We study superstable groups acting on trees. We prove that an action of an ω-stable group on a simplicial tree is trivial. This shows that an HNN-extension or a nontrivial free product with amalgamation is not ωstable. It is also shown that if G is a superstable group acting nontrivially on a Λ-tree, where Λ = Z or Λ = R, and if G is either α-connected and Λ = Z, or if the action is irreducible...

Ramsey’s theorem says that for every clique H1 and for every graph H2 with no edges, all graphs containing neither of H1,H2 as induced subgraphs have bounded order. What if, instead, we exclude a graph H1 with a vertex whose deletion gives a clique, and the complement H2 of another such graph? This no longer implies bounded order, but it implies tightly restricted structure that we describe. Th...

The effects of both an H1 receptor antagonist and an H2 receptor antagonist on changes in monovalent ion flux induced by topical sodium taurocholate were studied in antrectomised dogs fashioned with a denervated fundic pouch. The magnitude of taurocholate-induced ion flux was unaffected by topical administration of H1 or H2 receptor antagonists Parenteral administration of H1 or H2 receptor ant...

We consider the existence of at least one positive solution of the problem –D0+u(t) = f (t,u(t)), 0 < t < 1, under the circumstances that u(0) = 0, u(1) = H1(φ(u)) + ∫ E H2(s,u(s))ds, where 1 < α < 2, D α 0+ is the Riemann-Liouville fractional derivative, and u(1) = H1(φ(u)) + ∫ E H2(s,u(s))ds represents a nonlinear nonlocal boundary condition. By imposing some relatively mild structural condit...

The star-critical Ramsey number r∗(H1,H2) is the smallest integer k such that every red/blue coloring of the edges of Kn −K1,n−k−1 contains either a red copy of H1 or a blue copy of H2, where n is the graph Ramsey number R(H1,H2). We study the cases of r∗(C4, Cn) and R(C4,Wn). In particular, we prove that r∗(C4, Cn) = 5 for all n > 4, obtain a general characterization of Ramsey-critical (C4,Wn)...

In particular, the distance from a point x ∈ R to a hyperplane H where x / ∈ H , is given by the length of the perpendicular line segment from x to H . If two hyperplanes H1, H2 are parallel, their normal vectors are multiples of each other, so we can take a single normal vector u and write H1 = {x : (x, u) = α1} and H2 = {x : (x, u) = α2}. Take any x ∈ H1 . Then d(x,H2) is given by the perpend...

If a graph has no induced subgraph isomorphic to H1 or H2 then it is said to be (H1, H2)-free. Dabrowski and Paulusma found 13 open cases for the question whether the clique-width of (H1, H2)-free graphs is bounded. One of them is the class of (S1,2,2,triangle)-free graphs. In this paper we show that these graphs have bounded clique-width. Thus, also (P1+2P2,triangle)-free graphs have bounded c...

We present in this paper a self-reproducing comparator P system that simulates insertion sort. The comparator Πc is a degree–2 membrane and structured as μ = [h0 [h1 ]h1 [h2 ]h2 ]h0 . A maximizing Πc compares two multisets a and b where min(|a|, |b|) is stored in compartment h1 while max(|a|, |b|) is stored in compartment h2. A conditional reproduction rule triggers Πc to clone itself out via c...

Several lines of evidence suggest that brain histamine may be involved in the central control of food intake. The effect of histamine on feeding is mediated through three kinds of receptors (H1, H2, and H3). The present study was designed to investigate the effect of intracerebroventricular injection of histamine, promethazine (H1 antagonist) and ranitidine (H2 antagonist) on food intake of fre...