X.S. Lin’s original definition of twisted Alexander knot polynomial is generalized for arbitrary finitely presented groups. J. Cha’s fibering obstruction theorem is generalized. The group of a nontrivial virtual knot shown by L. Kauffman to have trivial Jones polynomial is seen also to have a faithful representation that yields a trivial twisted Alexander polynomial.

Case-control studies are used to determine if there is an association between an exposure and a specific health outcome. These studies proceed from effect (e.g. health outcome, condition, disease) to cause (exposure). Case-control studies assess whether exposure is disproportionately distributed between the cases and controls, which may indicate that the exposure is a risk factor for the health...

We regret to report the death of Mr. C. A. Morton, which took place on August 16th during a holiday in Switzerland. Charles Alexander Morton, known to many generations of students as " Peter," was born in Bristol in 1860, where his father, a surgeon in the H.E.I.C.S., lived after his retirement. He was educated at Clifton, and subsequently at St. Bartholomew's. Mr. Stanford Morton, of ophthalmo...

Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t]-submodules Im(1 − t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Zn[t ]/(t − a) where gcd(n, a) = 1 (called linear quandles) are isomorphic, as well as specific conditions on when two linear quandles are dual and which linear quandles are connected. ...

Alexander duality has, in the past, made its way into commutative algebra through Stanley-Reisner rings of simplicial complexes. This has the disadvantage that one is limited to squarefree monomial ideals. The notion of Alexander duality is generalized here to arbitrary monomial ideals. It is shown how this duality is naturally expressed by Bass numbers, in their relations to the Betti numbers ...

Male crickets (Orthoptera: Gryllidae) compete for females through direct physical aggression (ALEXANDER, 1961; BURK, 1983; BOAKE, 1984; DIXON & CADE, 1986) and acoustic signalling behaviour (ALEXANDER, 1975; CADE, 1979a). Females respond phonotactically to the calling songs of conspecific males by walking or flying to them (WALKER, 1957; ZARETSKY, 1972; ULAGARAJ & WALKER, 1973; PAUL, 1976; POPO...