Multiplicity of periodic solutions in bistable equations

We study the number of periodic solutions in two first order non-autonomous differential equations both of which have been used to describe, among other things, the mean magnetization of an Ising magnet in the time-varying external magnetic field. When the strength of the external field is varied, the set of periodic solutions undergoes a bifurcation in both equations. We prove that despite profound similarities between the equations, the character of the bifurcation can be very different. This results in a different number of coexisting stable periodic solutions in the vicinity of the bifurcation. As a consequence, in one of the models, the Suzuki-Kubo equation, one can effect a discontinuous change in magnetization by adiabatically varying the strength of the magnetic field.Comment: Fixed typos; added and reordered figures. 18 pages, 6 figures. An animation of orbits is available at http://www.maths.strath.ac.uk/~aas02101/bistable

Implied Certification under the False Claims Act

The False Claims Act prohibits fraud by government contractors, including a contractor\u27s false certification of compliance with the contract, statutes or regulations. In the early 1990s, some courts began holding that the act of requesting payment from the government implicitly represents such compliance for the purposes the FCA. Circuits are today split on the implied certification doctrine. This Article provides a theory of implied certification, suggests how the circuit split should be resolved and describes how contracting agencies should write contracts in light of the existing rule. There are good reasons for the implied certification rule: it is an information-forcing majoritarian default; it affirms the special ethical obligations of government contractors; and it addresses agency lassitude in drafting and monitoring performance. But implied certification also has its costs. Most importantly, it lowers the bar to frivolous qui tam actions and threatens to impose FCA liability for violations better addressed by more discretionary and nuanced regulatory responses. This Article recommends a narrow implied certification rule: the fact that a contract, statute or regulation conditions either participation in or payment for a contract on compliance with it should create a prima facie case that a claim for payment represents such compliance, shifting the burden to the defendant to show that FCA liability would interfere with other regulatory monitoring and enforcement mechanisms. The Article also recommends that contracting agencies pay more attention to the FCA when drafting contracts. They can approximate first-best results by requiring express certification of compliance with those duties for which FCA liability makes sense, and contracting-out of implied certification for those duties that are better enforced in other ways. In addition to these practical suggestions, the Article draws some general lessons about the contractual duties to cooperate, interpretive defaults in contract and tort, and the special ethical obligations of government contractors

Understanding State Government Appropriations For the Arts: 1976-1999

Using panel data analysis, we examine the relative importance of citizen and government characteristics on a highly discretionary and volatile budget item: state appropriations to arts agencies. Despite the unimportance of arts spending to most citizens, changes in arts spending appear to reflect citizen desires. Spending rises with per capita income, state revenues, and citizen political and social liberalism, but characteristics of state legislatures do not significantly affect spending.Department of Economics and W.T. Beebe Institute of Personnel and Employment Relations Working Paper 07-0

An Antitrust Analysis of the Case for Wireless Network Neutrality

The ongoing debate about possible implementation of regulatory rules requiring “network neutrality” for wireless telecommunications services is inherently about whether to impose a prohibition on the ability of network operators to control their vertical relationships. Antitrust analysis is well suited to analyze whether a wireless network neutrality rule is socially beneficial. Implementing network neutrality rules would be akin to using a per se antitrust rule regarding vertical relationships instead of the rule of reason analysis typically applied to vertical relationships in antitrust. Per se rules are used to prevent actions that rarely, if ever, have any pro-competitive benefits, such as price-fixing agreements. Rule of reason analysis is used when there are potential efficiency gains from the actions under investigation. Some vertical practices of the wireless carriers, such as bandwidth restrictions, may appear to be anticompetitive, but may also have plausible efficiency justifications so should be judged under rule of reason analysis. Economic examination of the wireless industry shows significant competition between networks which reduces the concern about vertical relationships, but some areas that should be monitored by antitrust and regulatory authorities. We propose several regulatory changes that would likely increase wireless competition and lessen the perceived need for prophlactic network neutrality rules while at the same time allowing efficiency-enhancing vertical relationships.network neutrality, wireless internet, antitrust,