in view of the rapid expansion of contact lens amongst the users, new dimensions have been added to the domain of ophthalmology: giant papillay conjunctivitis, a disease caused by different kinds of contact lens, appears weeks or months after they are used, although some patients are struck years later. the predominant symptoms are increased awareness of lenses, ocular itching, blurred vision a...

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.

Dropping separatedness in the definition of a toric variety, one obtains the more general notion of a toric prevariety. Toric prevarieties occur as ambient spaces in algebraic geometry and moreover they appear naturally as intermediate steps in quotient constructions. We first provide a complete description of the category of toric prevarieties in terms of convex–geometrical data, so–called sys...

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

In [Kat94b], Kato defined his notion of a log regular scheme and studied the local behavior of such schemes. A toric variety equipped with its canonical logarithmic structure is log regular. And, these schemes allow one to generalize toric geometry to a theory that does not require a base field. This paper will extend this theory by removing normality requirements.

BACKGROUND Visual outcome following repair of post-traumatic corneal perforation may not be optimal due to presence of irregular keratometric astigmatism. We performed a study to evaluate and compare rigid gas permeable contact lens and spectacles in visual rehabilitation following perforating corneal injuries. METHOD Eyes that had undergone repair for corneal perforating injuries with or wit...

We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for nonsingular toric Fano varieties. As applications we obtain new classification results, bounds of invariants and formulate conjectures concerning combinatoria...

Contact lens correction of astigmatism is reviewed. According to literature data, rigid gas permeable lenses are the lenses of choice in correction of irregular and high astigmatism. The crucial advantage of rigid gas permeable lenses is clear vision and stable correction of astigmatism. Soft toric lenses ensure quick adaptation and comfort. The most prominent disadvantage of soft toric contact...

We study confluent A-hypergeometric functions introduced by Adolphson [1]. In particular, we give their integral representations by using rapid decay homology cycles of Hien [17] and [18]. The method of toric compactifications introduced in [27] and [31] will be used to prove our main theorem. Moreover we apply it to obtain a formula for the asymptotic expansions at infinity of confluent A-hype...