More than being just a tool for expressing algorithms, a welldesigned programming language allows the user to express her ideas efficiently. The design choices however effect the efficiency of the algorithms written in the languages. It is therefore important to understand how such choices effect the expressibility of programming languages. The paper pursues the very low complexity programs by ...

Information about the spectral reflectance of a color surface is useful in many applications. Assuming that reflectance functions can be adequately approximated by a linear combination of a small number of basis functions and exploiting genetic algorithms, we address here the problem of synthesizing a spectral reflectance function, given the standard CIE 1931 tristimulus values. Different sets ...

In many iterative schemes, the precision of each step depends on the computational effort spent on that step. A method of specifying a suitable amount of computation at each step is described. The approach is adaptive and aimed at minimizing the overall computational cost subject to attaining a final iterate that satisfies a suitable error criterion. General and particular cost functions are co...

Despite the failure of naive analogs of the sum shuffle or the integral shuffle relations, we prove the existence of ‘shuffle’ relations for the multizeta values (for a general A, with a rational place at infinity) introduced [T04] by the author in the function field context. This makes the Fp-span of the multizeta values into an algebra. We effectively determine and prove all the Fp-coefficien...

The turnpike problem is one of the few “natural” problems that are neither known to be NP-complete nor solvable by efficient algorithms. We seek to study this problem in a more general setting. We consider the generalized problem which tries to resolve set A = {a1, a2, · · · , an} from pairwise function values {f(ai, aj)|1 ≤ i, j ≤ n} for a given bivariate function f . We call this problem the ...

Given a ∈ Z \ {±1, 0}, we consider the problem of enumerating the integers m coprime to a such that the order of a modulo m is square free. This question is raised in analogy to a result recently proved jointly with F. Saidak and I. Shparlinski where square free values of the Carmichael function are studied. The technique is the one of Hooley that uses the Chebotarev Density Theorem to enumerat...

1. Introduction. The irrationality of values of the zeta-function ζ(s) at odd integers s ≥ 3 is one of the most attractive problems in number theory. Inspite of a deceptive simplicity and more than two-hundred-year history of the problem, all done in this direction can easily be counted. It was only 1978, when Apéry [A] obtained the irrationality of ζ(3) by a presentation of " nice " rational a...

We obtain an asymptotic formula for the number of square-free values among p 1; for primes ppx; and we apply it to derive the following asymptotic formula for LðxÞ; the number of square-free values of the Carmichael function lðnÞ for 1pnpx; LðxÞ 1⁄4 ðkþ oð1ÞÞ x ln a x ; where a 1⁄4 0:37395y is the Artin constant, and k 1⁄4 0:80328y is another absolute constant. r 2003 Elsevier Inc. All rights r...

Let K be a number field, and let f ∈ K(x) be a nonconstant rational function. We study the sets { n ∑ i=1 f(xi) : xi ∈ K − {poles of f} }

Let ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler’s -function. Let q be a positive integer greater than 1 and γ denote Euler’s constant. We show that all the numbers ψ(a/q)+ γ, (a, q)= 1, 1 a q, are transcendental. We also prove that at most one of the numbers γ, ψ(a/q), (a, q)= 1, 1 a q, is algebraic. © 2007 Elsevier Inc. All rights reserved. MSC: primary 11J81...