Dynamical Friction Models for Black-Hole Binary Formation in AGN Disks

Stellar-mass black holes (sBH) embedded in gaseous disks of active galactic nuclei (AGN) can be important sources of detectable gravitational radiation for LIGO/Virgo when they form binaries and coalesce due to orbital decay. In this paper, we study the effect of gas dynamical friction (DF) on the formation of BH binaries in AGN disks using $N$-body simulations. We employ two simplified models of DF, with the force on the BH depending on $\Delta {\bf v}$, the velocity of the sBH relative to the background Keplerian gas. We integrate the motion of two sBH initially on circular orbits around the central supermassive black hole (SMBH), and evaluate the probability of binary formation under various conditions. We find that both models of DF (with different dependence of the frictional coefficient on $|\Delta{\bf v}|$) can foster the formation of binaries when the effective friction timescale $\tau$ satisfies $\Omega_{\rm K}\tau\lesssim 20-30$ (where $\Omega_{\rm K}$ is the Keplerian frequency around the SMBH): prograde binaries are formed when the DF is stronger (smaller $\tau$), while retrograde binaries dominate when the DF is weaker (larger $\tau$). We determine the distribution of both prograde and retrograde binaries as a function of initial orbital separation and the DF strength. Using our models of DF, we show that for a given sBH number density in the AGN disk, the formation rate of sBH binaries increases with decreasing $\tau$ and can reach a moderate value with a sufficiently strong DF.Comment: 17 pages, 13 figures, submitted to Ap

Enhancing Social Media Marketing with A Brand Post Management Process

In recent years, enterprises are increasingly using social media to enhance the marketing effects about their brands and services. As such, brand pages on social media sites with brand posts placed are commonly used for effecting desired marketing features such as advertisement of services and assistance of customers. Therefore, it has become an important objective for enterprises to enhance the effects of their brand pages via sufficient management mechanisms. For this purpose, we present in this paper a management process that focuses on the organization, execution, and control of brand posts to enhance their marketing effects

Test for Trade-Off between Return and Risk: Empirical Evidences from Chinese stock market

Abstract The Capital Asset Pricing Model (CAPM) is one of the most significant theories of modern finance and the cornerstone of all other asset pricing theories. It has been fifty or sixty years since this model established in 1952. Chinese scholars have made number of relevant empirical test for the applicable of CAPM in recent years, but the results are different. The objective of this paper is to test for trade-off between return and risk and research whether the Capital Asset Pricing Model (CAPM) is applicable to Chinese securities market, if not, what is the reason. This paper exam Capital Asset Pricing Model (CAPM) in China basing on monthly stock returns from 150 companies in Shanghai stock market for the period of 1/1/2012 to 12/31/2016. It concludes that in the Chinese stock market, there is insufficient evidence to proof the basic opinion that high risk is associated with high levels of return. What is more, beta is not related to excess returns, which also prove that CAPM is not applicable to Chinese securities market. Finally, interpretation of results and some suggestions are given