Generalized Supersymmetric Quantum Mechanics and Reflectionless Fermion Bags in 1+1 Dimensions

We study static fermion bags in the 1+1 dimensional Gross-Neveu and Nambu-Jona-Lasinio models. It has been known, from the work of Dashen, Hasslacher and Neveu (DHN), followed by Shei's work, in the 1970's, that the self-consistent static fermion bags in these models are reflectionless. The works of DHN and of Shei were based on inverse scattering theory. Several years ago, we offered an alternative argument to establish the reflectionless nature of these fermion bags, which was based on analysis of the spatial asymptotic behavior of the resolvent of the Dirac operator in the background of a static bag, subjected to the appropriate boundary conditions. We also calculated the masses of fermion bags based on the resolvent and the Gelfand-Dikii identity. Based on arguments taken from a certain generalized one dimensional supersymmetric quantum mechanics, which underlies the spectral theory of these Dirac operators, we now realize that our analysis of the asymptotic behavior of the resolvent was incomplete. We offer here a critique of our asymptotic argument.Comment: 33 pages, 2 figure

Using Ada: The deeper challenges

The Ada programming language and the associated Ada Programming Support Environment (APSE) and Ada Run Time Environment (ARTE) provide the potential for significant life-cycle cost reductions in computer software development and maintenance activities. The Ada programming language itself is standardized, trademarked, and controlled via formal validation procedures. Though compilers are not yet production-ready as most would desire, the technology for constructing them is sufficiently well known and understood that time and money should suffice to correct current deficiencies. The APSE and ARTE are, on the other hand, significantly newer issues within most software development and maintenance efforts. Currently, APSE and ARTE are highly dependent on differing implementer concepts, strategies, and market objectives. Complex and sophisticated mission-critical computing systems require the use of a complete Ada-based capability, not just the programming language itself; yet the range of APSE and ARTE features which must actually be utilized can vary significantly from one system to another. As a consequence, the need to understand, objectively evaluate, and select differing APSE and ARTE capabilities and features is critical to the effective use of Ada and the life-cycle efficiencies it is intended to promote. It is the selection, collection, and understanding of APSE and ARTE which provide the deeper challenges of using Ada for real-life mission-critical computing systems. Some of the current issues which must be clarified, often on a case-by-case basis, in order to successfully realize the full capabilities of Ada are discussed

Do States Free Ride in Antitrust Enforcement?

Recent research has documented a substantial role in antitrust enforcement by U.S. states. While many of the cases litigated involve small local firms, a non-trivial portion encompass multiplestate issues. Some previous literature has investigated whether states engage in free-riding behavior in environmental regulation, and whether governments free ride on private decisions in provision of public goods. In this paper, we analyze a sample of antitrust cases involving crossstate impacts (from the Multi-State Antitrust Database, provided by the National Association of Attorneys General) and explain the determinants of free-riding (which we define as participatingin a case, but not as a lead plaintiff). JEL classification: