Alkenyl N-pivaloylhydroxamates undergo an Ir(III)-catalyzed diamination of the alkene with simple exogenous secondary amines under extraordinarily mild reaction conditions. The regioselectivity of ...the diamination is controlled by the solvent and the electronics of the cyclopentadienyl (Cpx) ligand on Ir. On the basis of a set of mechanistic experiments, we propose that the relative rates of Ir(V)-nitrenoid formation versus attack on the amido-Ir-coordinated alkene by the exogenous amine determine the outcome of the reaction.
A relatively simple and general method for calculating the mutual inductance and self-inductance of both coaxial and noncoaxial cylindrical coils is given. For combinations of cylindrical coils, thin ...solenoids, pancake coils, and simple circular loops, the mutual inductance can be reduced to a one-dimensional integral of closed form expressions involving Bessel and related functions. Coaxial and noncoaxial cases differ only by the presence of an extra Bessel factor J 0 (sp) in the noncoaxial integral, where p is the perpendicular distance separating the coil axes and s is the variable of integration. The method is related to a recently given noncoaxial generalization of Ruby's formula for a nuclear radiation source and detector system, the analogy being close but not exact. In many cases, the Bessel function integral for the inductance can be easily evaluated directly using Maple or Mathematica. In other cases, it is better to transform the integral to a more numerically friendly form. A general analytical solution is presented for the inductance of two circular loops which lie in the same plane
An intramolecular Ir(III)-catalyzed regiodivergent oxyamination of unactivated alkenes provides valuable γ-lactams, γ-lactones and δ-lactams. The regioselectivity is controlled by the electronically ...tunable cyclopentadienyl Ir(III)-complexes enabling oxyamination via either 5-exo or 6-endo pathways. With respect to the mechanism, we propose a highly reactive 3.1.0 bicycle intermediate derived from Ir(V) nitrene-mediated aziridination to be a key intermediate toward the synthesis of γ-lactams.
ABSTRACT
The population of intermediate-mass black holes (IMBHs) in nearby dwarf galaxies plays an important ‘ground truth’ role in exploring black hole formation and growth in the early Universe. In ...the dwarf elliptical galaxy SDSS J090613.77+561015.2 (z = 0.0465), an accreting IMBH has been revealed by optical and X-ray observations. Aiming to search for possible radio core and jet associated with the IMBH, we carried out very long baseline interferometry (VLBI) observations with the European VLBI Network at 1.66 GHz. Our imaging results show that there are two 1-mJy components with a separation of about 52 mas (projected distance 47 pc) and the more compact component is located within the 1σ error circle of the optical centroid from available Gaia astrometry. Based on their positions, elongated structures and relatively high brightness temperatures, as well as the absence of star-forming activity in the host galaxy, we argue that the radio morphology originates from the jet activity powered by the central IMBH. The existence of the large-scale jet implies that violent jet activity might occur in the early epochs of black hole growth and thus help to regulate the co-evolution of black holes and galaxies.
ABSTRACT
Dwarf galaxies are characterized by a very low luminosity and low mass. Because of significant accretion and ejection activity of massive black holes, some dwarf galaxies also host ...low-luminosity active galactic nuclei (AGNs). In a few dwarf AGNs, very long baseline interferometry (VLBI) observations have found faint non-thermal radio emission. SDSS J090613.77+561015.2 is a dwarf AGN owning an intermediate-mass black hole (IMBH) with a mass of $M_\mathrm{BH} = 3.6^{+5.9}_{-2.3}\times 10^5 \mathrm{ M}_{\odot }$ and showing a rarely seen two-component radio structure in its radio nucleus. To further probe their nature, i.e. the IMBH jet activity, we performed additional deep observations with the European VLBI Network (EVN) at 1.66 and 4.99 GHz. We find the more diffuse emission regions and structure details. These new EVN imaging results allow us to reveal a two-sided jet morphology with a size up to about 150 mas (projected length ∼140 pc) and a radio luminosity of about 3 × 1038 erg s−1. The peak feature has an optically thin radio spectrum and thus more likely represents a relatively young ejecta instead of a jet base. The EVN study on SDSS J090613.77+561015.2 demonstrates the existence of episodic, relatively large-scale, and powerful IMBH jet activity in dwarf AGNs. Moreover, we collected a small sample of VLBI-detected dwarf AGNs and investigated their connections with normal AGNs. We notice that these radio sources in the dwarf AGNs tend to have steep spectra and small linear sizes, and possibly represent ejecta from scaled-down episodic jet activity.
A method related to Wronskians has recently been applied to derive many indefinie integrals involving Bessel functions and associated Legendre functions. Here the same method is applied to derive ...indefinite integrals of Whittaker functions and Gauss hypergeometric functions. All the integrals presented here appear to be new and are derived either directly from Wronskians or from a differential equation related to Wronskians. All the results presented have been checked numerically using Mathematica.
We present a formalism for continuum and line emission from random clumpy media together with its application to problems of current interest, including CO spectral lines from ensembles of clouds and ...radio emission from H ii regions, supernovae, and star-forming regions. For line emission, we find that the effects of clump opacity on observed line ratios can be indistinguishable from variations of intrinsic line strengths, adding to the difficulties in determining abundances from line observations. Our formalism is applicable to arbitrary distributions of cloud properties, provided the cloud volume filling factor is small; numerical simulations show it to hold up to filling factors of ∼10%. We show that irrespective of the complexity of the cloud ensemble, the radiative effect of clumpiness can be parameterized at each frequency by a single multiplicative correction to the overall optical depth; this multiplier is derived from appropriate averaging over individual cloud properties. Our main finding is that cloud shapes have only a negligible effect on radiation propagation in clumpy media; the results of calculations employing point-like clouds are practically indistinguishable from those for finite-sized clouds with arbitrary geometrical shapes.
Many indefinite integrals are derived for Bessel functions and associated Legendre functions from particular transformations of their differential equations which are closely linked to Wronskians. A ...large portion of the results for Bessel functions is known, but all the results for associated Legendre functions appear to be new. The method can be applied to many other special functions. All results have been checked by differentiation using Mathematica.
The exponential integral function Ei(x) is given as an indefinite integral of an elementary expression. This allows a second-order linear differential equation for the function to be constructed, ...which is of conventional form. A limitless number of differential equations can be derived from the original by elementary transformations, and many integrals are given by applying the method of fragments to some of these transformed equations. Results are presented here both for simple transformations and other transformations obtained by solving simple Riccati equations. Some of the Integrals are presented combine Ei(x) with Bessel functions, modified Bessel functions and Whittaker functions. All results have been checked by differentiation using Mathematica.
A method was presented recently for deriving integrals of special functions using two kinds of integrating factor for the homogeneous second-order linear differential equations which many special ...functions obey. The classical orthogonal polynomials are well suited for this method, and results are given here for Jacobi polynomials. Results have been previously presented for Gegenbauer, Hermite and Laguerre polynomials. All the integrals presented here appear to be new and have been checked using Mathematica.
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