PURPOSE To evaluate the efficacy, safety, and predictability of sequential implantation of Keraring intrastromal corneal ring segments (ICRS) and an Implantable Collamer Lens phakic intraocular lens (pIOL) with corneal relaxing incisions for refractive correction of keratoconus. SETTING Fernández-Vega Ophthalmological Institute, Oviedo, Spain. DESIGN Cohort study. METHODS This study compr...

This is an expository article on “A mathematical theory of the topological vertex” by J. Li, K. Liu, J. Zhou, and the author.

We study A-hypergeometric functions introduced by Gelfand-KapranovZelevinsky [4] and prove a formula for the eigenvalues of their monodromy automorphisms defined by the analytic continuaions along large loops contained in complex lines parallel to the coordinate axes. The method of toric compactifications introduced in [12] and [16] will be used to prove our main theorem.

1 Four constructions 1 1.1 First construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Second construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Third construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Fourth construction . . . . . . . . . . . . . . . . . . . . . . . . . . ...

A symplectic toric orbifold is a compact connected orbifold M , a symplectic form ω on M , and an effective Hamiltonian action of a torus T on M , where the dimension of T is half the dimension of M . We prove that there is a one-to-one correspondence between symplectic toric orbifolds and convex rational simple polytopes with positive integers attached to each facet.

This note proves combinatorially that the intersection pairing on the middle-dimensional compactly supported cohomology of a toric hyperkähler variety is always definite, providing a large number of non-trivial L2 harmonic forms for toric hyperkähler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of L2 harmonic forms on complete hyperk...

BACKGROUND To evaluate the rotational stability of the three types of AcrySof SA60TT toric intraocular lenses (Alcon, Switzerland) in cataract surgery after the first postoperative week. METHODS A retrospective study of 44 eyes in 33 patients. All patients underwent similar uncomplicated phacoemulsification cataract surgery. Seven eyes with corneal astigmatism of less than 1.5 D were implante...