PURPOSE To determine the effect of using toric soft contact lenses on corneal biomechanical properties. METHODS We enrolled 33 healthy patients with mean age of 23.18 ± 4.06 and minimal cylinder power of 1 D (-1.98 ± 0.808 SD) and negative history of contact lens use; keratoconic patients were excluded from the study. Toric soft contact lenses (BIOFINITY, Comfilcon A, Coopervision, Southampto...

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

AIM The aim of this research was to evaluate vector analysis after implantation of toric intraocular lenses (IOLs) without deviation from the intended axis. METHODS The study included 18 eyes of 16 patients who underwent cataract surgery with the insertion of a toric implant (AcrySof IQ Toric). The postoperative IOL meridian placement completely corresponded to that planned. Using vector anal...

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.

OBJECTIVE To determine whether texturing the optic edge of the intraocular lens reduces photic symptoms in patients with square-edged acrylic intraocular lense implants. METHODS Sixty patients underwent routine phacoemulsification performed by a single surgeon and were prospectively randomized to receive either the standard AcrySof MA30 intraocular lens (Alcon Laboratories, Ft Worth, Tex) (gr...

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...