Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds

In this paper we investigate equivariant Morita theory for algebras with momentum maps and compute the equivariant Picard groupoid in terms of the Picard groupoid explicitly. We consider three types of Morita theory: ring-theoretic equivalence, *-equivalence and strong equivalence. Then we apply these general considerations to star product algebras over symplectic manifolds with a Lie algebra symmetry. We obtain the full classification up to equivariant Morita equivalence.Comment: 28 pages. Minor update, fixed typos

Copyright, Containers, and the Court: A Reply to Professor Leaffer

The author finds little with which to be pleased in the Court’s recent copyright cases. The Court seems to be fighting a holding action, fending off the future by resolutely gazing backward. While the Court has not itself enlarged copyright, it has not meaningfully evaluated Congress’s power to do so, and its decisions freeze copyright into a moment in time long past. Until copyright law recognizes that content is no longer container-bound, it will continue to flounder, desperately seeking analogies to the past and missing the significance of the technological changes all around us. That said, the author agrees with Professor Leaffer that the future is not black but gray. The author believes that there is still much that can be done about the expansion of copyright and its increasing concentration into the hands of a media oligopoly, beginning with an awakening of public concern with those vital rights that are eroded as copyright expands. As long as that can happen, there is hope. Sadly, if that does not happen, then the author does not think either Congress or the Court will save us from ourselves

The Sarbanes-Oxley Act: A Bird\u27s-eye View

It is the goal of this article to provide a brief reference to the multitude of changes in the law wrought by SOX. The author\u27s hope is that this will be of use to students, scholars, and practitioners seeking an overview of the extensive changes resulting from this legislation. The discussion is broader than it is deep; indeed, a work attempting to examine SOX in depth would soon become a treatise and not just an article. The remainder of this article, then, will seek to provide a big-picture view of SOX: Part II of this article will address SOX regulation of professionals, including accountants, lawyers, and securities analysts. Part III will address SOX\u27s attempts to enhance corporate disclosure. Part IV will examine SOX\u27s efforts to reform corporate governance. Part V will examine SOX\u27s provisions dealing with enforcement of the law. Finally, Part VI will provide a brief conclusion

Dragging a polymer chain into a nanotube and subsequent release

We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method. The nanotube is a long channel opened at one end and its diameter $D$ is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position $x$ inside the tube: the free energy of confinement, the average end-to-end distance, the average number of imprisoned monomers, and the average stretching of the confined part of the chain for various values of $D$ and for the number of monomers in the chain, $N$. We show that when the chain end is dragged by a certain critical distance $x^*$ into the tube, the polymer undergoes a first-order phase transition whereby the remaining free tail is abruptly sucked into the tube. This is accompanied by jumps in the average size, the number of imprisoned segments, and in the average stretching parameter. The critical distance scales as $x^*\sim ND^{1-1/\nu}$. The transition takes place when approximately 3/4 of the chain units are dragged into the tube. The theory presented is based on constructing the Landau free energy as a function of an order parameter that provides a complete description of equilibrium and metastable states. We argue that if the trapped chain is released with all monomers allowed to fluctuate, the reverse process in which the chain leaves the confinement occurs smoothly without any jumps. Finally, we apply the theory to estimate the lifetime of confined DNA in metastable states in nanotubes.Comment: 13pages, 14figure