The Wells exact sequence for the automorphism group of a group extension

AbstractWe obtain an explicit description of the Wells map for the automorphism group of a group extension in the full generality and investigate the dependency of this map on group extensions. Some applications are given

Understanding big consumer opinion data for market-driven product design

Big consumer data provide new opportunities for business administrators to explore the value to fulfil customer requirements (CRs). Generally, they are presented as purchase records, online behaviour, etc. However, distinctive characteristics of big data, Volume, Variety, Velocity and Value or ‘4Vs’, lead to many conventional methods for customer understanding potentially fail to handle such data. A visible research gap with practical significance is to develop a framework to deal with big consumer data for CRs understanding. Accordingly, a research study is conducted to exploit the value of these data in the perspective of product designers. It starts with the identification of product features and sentiment polarities from big consumer opinion data. A Kalman filter method is then employed to forecast the trends of CRs and a Bayesian method is proposed to compare products. The objective is to help designers to understand the changes of CRs and their competitive advantages. Finally, using opinion data in Amazon.com, a case study is presented to illustrate how the proposed techniques are applied. This research is argued to incorporate an interdisciplinary collaboration between computer science and engineering design. It aims to facilitate designers by exploiting valuable information from big consumer data for market-driven product design

Studying newborn neutron stars by the transient emission after stellar collapses and compact binary mergers

The formation of neutron stars (NSs), both from collapses of massive stars and mergers of compact objects, can be usually indicated by bright transients emitted from explosively-ejected material. In particular, if the newborn NSs can rotate at a millisecond period and have a sufficiently high magnetic field, then the spin-down of the NSs would provide a remarkable amount of energy to the emitting material. As a result, super-luminous supernovae could be produced in the massive stellar collapse cases, while some unusual fast evolving and luminous optical transients could arise from the cases of NS mergers and accretion-induced collapses of white dwarfs. In all cases, if the dipolar magnetic fields of the newborn NSs can be amplified to be as high as $10^{15}$ G, a relativistic jet could be launched and then a gamma-ray burst can be produced as the jet successfully breaks out from the surrounding nearly-isotropic ejected material.Comment: 10 pages, 9 pictures, to appear in the AIP Proceedings of the Xiamen-CUSTIPEN Workshop on the EOS of Dense Neutron-Rich Matter in the Era of Gravitational Wave Astronomy, Jan. 3-7, Xiamen, Chin