The complete symmetry groups of systems of linear second order ordinary differential equations are considered in the context of the simple harmonic oscillator. One finds that in general the representation of the complete symmetry group is not unique and in the particular case of a four-dimensional system there are two distinct complete symmetry groups. The results for general second order linea...

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situation where the data variance is already partially explained by other factors, for example sparse c...

OBJECTIVE To quantitatively document changes in corneal refractive parameters in relation to the progression of keratoconus over years. DESIGN Retrospective observational case series. PARTICIPANTS Eighty-five eyes of 64 patients with keratoconus who had undergone videokeratography examinations at least twice with an interval of 1 year or longer between each examination. METHODS By means o...

purpose : to compare the visual and refractive outcomes of laser in situ keratomileusis (lasik) versus laser assisted subepithelial keratectomy (lasek) in the treatment of low to moderate myopia and astigmatism methods : a retrospective comparative case series study comprised 2,474 eyes of patients with manifest refraction spherical component lower than -5.00 diopters (d) and cylinder component...

purpose: to report the results of photorefractive keratectomy (prk) with mitomycin-c (mmc) to correct myopia and astigmatism in patients who had previously undergone penetrating keratoplasty (pkp). methods: thirty-eight eyes of 32 patients underwent prk with mmc to correct astigmatism and myopia following pkp. result: mean spherical equivalent (se) was -5.2±4.7 d (diopter) and mean astigmatism ...

A mathematical model for the simulation of spherical bubble dynamics in binary alkane mixtures is presented. Detailed heat and mass transfer phase transition are resolved, air absorption desorption considered. As example mixtures, high-volatile heptane low-volatile dodecane investigated. The component shows a convective counter-intuitive transport opposite to diffusion flux. staggered flux asso...