We discuss some problems in number theory posed by-Duro Kurepa, including the so-called left factorial hypothesis that an odd prime p does not divide 0! + 1! + · · · + (p − 1)!. 1. Introduction-D. Kurepa posed several problems in number theory that drew attention of many workers in number theory. Certainly, the most known of his problems is the so called left factorial hypothesis, which is stil...

We present two benchmark suites for CORBA brokers, targeted at the broker vendor and user audiences respectively. The vendor suite is a result of several benchmarking projects with industrial partners, and covers the entire functionality of a CORBA broker. The user suite is simplified to give an overview of the basic factors influencing broker performance, and is complemented with an approach f...

A b s t r a c t . The fastest known algorithms in classical algebra make use of signature functions. That is, reducing computat ion with formulae to computing with the integers modulo p, by substi tut ing random numbers for variables, and mapping constants modulo p. This idea is exploited in specific algorithms in computer algebra systems, e.g. algorithms for polynomial greatest common divisors...

Given n polynomials in n variables of respective degrees d1, . . . , dn, and a set of monomials of cardinality d1 . . . dn, we give an explicit subresultant-based polynomial expression in the coefficients of the input polynomials whose non-vanishing is a necessary and sufficient condition for this set of monomials to be a basis of the ring of polynomials in n variables modulo the ideal generate...

The squarefree decomposition of a univariate polynomial, P (y) ∈ K[y], K being a characteristic zero field, is one of the most basic problems in computer algebra (after the greatest common divisor computation, probably the most basic one). The parametric case has not usually been considered in the literature and this paper is dedicated to showing how the case of a single parameter can easily be...

A conflict-avoiding code (CAC) C of length n with weight k is a family of binary sequences of length n and weight k satisfying ∑ 0≤t≤n−1 xitxj,t+s ≤ 1 for any distinct codewords xi = (xi0, xi1, . . . , xi,n−1) and xj = (xj0, xj1, . . . , xj,n−1) in C and for any integer s, where the subscripts are taken modulo n. A CAC with maximal code size for given n and k is said to be optimal. A CAC has be...

We test whether immigrants are more prone to support terror than natives because of lower opportunity costs, using the international World Values Survey data. We show that, in general, economically, politically and socially non-integrated persons are more likely to accept using violence for achieving political goals, consistent with the economic model of crime. We also find evidence for the des...

Let S be a set. For an arithmetical map ψ : Z → S, if for some n ∈ Z = {1, 2, 3, · · · } we have ψ(x+ n) = ψ(x) for all x ∈ Z, then we say that ψ is periodic modulo n and n is a period of ψ. Let P(S) denote the set of all periodic maps ψ : Z → S. If m,n ∈ Z are periods of a map ψ ∈ P(S), then the greatest common divisor (m,n) is also a period of ψ, for we can write (m,n) in the form am + bn wit...