This paper presents a high-speed method for accurate function approximations. This method employs parallel table lookups followed by multi-operand addition. It takes advantage of leading zeros and symmetry in the table entries to reduce the table sizes. By increasing the number of tables and the number of operands in the multi-operand addition, the amount of memory is signiicantly reduced. This...

We present, for both minkowskian and euclidean signatures, short derivations of the diagonal Einstein metrics for Bianchi type II, III and V. For the first two cases we show the integrability of the geodesic flow while for the third case a somewhat unusual bifurcation phenomenon takes place: for minkowskian signature elliptic functions are essential in the metric while for euclidean signature o...

IP* sets and central sets are subsets of N which arise out of applications of topological dynamics to number theory and are known to have rich combinatorial structure. Spectra of numbers are often studied ([3], [15], [16], [30], [31], [32]) sets of the form {[nα+ γ] : n ∈ N}. Iterated spectra are similarly defined with n coming from another spectrum. Using elementary, dynamical, and algebraic a...

Abstract. We say that an integer n is k–free (k ≥ 2) if for every prime p the valuation vp(n) < k. If f : N → Z, we consider the enumerating function S f (x) defined as the number of positive integers n ≤ x such that f(n) is k–free. When f is the identity then S f (x) counts the k–free positive integers up to x. We review the history of S f (x) in the special cases when f is the identity, the c...

Abstract: Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the xt-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schrödinger equation. In the reflectionless case such solutions reduce to pure N -soliton solutions. An il...

A very simple test, introduced by Ziv, allows one to determine if an approximation to the value f(x) of an elementary function at a given point x suffices to return the floating-point number nearest f(x). The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the ...

The association between physical fitness and blood pressure was studied in 2061 children selected from all fourth graders in 44 elementary schools in the New York City area. Their blood pressure and physical fitness were measured on two consecutive examinations 1 year apart. Systolic and diastolic blood pressure were highest in children with poor physical fitness. The change in physical fitness...

Corrections to Newton’s gravitational law inspired by extra dimensional physics and by the exchange of light and massless elementary particles between the atoms of two macrobodies are considered. These corrections can be described by the potentials of Yukawa-type and by the power-type potentials with different powers. The strongest up to date constraints on the corrections to Newton’s gravitati...

In this paper the Christoffel numbers av n for ultraspherical weight functions wk , wx(x) = (\ -x ) ~ ' , are investigated. Using only elementary functions, we state new inequalities, monotonicity properties and asymptotic approximations, which improve several known results. In particular, denoting by dv „ the trigonometric representation of the Gaussian nodes, we obtain for À e [0, 1] the ineq...

This paper concerns the problem of the control of linear systems by means of feedback from delayed output, where the delay is known and time-varying. The main advantage of the approach is that it can be applied to systems with any delay bound, i.e. not only small delays. The predictor is based on a combination of finite-dimensional elementary predictors whose number can be suitably chosen to co...