In this paper, we construct a neat description of the passage from crossed squares of commutative algebras to 2-crossed modules analogous to that given by Conduché in the group case. We also give an analogue, for commutative algebra, of T.Porter’s [13] simplicial groups to n-cubes of groups which implies an inverse functor to Conduché’s one.

This paper is prompted by work of Grandjee an and Ladra on homol-ogy crossed modules. We deene the homology of a crossed module in dimensions one and two via the equivalence of categories with group objects in groupoids. We show that for any perfect crossed module, its second homology crossed module occurs as the kernel of its universal central extension as deened by Norrie. Our rst homology is...

Lateral medullary infarction (LMI) or Wallenberg syndrome is a type of brain stem stroke, more specifically, a type of crossed brain stem syndrome. LMI is a well-described entity with several documented typical characteristics including pain and temperature impairment in the ipsilateral to the lesion side of the face and the contralateral side of the trunk and limbs. We present a case of LMI wh...

A smooth curve is a map γ from a compact interval I of the real line to the plane, which is C∞ and such that ||γ ′(t)|| > 0 for any t ∈ I (this last property is called regularity). Any such curve can (and will be considered to) be arc-length reparametrised (i.e. ∀t ∈ I, ||γ ′(t)||= 1). We can approximate such a curve by drawing a square grid of mesh h on the plane, and look at the sequence of s...

The feasibility of using railroad flatcars (RRFCs) as the superstructure for bridges on lowvolume roads has been investigated in two previous research projects at Iowa State University. The results of these projects verified that RRFCs are efficient and economical alternatives for low-volume road bridges. Two county engineers involved with the RRFC project cited cost as the main factor for choo...