Generalized moonshine II: Borcherds products

The goal of this paper is to construct infinite dimensional Lie algebras using infinite product identities, and to use these Lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex algebras and Lie algebras. The Lie algebras that we construct conjecturally appear in an orbifold conformal field theory with symmetries given by the monster simple group. We introduce vector-valued modular functions attached to families of modular functions of different levels, and we prove infinite product identities for a distinguished class of automorphic functions on a product of two half-planes. We recast this result using the Borcherds-Harvey-Moore singular theta lift, and show that the vector-valued functions attached to completely replicable modular functions with integer coefficients lift to automorphic functions with infinite product expansions at all cusps. For each element of the monster simple group, we construct an infinite dimensional Lie algebra, such that its denominator formula is an infinite product expansion of the automorphic function arising from that element's McKay-Thompson series. These Lie algebras have the unusual property that their simple roots and all root multiplicities are known. We show that under certain hypotheses, characters of groups acting on these Lie algebras form functions on the upper half plane that are either constant or invariant under a genus zero congruence group.Comment: v3: final version, minor corrections and explanations added, 41 page

Options for Revenue Generation in Post-Conflict Environments (revision)

In the wake of violent conflict, a key element of building a durable peace is building a state with the ability to collect and manage public resources. To implement peace accords and to provide public services, the government must be able to collect revenue, allocate resources, and manage expenditure in a manner that is regarded by its citizens as effective and equitable. In this new PERI Working Paper, Michael Carnahan of the Australian National University grapples with the impact of conflict on policy, administrative systems, and overall activity, as well as the impact of pressures from the international community. The author makes five specific recommendations, including a link between revenue collections and donor aid, a reassessment of U.N. policies, changes in tax policies for foreign workers and donors' contractors, and establishing urban land taxation systems. This study is part of a series on Public Finance in Post-Conflict Environments, published jointly by PERI and New York University's Center on International Cooperation.�(Revised December 2007)Revenue mobilization; postconflict reconstruction; taxation; external assistance; tax exemptions

DMA precise time and time interval requirements

Defense Mapping Agency timing requirements ranging from milliseconds to tenths of nanoseconds and its use of geodetic astronomy and satellite geodesy programs are discussed in detail