Universality in the Shape Dependence of Holographic R\'enyi Entropy for General Higher Derivative Gravity

We consider higher derivative gravity and obtain universal relations for the shape coefficients $(f_a, f_b, f_c)$ of the shape dependent universal part of the R\'enyi entropy for four dimensional CFTs in terms of the parameters $(c, t_2, t_4)$ of two-point and three-point functions of stress tensors. As a consistency check, these shape coefficients $f_a$ and $f_c$ satisfy the differential relation as derived previously for the R\'enyi entropy. Interestingly, these holographic relations also apply to weakly coupled conformal field theories such as theories of free fermions and vectors but are violated by theories of free scalars. The mismatch of $f_a$ for scalars has been observed in the literature and is due to certain delicate boundary contributions to the modular Hamiltonian. Interestingly, we find a combination of our holographic relations which are satisfied by all free CFTs including scalars. We conjecture that this combined relation is universal for general CFTs in four dimensional spacetime. Finally, we find there are similar universal laws for holographic R\'enyi entropy in general dimensions.Comment: 32 pages,0 figures, references added, appendix added, accepted for publication in JHE

Optimal Recovery of Elastic Properties for Anisotropic Materials through Ultrasonic Measurements

Full knowledge of material elastic properties is required to facilitate design in many applications. The existence of misorientation between the geometric axes of the part and the material symmetry axes has in particularly created challenged in design of composite structure. In this thesis the potential for optimal identification of material symmetries for a general anisotropic material through a water immersion technique is explored. The concept is extensible to any class of symmetry groups and does not assume a-priori knowledge of the material. Initial experimental results for determining the elastic constants as well as locating the symmetry planes are presented. Many materials have not been investigated completely by a method such as the one described. The specific contribution of this work is to demonstrate this process for experimental data sets. The primary focus is on carbon-carbon composite material. The method is demonstrated using a single crystal with known properties

Chinese Companies Cross-Border Mergers and Acquisitions Performance: Evidence from Inward and Outward Deals

This dissertation focuses on the Chinese cross-border M&As (mergers and acquisitions) market of public companies’ performance. The study precisely identifies short-term performance surrounding a M&A announcement that a public Chinese company is acquiring an overseas firm or is being targeted. The key words of these three chapters are method of payment, public status, and acquirer industry. This study measures short-term performance by investigating CARs (cumulative average abnormal returns). The windows are approximately 2 days and 5 days before and after a M&A announcement. The time span is 15 years (2002–2016) for Chinese public companies’ cross-border transactions and 23 years (1994-2016) for transactions targeting Chinese public companies. The first chapter demonstrates that cash transactions outperform stock transactions although more public Chinese companies chose stock to finance transactions. The second chapter demonstrates that an acquired public overseas target underperforms compared with targeting private companies. In addition, the transaction volume indicates that most bidder companies made the right decision. The third chapter demonstrates that overseas financial institutions are more likely (over 60% of transactions) to acquire Chinese public companies in all industries. These investors do bring abnormal returns to their target companies