Bacteriophage T7 encodes an essential inhibitor of the Escherichia coli host RNA polymerase (RNAP), the product of gene 2 (Gp2). We determined a series of X-ray crystal structures of E. coli RNAP holoenzyme with or without Gp2. The results define the structure and location of the RNAP σ(70) subunit domain 1.1(σ(1.1)(70)) inside the RNAP active site channel, where it must be displaced by the DNA...

Let KG be the group ring of a group G over a commutative ring K with unity. The rings KG are described for which xxσ = xσx for all x = ∑ g∈G αgg ∈ KG, where x → xσ = ∑ g∈G αgf(g)σ(g) is an involution of KG; here f : G → U(K) is a homomorphism and σ is an antiautomorphism of order two of G. Let R be a ring with unity. We denote by U(R) the group of units of R. A (bijective) map : R → R is called...

C Maximum likelihood estimation C.1 Building the likelihoood function Let Θ = (Θ1; Θ2) = (σ , σ η, σ u, π; β1, λ1, β2, λ2, φ) be the vector of parameters. Let X = (x1,s,t, x2,s,t, r1,s,t, r2,s,t) be the vector of observables, with r2 = p2− p1 and r1 = p1. Let 1(x) be an indicator variable equal to 1 if the event x has occured, and 0 otherwise. Let g(x) be the standard normal PDF and G(x) the st...

We study normal criterion of meromorphic functions shared values, we obtain the following. Let F be a family of meromorphic functions in a domain D, such that function f ∈ F has zeros of multiplicity at least 2, there exists nonzero complex numbers bf , cf depending on f satisfying i bf/cf is a constant; ii min{σ 0, bf , σ 0, cf , σ bf , cf ≥ m} for some m > 0; iii 1/ck−1 f f ′ k z f z / b f/c ...

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...

We examine a Markov tree (MT) model for option pricing in which the dynamics of the underlying asset are modeled by a non-IID process. We show that the discrete probability mass function of log returns generated by the tree is closely approximated by a continuous mixture of two normal distributions. Using this normal mixture distribution and risk-neutral pricing, we derive a closed-form express...