25,504 research outputs found
Palladium-catalyzed difluoromethylation of heteroaryl chlorides, bromides and iodides.
A palladium-catalyzed difluoromethylation of a series of heteroaryl chlorides, bromides and iodides under mild conditions is described. A wide range of heteroaryl halides such as pyridyl, pyrimidyl, pyrazyl, funanyl, thienyl, pyazolyl, imidazolyl, thiazolyl, and oxazolyl halides were efficiently difluoromethylated, thus providing medicinal chemists an alternative choice for the preparation of drug candidates with the difluoromethylated heteroarene unit
A semi-proximal-based strictly contractive Peaceman-Rachford splitting method
The Peaceman-Rachford splitting method is very efficient for minimizing sum
of two functions each depends on its variable, and the constraint is a linear
equality. However, its convergence was not guaranteed without extra
requirements. Very recently, He et al. (SIAM J. Optim. 24: 1011 - 1040, 2014)
proved the convergence of a strictly contractive Peaceman-Rachford splitting
method by employing a suitable underdetermined relaxation factor. In this
paper, we further extend the so-called strictly contractive Peaceman-Rachford
splitting method by using two different relaxation factors, and to make the
method more flexible, we introduce semi-proximal terms to the subproblems. We
characterize the relation of these two factors, and show that one factor is
always underdetermined while the other one is allowed to be larger than 1. Such
a flexible conditions makes it possible to cover the Glowinski's ADMM whith
larger stepsize. We show that the proposed modified strictly contractive
Peaceman-Rachford splitting method is convergent and also prove
convergence rate in ergodic and nonergodic sense, respectively. The numerical
tests on an extensive collection of problems demonstrate the efficiency of the
proposed method
On the masses of black-holes in radio-loud quasars
The central black-hole masses of a sample of radio-loud quasars are estimated
by using the data of line-width and the optical continuum
luminosity. The vast majority of the quasars in this sample have black-hole
masses larger than , while a few quasars may contain
relatively smaller black-holes. We found a significant anti-correlation between
the radio-loudness and the central black-hole mass. It might imply that the jet
formation is governed by the black-hole mass.Comment: 5 pages, two figures are added, accepted by MNRAS Letter
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