In this paper we investigate the spectrum of super-simple 2-(v, 5, 1) directed designs (or simply super-simple 2-(v, 5, 1)DDs) and also the size of their smallest defining sets. We show that for all v ≡ 1, 5 (mod 10) except v = 5, 15 there exists a super-simple (v, 5, 1)DD. Also for these parameters, except possibly v = 11, 91, there exists a super-simple 2-(v, 5, 1)DD whose smallest defining s...

T he March 16, 2003, edition of The New York Times Magazine’s cover reads, “Half of What Doctors Know Is Wrong.” Inside, the lead story, entitled “The Biggest Mistake of Their Lives,” chronicles the struggles of four survivors of medical errors. The article also makes a projection that in 2003, as many as 98,000 people in the United States would die as a result of medical errors (Burton 2003). ...

Let G be a (p, q) graph and let f : V (G) → {1, 2, 3, · · · , p + q} be an injection. For each edge e = uv, let f∗(e) = (f(u)+f(v))/2 if f(u)+f(v) is even and f∗(e) = (f(u)+f(v)+1)/2 if f(u) + f(v) is odd. Then f is called a super mean labeling if f(V ) ∪ {f∗(e) : e ∈ E(G)} = {1, 2, 3, · · · , p+ q}. A graph that admits a super mean labeling is called a super mean graph. In this paper we presen...

I show that the classical Toda models built on superalgebras, and obtained from a reduction with respect to an Sl(2) algebra, are ”linearly supersymmetrizable” (by adding spin 1/2 fields) if and only if the Sl(2) is the bosonic part of an OSp(1|2) algebra. In that case, the model is equivalent to the one constructed from a reduction with respect to the OSp(1|2) algebra, up to spin 1/2 fields. T...

A systematic construction of super W-algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by Hamiltonian reduction. A classification, according to the conformal spin defined by an improved energymomentum tensor, is discussed in general terms for all super L...