In order to examine the relationship between the black hole mass MBH and stellar velocity dispersion σ∗ in radio-loud active galactic nuclei (AGNs), we study two effects which may cause the uncertainty of black hole mass estimates for radio-loud AGNs: the relativistic beaming effect on the observed optical continuum radiation and the orientation effect on broad emission line width. After correc...

We prove in an elementary fashion that the image of a commutative monotone σ-complete C-algebra under a σ-normal morphism is again monotone σ-complete and give an application of this result in spectral theory.

Let σ={σi:i∈I} be a partition of the set all prime numbers. A subgroup H finite group G is said to σ-subnormal in if can joined by chain subgroups H=H0⊆H1⊆⋯⊆Hn=G where, for every j=1,⋯,n, Hj−1 normal Hj or Hj/CoreHj(Hj−1) σi-group some i∈I. B soluble normalising Nσ-residual non-σ-subnormal G, where Nσ saturated formation σ-nilpotent groups. We show that normalises does not have section σ-residu...

Let X1,…,Xn be i.i.d. random variables sampled from a normal distribution N(μ,Σ) in Rd with unknown parameter θ=(μ,Σ)∈Θ:=Rd×C+d, where C+d is the cone of positively definite covariance operators Rd. Given smooth functional f:Θ↦R1, goal to estimate f(θ) based on X1,…,Xn. Θ(a;d):=Rd×{Σ∈C+d:σ(Σ)⊂[1/a,a]},a≥1, σ(Σ) spectrum Σ. θˆ:=(μˆ,Σˆ), μˆ sample mean and Σˆ covariance, observations For an arbit...