. H. Law, Panayotis G. Kevrekidis
University Faculty Publications and Creative Works
In this paper we consider the existence and spectral stability of excited states in two-species Bose-Einstein condensates in the case of a pancake magnetic trap. Each new excited state found in this paper is to leading order a linear combination of two one-species dipoles, each of which is a spectrally stable excited state for one-species condensates. The analysis is done via a Lyapunov-Schmidt reduction and is valid in the limit of weak nonlinear interactions. Some conclusions, however, can be made at this limit which remain true even when the interactions are large.
Laguerre Arc Length From Distance Functions, David E. Barrett, Michael Bolt
Laguerre Arc Length From Distance Functions, David E. Barrett, Michael Bolt
University Faculty Publications and Creative Works
For the Laguerre geometry in the dual plane, invariant arc length is shown to arise naturally through the use of a pair of distance functions. These distances are useful for identifying equivalence classes of curves, within which the extremal curves are proved to be strict maximizers of Laguerre arc length among three-times differentiable curves of constant signature in a prescribed isotopy class. For smoother curves, it is shown that Laguerre curvature determines the distortion of the distance functions. These results extend existing work for the Möbius geometry in the complex plane. © 2010 International Press.
Laguerre Arc Length From Distance Functions, David E. Barrett, Michael Bolt
Laguerre Arc Length From Distance Functions, David E. Barrett, Michael Bolt
University Faculty Publications and Creative Works
For the Laguerre geometry in the dual plane, invariant arc length is shown to arise naturally through the use of a pair of distance functions. These distances are useful for identifying equivalence classes of curves, within which the extremal curves are proved to be strict maximizers of Laguerre arc length among three-times differentiable curves of constant signature in a prescribed isotopy class. For smoother curves, it is shown that Laguerre curvature determines the distortion of the distance functions. These results extend existing work for the Möbius geometry in the complex plane