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Phase Singularities to Polarization Singularities
2020Polarization singularities are superpositions of orbital angular momentum (OAM) states in orthogonal circular polarization basis. The intrinsic OAM of light beams arises due to the helical wavefronts of phase singularities. In phase singularities, circulating phase gradients and, in polarization singularities, circulating ϕ12 Stokes phase gradients are
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Singular singular-perturbation problems
1977Abstract : Consider initial problems for nonlinear singularly perturbed systems of the form epsilon sub z dot = f(z,t,epsilon) in the singular situation that f sub z(z,t,0) has a nontrivial null space. Under appropriate hypotheses, such problems have asymptotic solutions as epsilon approaches 0 for t or = 0 consisting of the sum of a function of t and ...
R. E. O'Malley, J. E. Flaherty
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Journal of Knot Theory and Its Ramifications, 1997
In Vassiliev theory, there is a natural monoid homomorphism from n-strand singular braids to the group algebra of n-strand braid group. J. Birman conjectured that this monoid homomorphism is injective. We show that the monoid homomorphism is injective on braids with up to three singularities and that Birman's conjecture is equivalent to that singular ...
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In Vassiliev theory, there is a natural monoid homomorphism from n-strand singular braids to the group algebra of n-strand braid group. J. Birman conjectured that this monoid homomorphism is injective. We show that the monoid homomorphism is injective on braids with up to three singularities and that Birman's conjecture is equivalent to that singular ...
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The singular of the singular: singular propositions and the not-all
2018Raul Moncayo, Magdalena Romanowicz
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Singular perturbations and singular arcs. I
1975O'Malley, Robert E. jun. +1 more
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