purpose : to determine the association between astigmatism and spherical refractive error in a clinical population methods : in this cross-sectional study, 2,000 patients who presented to our optometry clinic were enrolled. all were tested for objective refraction with a nidek ar-310a auto refractometer, and non-cycloplegic refraction. for those under 15 years of age, cycloplegic refraction was...

The purpose of this paper is to establish Lp error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular, the Bernstein inequality estimates Lp Bessel-potential Sobolev norms of functions in this space in terms of the minimal separation and the Lp norm of the functi...

The influence of a dust grain mixture consisting of spherical dust grains with different radii and/or chemical composition on the resulting temperature structure and spectral energy distribution of a circumstellar shell is investigated. The comparison with the results based on an approximation of dust grain parameters representing the mean optical properties of the corresponding dust grain mixt...

In this paper, the cubic spherical optimization problems, including the cubic one-spherical/two-spherical/three-spherical optimization problems, are discussed. We first show that the two-spherical optimization problem is a special case of the three-spherical optimization problem. Then we show that the one-spherical optimization problem and the two-spherical optimization problem have the same op...

We study the behaviour of spherical Voids in Lagrangian perturbation theories L(n), of which the Zel’dovich approximation is the lowest order solution L(1). We find that at early times higher order L(n) give an increasingly accurate picture of Void expansion. However at late times particle trajectories in L(2) begin to turnaround and converge leading to the contraction of a Void, a sign of path...

1. Calculus on spheres 2. Spherical Laplacian from Euclidean 3. Eigenvectors for the spherical Laplacian 4. Invariant integrals on spheres 5. L spectral decompositions on spheres 6. Sup-norms of spherical harmonics on Sn−1 7. Pointwise convergence of Fourier-Laplace series 8. Irreducibility of representation spaces for O(n) 9. Hecke’s identity • Appendix: Bernstein’s proof of Weierstraß approxi...

The settling dynamics of spherical and elliptical particles in a viscous Newtonian fluid are investigated numerically using a finite difference technique. The terminal velocity for spherical particles is calculated for different system sizes and the extrapolated value for an infinite system size is compared to the Oseen approximation. Special attention is given to the settling and tumbling moti...

We investigate numerically a density functional theory (DFT) for strongly confined ionic solutions in the canonical ensemble by comparing predictions of ionic concentration profiles and pressure for the double-layer configuration to those obtained with Monte Carlo (MC) simulations and the simpler Poisson-Boltzmann (PB) approach. The DFT consists of a bulk (ion-ion) and an ion-solid part. The bu...