purpose: to evaluate changes in anterior chamber (ac) parameters before and one month after nd:yag capsulotomy. methods: a total of 30 eyes from 27 patients with posterior capsule opacification graded 2-4 with surgical history of uneventful phacoemulsification and acrylic foldable iol implantation were included in this study. before capsulotomy and one month later, anterior chamber depth, volum...

background: separate radon and thoron measurements in soil are very important in assessment of internal exposure due to inhalation of such radioactive gases. materials and methods: in this study, a low cost, small size, passive diffusion chamber has been developed for simple measurement of radon-222 and radon-220(thoron) gases separately in soil. the diffusion chamber consists of two films and ...

We answer a question raised by M. Chuaqui, P. Duren, and B. Osgood by showing that a conformal mapping of a simply connected domain cannot take two circles onto two proper ellipses. The goal of this note is to prove the following. Proposition 1. Let Ω be a simply connected domain on C = C ∪ {∞} containing circles (on C) C1 and C2, C1 = C2. Let f be a conformal mapping from Ω into C. If f maps e...

‎Based on a definition for circle in Finsler space‎, ‎recently proposed by one of the present authors and Z‎. ‎Shen‎, ‎a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

Figure 1: An Apollonian Circle Packing Apollonius’s Theorem states that given three mutually tangent circles, there are exactly two circles which are tangent to all three. Apollonian circle packings are produced by repeating the construction of mutually tangent circles to fill all remaining spaces. A remarkable consequence of Descartes’ Theorem is if the initial four tangent circles have integr...

Presented in this paper is a sweepline algorithm to compute the Voronoi diagram of a set of circles in a two-dimensional Euclidean space. The radii of the circles are non-negative and not necessarily equal. It is allowed that circles intersect each other, and a circle contains others. The proposed algorithm constructs the correct Voronoi diagram as a sweepline moves on the plane from top to bot...

In two dimensions, start with three mutually tangent circles, with disjoint interiors (a circle with negative radius has the point at infinity in its interior). We can draw two new circles that touch these three, and then six more in the gaps that are formed, and so on. This procedure generates an (infinite) Apollonian packing of circles. We show that the sum of the bends (curvatures) of the ci...