AIM The aim of our study was to evaluate the outcome of cataract surgeries with implantation of intraocular trifocal toric lens, and to study the accuracy of astigmatism correction, lens rotational stability, and safety of the procedures. PATIENTS AND METHODS Our study comprised 22 eyes of 16 patients who underwent unilateral or bilateral implantation of AT LISA tri toric 939MP, or its implan...

We consider the action of a subtorus of the big torus on a toric variety. The aim of the paper is to define a natural notion of a quotient for this setting and to give an explicit algorithm for the construction of this quotient from the combinatorial data corresponding to the pair consisting of the subtorus and the toric variety. Moreover, we study the relations of such quotients with good quot...

We present a patient with marginal corneal degeneration and corneal astigmatism of more than 10.0 diopters (D). A toric phakic intraocular lens (IOL) of 7.0 D cylindrical power was implanted in both eyes to correct the high astigmatism. An uncorrected visual acuity of 20/40 was achieved in both eyes, and the best corrected visual acuity improved by 4 Snellen lines to 20/20 in both eyes. Refract...

PURPOSE This study aimed to compare ocular wavefront aberrations for pupil diameters of 4 mm and 6 mm, and contrast sensitivity, in eyes with AcrySof IQ and AcrySof Natural intraocular lenses (IOLs). METHODS Sixty eyes of 60 patients were enrolled in this prospective randomized study. After phacoemulsification the eyes received either AcrySof IQ SN60WF or AcrySof Natural SN60AT IOLs. One mont...

Lower- and higher-order wave-front aberrations of soft contact lenses were accurately measured with a Shack-Hartmann wave-front sensor. The soft contact lenses were placed in a wet cell filled with lens solution to prevent surface deformation and desiccation during measurements. Aberration measurements of conventional toric and multifocal soft contact lenses and a customized soft contact lens h...

Sutureless, glueless, scleral fixation of an intraocular lens is a known technique of fixing a lens in the scleral pockets. However, this technique is applied to single-piece and toric lenses instead of 3-piece lenses, allowing the advantage of the use of premium lenses in patients with poor capsular support. Favourable results without complications of pigment dispersion, iris transillumination...

Smooth toric Fano varieties are classified up to dimension 4. In dimension 2, there are five toric Del Pezzo surfaces: P, P1×P1, and Si, the blowup of P in i points, for i = 1, 2, 3. There are 18 toric Fano 3-folds [2, 20] and 124 toric Fano 4-folds [4, 17]. In higher dimensions, little is known about them and many properties that hold in low dimensions are not known to hold in general. Let X b...

We consider a set of toric Calabi–Yau varieties which arise as deformations of the small resolutions of type A surface singularities. By careful analysis of the heuristics of B-brane transport in the associated GLSMs, we predict the existence of a mixed braid group action on the derived category of each variety, and then prove that this action does indeed exist. This generalizes the braid group...

Generalizing toric varieties, we introduce toric Deligne-Mumford stacks. The main result in this paper is an explicit calculation of the orbifold Chow ring of a toric Deligne-Mumford stack. As an application, we prove that the orbifold Chow ring of the toric Deligne-Mumford stack associated to a simplicial toric variety is a flat deformation of (but is not necessarily isomorphic to) the Chow ri...