A longstanding open problem is whether there exists a non-syntactical model of the untyped λ-calculus whose theory is exactly the least λ-theory λβ . In this paper we investigate the more general question of whether the equational/order theory of a model of the untyped λ-calculus can be recursively enumerable (r.e. for brevity). We introduce a notion of effective model of λ-calculus, which cove...

A longstanding open problem is whether there exists a non-syntactical model of the untyped λ-calculus whose theory is exactly the least λ-theory λβ . In this paper we investigate the more general question of whether the equational/order theory of a model of the untyped λ-calculus can be recursively enumerable (r.e. for brevity). We introduce a notion of effective model of λ-calculus, which cove...

Background: Bacterial sepsis is highly prevalent among premature infants. Amikacin is an antibiotic widely recommended for the treatment of neonatal sepsis, one of the consequences of which might be nephrotoxicity. The present study aimed to compare the efficacy and nephrotoxicity of multiple daily dosing (MDD) and once-daily dosing (ODD) of amikacin in preterm infants suspected of sepsis. Met...

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...

An irreducibly odd graph is a graph such that each vertex has odd degree and for every pair of vertices, a third vertex in the graph is adjacent to exactly one of the pair. This family of graphs was introduced recently by Manturov [1] in relation to free knots. In this paper, we show that every graph is the induced subgraph of an irreducibly odd graph. Furthermore, we prove that irreducibly odd...

The complement of a graph G is denoted by G. χ(G) denotes the chromatic number and ω(G) the clique number of G. The cycles of odd length at least five are called odd holes and the complements of odd holes are called odd anti-holes. A graph G is called perfect if, for each induced subgraph G of G, χ(G) = ω(G). Classical examples of perfect graphs consist of bipartite graphs, chordal graphs and c...

We bound the mean distance in a connected graph which is not a tree in function of its order n and its girth g. On one hand, we show that mean distance is at most n+1 3 − g(g−4) 12n(n−1) if g is even and at most n+1 3 − g(g−1) 12n(n−1) if g is odd. On the other hand, we prove that mean distance is at least ng 4(n−1) unless G is an odd cycle.