A Conformal Field Theory of Extrinsic Geometry of 2-d Surfaces

In the description of the extrinsic geometry of the string world sheet regarded as a conformal immersion of a 2-d surface in $R^3$, it was previously shown that, restricting to surfaces with $h\surd{g}\ =\ 1$, where $h$ is the mean scalar curvature and $g$ is the determinant of the induced metric on the surface, leads to Virasaro symmetry. An explicit form of the effective action on such surfaces is constructed in this article which is the extrinsic curvature analog of the WZNW action. This action turns out to be the gauge invariant combination of the actions encountered in 2-d intrinsic gravity theory in light-cone gauge and the geometric action appearing in the quantization of the Virasaro group. This action, besides exhibiting Virasaro symmetry in $z$-sector, has $SL(2,C)$ conserved currents in the $\bar{z}$-sector. This allows us to quantize this theory in the $\bar{z}$-sector along the lines of the WZNW model. The quantum theory on $h\surd{g}\ =\ 1$ surfaces in $R^3$ is shown to be in the same universality class as the intrinsic 2-d gravity theory.Comment: 30 page

A Computer Code for Generating Plots of Load Distribution on Spanwise Sections on a wing

A computer code is developed to generate plots using UNIVAC 1100 system and CALCOMP 1039 plotter. The plots give spanwise load distribution on wings

Merger Mechanisms

A firm can merge with one of n potential partners. The owner of each firm has private information about both his firm's stand-alone value and a component of the synergies that would be realized by the merger involving his firm. We characterize incentive-efficient mechanisms in two cases. First, we assume that the value of any newly formed partnership is verifiable, hence transfers can be made contingent on the new information accruing after the merger. Second, we study the case of uncontingent rules. In the first case, we show that it is not optimal, in general, to redistribute shares of non-merging firms, and identify necessary and sufficient conditions for the implementability of efficient merger rules. In the second case, we show that the first-best can be obtained i) always, if the synergy values are privately known but the firms' stand-alone values are observable; ii) only with sufficiently large synergies, if the firms' stand-alone are privately known; and iii) never, if the set of feasible mechanisms is restricted to "auctions in shares".

Merger Mechanisms

A firm can merge with one of n potential partners. The owner of each firm has private information about both his firm’s stand-alone value and a component of the synergies that would be realized by the merger involving his firm. We characterize incentive-efficient mechanisms in two cases. First, we assume that the value of any newly formed partnership is verifiable, hence transfers can be made contingent on the new information accruing after the merger. Second, we study the case of uncontingent rules. In the first case, we show that it is not optimal, in general, to redistribute shares of non-merging firms, and identify necessary and sufficient conditions for the implementability of efficient merger rules. In the second case, we show that the first-best can be obtained i) always, if the synergy values are privately known but the firms’ stand-alone values are observable; ii) only with sufficiently large synergies, if the firms’ stand-alone are privately known; and iii) never, if the set of feasible mechanisms is restricted to “auctions in shares”.Mechanism design, Merger