Many software engineers try very hard not to use the word “reuse” because many methods and tools intended to promote reuse have failed to meet expectations. As soon as they learn that a software product line involves reuse they turn away quickly. The “attached process” that accompanies every core asset in a product line makes software reuse effective instead of frustrating. In this issue of Str...

Let 2S4 denote the double cover of S4 corresponding to the element in H(S4,Z/2Z) where transpositions lift to elements of order 2 and the product of two disjoint transpositions to elements of order 4. Given an elliptic curve E, let E[2] denote its 2-torsion points. Under some conditions on E elements in H(GalQ, E[2])\{0} correspond to Galois extensions N of Q with Galois group (isomorphic to) S...

This paper will prove that essentially only the obvious recurrences have almost all primes as divisors. An integer n is a divisor of a recurrence if n divides some term of the recurrence. In this paper, "almost all primes" will be taken interchangeably to mean either all but finitely many primes or all but for a set of Dirichlet density zero in the set of primes. In the context of this paper, t...

Abstract: We present three remarks on Goldbach’s problem. First we suggest a refinement of Hardy and Littlewood’s conjecture for the number of representations of 2n as the sum of two primes positing an estimate with a very small error term. Next we show that if a strong form of Goldbach’s conjecture is true then every even integer is the sum of two primes from a rather sparse set of primes. Fin...

Abstract Let denote the maximal number of different primes that may occur in order a finite solvable group G , all elements which have orders divisible by at most n distinct primes. We show for . As an application, we improve on recent bound Hung and Yang arbitrary groups.

It was proven by Emma Lehmer that for almost all odd primes p, F2p is a Fibonacci pseudoprime. In this paper, we generalize this result to Lucas sequences {Uk}. In particular, we find Lucas sequences {Uk} for which either U2p is a Lucas pseudoprime for almost all odd primes p or Up is a Lucas pseudoprime for almost all odd primes p.

Models of written word recognition in languages using the Roman alphabet assume that a word's visual form is quickly mapped onto abstract units. This proposal is consistent with the finding that masked priming effects are of similar magnitude from lowercase, uppercase, and alternating-case primes (e.g., beard-BEARD, BEARD-BEARD, and BeArD-BEARD). We examined whether this claim can be readily ge...

We examined the effect of linguistic comprehension on early perceptual encoding in a series of electrophysiological and behavioral studies on humans. Using the fact that pictures of faces elicit a robust and reliable evoked response that peaks at ∼170 ms after stimulus onset (N170), we measured the N170 to faces that were preceded by primes that referred to either faces or scenes. When the prim...

Listeners often categorize phonotactically illegal sequences (e.g., /dla/ in English) as phonemically similar legal ones (e.g., /gla/). In an earlier investigation of such an effect in Japanese, Dehaene-Lambertz, Dupoux, and Gout (2000) did not observe a mismatch negativity in response to deviant, illegal sequences, and therefore argued that phonotactics constrain early perceptual processing. I...

This is a survey article on primality testing and general methods for recognizing primes. We also look at methods for generating random primes since this is valuable in cryptographic methods such as the RSA cipher. Mathematics Subject Classification: Primary: 11A41; Secondary: 11A51