We propose a matrix approach to the computation of BattleLemarié's wavelets. The Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a B-spline of order m . The polynomial is the symbol of a bi-infinite matrix B associated with a B-spline of order 2m . We approximate this bi-infinite ma...

We present a constructive existence proof that every real skew-Hamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasi-Jordan canonical form via symplectic similarity. We show further that every W has infinitely many real Hamiltonian square roots, and give a lower bound on the dimension of the set of all suc...

BACKGROUND AND AIMS Polishing may increase the surface roughness of composites, with a possible effect on bacterial growth and material properties. This preliminary in vitro study evaluates the effect of three different polishing systems (PoGo polishers, Enhance, Venus Supra) on six direct resin composites (Gradia Direct, Venus, Venus Diamond, Enamel Plus HFO, Tetric Evoceram, Filtek Supreme XT...

Given an n × n symmetric positive definite matrix A and a vector ~c, two numerical methods for approximating A1/2~c are developed, analyzed, and computationally tested. The first method applies a Newton iteration to a specific nonlinear system to approximate A1/2~c while the second method applies a step-control method to numerically solve a specific initial-value problem to approximate A1/2~c. ...

Friction and wear tests were performed on AISI 1045 steel specimens with different initial roughness parameters, machined by a creep-feed dry grinding process, to study the friction and wear behavior on a pin-on-disc tester in dry sliding conditions. Average surface roughness (Ra), root mean square (Rq), skewness (Rsk) and kurtosis (Rku) were involved in order to analyse the influence of the fr...

The aim of this study was to characterize prolonged standing and its effect on postural control in elderly individuals in comparison to adults. It is unknown how elderly individuals behave during prolonged standing and how demanding such a task is for them. We recorded the center of pressure (COP) position of 14 elderly subjects and 14 adults while they performed prolonged standing (30 min) and...

In a fuzzy classifier with ellipsoidal regions, each cluster is approximated by a center and a covariance matrix, and the membership function is calculated using the inverse of the covariance matrix. Thus when the number of training data is small, the covariance matrix becomes singular and the generalization ability is degraded. In this paper, during the symmetric Cholesky factorization of the ...

We say that a C∗-algebra A is approximately square root closed, if any normal element in A can be approximated by a square of a normal element in A. We study when A is approximately square root closed, and have an affirmative answer for AI-algebras, Goodearl type algebras over the torus, purely infinite simple unital C∗-algebras etc.

A new method for the high-speed computation of double-precision floating-point reciprocal, division, square root, and inverse square root operations is presented in this paper. This method employs a second-degree minimax polynomial approximation to obtain an accurate initial estimate of the reciprocal and the inverse square root values, and then performs a modified Goldschmidt iteration. The hi...