The tensor product in the theory of Frobenius manifolds

We introduce the operation of forming the tensor product in the theory of analytic Frobenius manifolds. Building on the results for formal Frobenius manifolds which we extend to the additional structures of Euler fields and flat identities, we prove that the tensor product of pointed germs of Frobenius manifolds exists. Furthermore, we define the notion of a tensor product diagram of Frobenius manifolds with factorizable flat identity and prove the existence such a diagram and hence a tensor product Frobenius manifold. These diagrams and manifolds are unique up to equivalence. Finally, we derive the special initial conditions for a tensor product of semi--simple Frobenius manifolds in terms of the special initial conditions of the factors.Comment: 41 pages, amslatex, uses xy-te

Does Risk Aversion Make a Case for Conservatism

Dr. Perhac argues that risk aversion, alone, and assuming it is justifiable, does not support the prefer ability of overstating, as opposed to understating, mean risk

Effect of Research and Development and Market Concentration on Merger Outcomes -- An Event Study of U.S. Horizontal Mergers

This study examines the pattern of abnormal returns for merging companies and rivals to determine investor expectations regarding the impact of horizontal mergers challenged by the government. Prior studies have indicated that the government may have challenged efficiency-enhancing mergers as evidenced by the pattern of abnormal returns to rivals during merger events. This study examines those patterns using challenged mergers from 1997 to 2007, and it adds to the literature by assessing the effect that R&D intensity and change in HHI have on the returns to rivals and merging firms. The paper finds that the pattern of abnormal returns is a result of the different effects that antitrust complaints and merger outcomes have on rivals based on R&D intensity and change in industry concentration. This finding suggests that the government may have been properly vigilant in challenging mergers over the past 10 years in basic industries that have high levels of market concentration. However, it also may have allowed collusive mergers to proceed in R and D intensive industries.mergers, Research and Development, Strategic Protection, market concentration, event study