Observations show that the accretion ows in low-luminosity active galactic nuclei (LLAGNs) probably have a two-component structure with an inner hot, optically thin, advection dominated accretion flow (ADAF) and an outer truncated cool, optically thick accretion disk. As shown by Taam et al. (2012), within the framework of the disk evaporation model, the truncation radius as a function of mass accretion rate is strongly affected by including the magnetic field. We define the parameter β as pm = B2=8π = (1 - β)ptot, (where ptot = pgas + pm, pgas is gas pressure and pm is magnetic pressure) to describe the strength of the magnetic field in accretion ows. It is found that an increase of the magnetic field (decreasing the value of β) results in a smaller truncation radius for the accretion disk. We calculate the emergent spectrum of an inner ADAF + an outer truncated accretion disk around a supermassive black hole by considering the effects of the magnetic field on the truncation radius of the accretion disk. By comparing with observations, we found that a weaker magnetic field (corresponding to a bigger value of β) is required to match the observed correlation between L2-10keV/LEdd and the bolometric correction K2-10keV, which is consistent with the physics of the accretion ow with a low mass accretion rate around a black hole.

Customer loyalty programs have been widely adopted for customer relationship management all over the world. The proliferation of loyalty programs causes program competition which weakens the effectiveness of loyalty programs at the end of customers. In general, existed research suggests that the increasing competition among rival programs in a single industry may cancel out the expected roles of loyalty programs (Mägi, 2003). For example, program competition is a substantial threat to customer lifetime value and share of wallet (Leenheer, van Heerde, Bijmolt, & Smidts, 2007; Meyer-Waarden, 2007). Liu and Yang (2009) find the sales impact of a single loyalty program diminishes as program competition increases. Their study also shows this negative effect is weaker in a highly expandable product category. Although previous studies have examined the suppressive effect of program competition on financial outcomes of loyalty programs, little research has explored its role on attitudinal customer loyalty formation process. This study aims to explore the differential roles of program competition on two formation processes of customer loyalty. It intends to contribute to the loyalty programs literature in two aspects. First, this study examines two routines of customer loyalty formation in the context of loyalty programs. That is, a company can leverage program offerings to build customer loyalty through increased customer satisfaction or strengthened customer identification with the company. Second, this study examines the moderating roles of program competition on those two loyalty-generating routines. Specifically, it finds customer identification is more important for building customer loyalty at the presence of program loyalty.