The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers ... the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and s...

A family of proteins has been identified whose members, the Shanks, physically link two major receptor complexes at excitatory synapses - NMDA receptors and metabotropic glutamate receptors.

Anecdotal evidence suggests that the struggling behavior of shackled broiler chickens may be positively related to compression of the shank and the probable associated discomfort: birds with large shanks tend to struggle more violently than do those with smaller shanks. Males are generally heavier and have thicker shanks than females. Therefore, we tested the hypothesis that, because the leg ga...

In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X +nY , n ≥ 1. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n = 2. In this paper, we prove that in fact this constant is unbounded as one runs throu...