On the intersection of free subgroups in free products of groups

Let (G_i | i in I) be a family of groups, let F be a free group, and let G = F *(*I G_i), the free product of F and all the G_i. Let FF denote the set of all finitely generated subgroups H of G which have the property that, for each g in G and each i in I, H \cap G_i^{g} = {1}. By the Kurosh Subgroup Theorem, every element of FF is a free group. For each free group H, the reduced rank of H is defined as r(H) = max{rank(H) -1, 0} in \naturals \cup {\infty} \subseteq [0,\infty]. To avoid the vacuous case, we make the additional assumption that FF contains a non-cyclic group, and we define sigma := sup{r(H\cap K)/(r(H)r(K)) : H, K in FF and r(H)r(K) \ne 0}, sigma in [1,\infty]. We are interested in precise bounds for sigma. In the special case where I is empty, Hanna Neumann proved that sigma in [1,2], and conjectured that sigma = 1; almost fifty years later, this interval has not been reduced. With the understanding that \infty/(\infty -2) = 1, we define theta := max{|L|/(|L|-2) : L is a subgroup of G and |L| > 2}, theta in [1,3]. Generalizing Hanna Neumann's theorem, we prove that sigma in [theta, 2 theta], and, moreover, sigma = 2 theta if G has 2-torsion. Since sigma is finite, FF is closed under finite intersections. Generalizing Hanna Neumann's conjecture, we conjecture that sigma = theta whenever G does not have 2-torsion.Comment: 28 pages, no figure

LTA bibliography

This bibliography includes publications which deal with airship design, engineering, stress calculations, and historical information

Correlated Equilibria of Classical Strategic Games with Quantum Signals

Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve even better efficiency than in any correlated equilibrium with classical signals, and find the answer to be positive.Comment: 8 pages, LaTe

The Slate all metal airship

The development of the Slate all metal airship City of Glendale built and completed in 1930 is presented. The airship facilities are discussed. Pertinent data which led to other engineering accomplishments for aviation are shown. The SMD-100 concept is presented along with a brief commentary on the costs and problems involved in such an airship design and the application of the hoisting and elevator facilities to airship development

Learning and Communication in Sender-Receiver Games: An Econometric Investigation

Learning and communication play important roles in coordinating activities. Game theory and experiments have made a significant contribution to our understanding and appreciation for the issues surrounding learning and communication in coordination. However, the results of past experimental studies provide conflicting results about the performance of learning models. Moreover, the interaction between learning and communication has not been systematically investigated. Our long run objective is to overcome the conflicting results and to provide a better understanding of the interaction. To this end, we econometrically investigate a sender-receiver game environment where communication is necessary for coordination and learning is essential for communication.

Airship economics

Projected operating and manufacturing costs of a large airship design which are considered practical with today's technology and environment are discussed. Data and information developed during an 18-month study on the question of feasibility, engineering, economics and production problems related to a large metalclad type airship are considered. An overview of other classic airship designs are provided, and why metalclad was selected as the most prudent and most economic design to be considered in the 1970-80 era is explained. Crew operation, ATC and enroute requirements are covered along with the question of handling, maintenance and application of systems to the large airship

Energy Loss from Reconnection with a Vortex Mesh

Experiments in superfluid 4He show that at low temperatures, energy dissipation from moving vortices is many orders of magnitude larger than expected from mutual friction. Here we investigate other mechanisms for energy loss by a computational study of a vortex that moves through and reconnects with a mesh of small vortices pinned to the container wall. We find that such reconnections enhance energy loss from the moving vortex by a factor of up to 100 beyond that with no mesh. The enhancement occurs through two different mechanisms, both involving the Kelvin oscillations generated along the vortex by the reconnections. At relatively high temperatures the Kelvin waves increase the vortex motion, leading to more energy loss through mutual friction. As the temperature decreases, the vortex oscillations generate additional reconnection events between the moving vortex and the wall, which decrease the energy of the moving vortex by transfering portions of its length to the pinned mesh on the wall.Comment: 9 pages, 10 figure