We show that black holes grow substantially by accretion at close to Eddington rates. Using a complete sample of soft X-ray selected AGNs, Grupe & Mathur (2004) have shown that narrow line Seyfert 1 galaxies, as a class, lie below the MBH–σ relation of normal galaxies. Some NLS1s, however, lie on or close to the MBH–σ relation. Here we show that not all NLS1s accrete at close to Eddington rates...

Given a DFA M , can we find an equivalent DFA (i.e., one that recognizes the same language as M) with the minimum possible number of states? This is a very natural question, and has important applications to the efficiency of procedures that use finite automata. In this note, we will see an efficient algorithm that solves this problem. To begin, we need a couple of definitions. Let M be any DFA...

Let T be a counterexample to Vaught’s conjecture. Let ET denote the isomorphism equivalence relation of T . Let Fω1 be the countable admissible ordinal equivalence relation defined on ω2 by x Fω1 y if and only if ωx 1 = ω y 1 . This note will show that in L and set-generic extensions of L, ¬(ET ≤∆11 Fω1 ). Using ZFC, if T is a non-minimal counterexample to Vaught’s conjecture, then ¬(ET ≤∆11 Fω...

Let A be a set. One can verify that 〈A, idA〉 is discrete. The following proposition is true (1) For every set X such that ∇X ⊆ idX holds X is trivial. Let A be a relational structure. We say that A is diagonal if and only if: (Def. 1) The internal relation of A ⊆ idthe carrier of A. Let A be a non trivial set. Observe that 〈A,∇A〉 is non diagonal. We now state the proposition (2) For every refle...

INTRODUCTION ................................................................... 91 Summary of previous work with seedling chlorophyll-factors ........................... 92 White and virescent-white relation (Ww Vv) ..................................... 92 93 Trihybrid relations (UVvWw) ..................................................... 95 PI, FI, FZ and Fa data of cross UVvWW X LLVVWw. . ....

We introduce a notion of L-Betti numbers for locally compact, second countable, unimodular groups. We study the relation to the standard notion of L-Betti numbers of countable discrete groups for lattices. In this way, several new computations are obtained for countable groups, including lattices in algebraic groups over local elds, and Kac-Moody lattices. We also extend the vanishing of reduce...

The Fibonacci polynomials are defined by the recursion relation Fn+2{x) = xF„+l(x) + Fn(x), (1) with the initial values Fx(x) = 1 and F2(x) = x. When x = l, Fn(x) is equal to the /1 Fibonacci number, Fn. The Lucas polynomials, Ln(x) obey the same recursion relation, but have initial values Li(x) = x and L^x) = x +2. Explicit expressions for the zeros of the Fibonacci and Lucas polynomials have ...

The size-luminosity relation of early-type Brightest Cluster Galaxies (BCGs), Re ∝ L , is steeper than that for the bulk of the early-type galaxy population, for which Re ∝ L . This is true if quantities derived from either deVaucouleur or Sersic fits to the surface brightness profiles are used. Contamination from an intra-cluster light component centered on the BCG, with similar parameters to ...