Necessary and sufficient conditions for an Ore extension S = R[x;σ, δ] to be a PI ring are given in the case σ is an injective endomorphism of a semiprime ring R satisfying the ACC on annihilators. Also, for an arbitrary endomorphism τ of R, a characterization of Ore extensions R[x; τ ] which are PI rings is given, provided the coefficient ring R is noetherian.

Phosphatidylinositol (PI) 3-kinase plays an important role in the signalling of cell growth. We previously purified two types of PI 3-kinase from bovine thymus, a monomer from (PI 3-kinase I) and a heterodimer form (PI 3-kinase II) [Shibasaki, Homma and Takenawa (1991) J. Biol. Chem. 266, 8108-8114]. Here we examine the properties of these purified PI 3-kinases. Both PI 3-kinases were inhibited...

in this paper, we present some inequalities for the co-pi index involving the some topological indices, the number of vertices and edges, and the maximum degree. after that, we give a result for trees. in addition, we give some inequalities for the largest eigenvalue of the co-pi matrix of g.

where ai(t) = Pi + εQi cos2t, where Pi,Qi and ε are given constants, and where it is assumed that when ε=0 this system exhibits a pair of linearly independent solutions of period 2π . Since the driver cos2t has period π , we have the ingredients for a 2:1 subharmonic resonance which typically results in a tongue of instability involving unbounded solutions when ε >0. We present conditions on th...

Phosphoinositide (PI) 3-kinase was first observed in 1984 as a minor inositol lipid kinase activity associated with immunoprecipitated oncogene products (e.g. Src, Abl and polyoma mT antigen) and present in activated growth factor receptor complexes (e.g. PDGF receptor). In 1988, the enzyme associated with this activity was found to have the novel ability to phosphorylate the 3 position hydroxy...