PURPOSE To determine whether rotational stability is improved with the longer Staar toric intraocular lens (IOL). SETTING A private practice, Los Altos, California, USA. METHODS Staar Surgical manufactures toric plate-haptic IOLs under +24.0 diopters (D) in 2 lengths. Fifty consecutive eyes requiring toric IOL spherical powers less than +24.0 D received the longer toric IOL (TL; 11.2 mm) us...

Simultaneous tiling for several different translational sets has been studied rather extensively, particularly in connection with the Steinhaus problem. The study of orthonormal wavelets in recent years, particularly for arbitrary dilation matrices, has led to the study of multiplicative tilings by the powers of a matrix. In this paper we consider the following simultaneous tiling problem: Give...

We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degree polynomials. We prove a lower bound of Ω (√ d t ) for writing an explicit univariate degree-d polynomial f(x) as a sum of powers of degree-t polynomials.

Simultaneous tiling for several different translational sets has been studied rather extensively, particularly in connection with the Steinhaus problem. The study of orthonormal wavelets in recent years, particularly for arbitrary dilation matrices, has led to the study of multiplicative tilings by the powers a matrix. In this paper we consider the following simultaneous tiling problem: Given a...

We explore the connection between ideals of fat points (which correspond to subschemes of Pn obtained by intersecting (mixed) powers of ideals of points), and piecewise polynomial functions (splines) on a d-dimensional simplicial complex ∆ embedded in R. Using the inverse system approach introduced by Macaulay [11], we give a complete characterization of the free resolutions possible for ideals...

‎Let $R$ be a $*$-prime ring with center‎ ‎$Z(R)$‎, ‎$d$ a non-zero $(sigma,tau)$-derivation of $R$ with associated‎ ‎automorphisms $sigma$ and $tau$ of $R$‎, ‎such that $sigma$‎, ‎$tau$‎ ‎and $d$ commute with $'*'$‎. ‎Suppose that $U$ is an ideal of $R$ such that $U^*=U$‎, ‎and $C_{sigma,tau}={cin‎ ‎R~|~csigma(x)=tau(x)c~mbox{for~all}~xin R}.$ In the present paper‎, ‎it is shown that if charac...