Sharp polynomial bounds on the number of Pollicott-Ruelle resonances

We give a sharp polynomial bound on the number of Pollicott-Ruelle resonances. These resonances, which are complex numbers in the lower half-plane, appear in expansions of correlations for Anosov contact flows. The bounds follow the tradition of upper bounds on the number of scattering resonances and improve a recent bound of Faure-Sj\"ostrand. The complex scaling method used in scattering theory is replaced by an approach using exponentially weighted spaces introduced by Helffer-Sj\"ostrand in scattering theory and by Faure-Sj\"ostrand in the theory of Anosov flows.Comment: 18 pages; minor revision based on referee's comments. To appear in Erg. Theory Dyn. Sys

A study of academic preparation of biology and general science teachers in relation to school size in Kansas, 1963-64

Call number: LD2668 .R4 1964 W18

Southwest Border Violence: Issues in Identifying and Measuring Spillover Violence

[Excerpt] There has been a recent increase in the level of drug trafficking-related violence within and between the drug trafficking organizations in Mexico. This violence has generated concern among U.S. policy makers that the violence in Mexico might spill over into the United States. Currently, U.S. federal officials deny that the recent increase in drug trafficking-related violence in Mexico has resulted in a spillover into the United States, but they acknowledge that the prospect is a serious concern. Currently, no comprehensive, publicly available data exist that can definitively answer the question of whether there has been a significant spillover of drug trafficking-related violence into the United States. Although anecdotal reports have been mixed, U.S. government officials maintain that there has not yet been a significant spillover. In an examination of data that could provide insight into whether there has been a significant spillover in drug trafficking-related violence from Mexico into the United States, CRS analyzed violent crime data from the Federal Bureau of Investigation’s Uniform Crime Report program. The data, however, do not allow analysts to determine what proportion of the violent crime rate is related to drug trafficking or, even more specifically, what proportion of drug trafficking-related violent crimes can be attributed to spillover violence. In conclusion, because the trends in the overall violent crime rate may not be indicative of trends in drug trafficking-related violent crimes, CRS is unable to draw definitive claims about trends in drug trafficking-related violence spilling over from Mexico into the United States. This report will be updated as circumstances warrant

Asymptotics of class numbers

A "simple trace formula" is used to derive an asymptotic result for class numbers of complex cubic orders.Comment: 37 page

Multiplicities of Periodic Orbit Lengths for Non-Arithmetic Models

Multiplicities of periodic orbit lengths for non-arithmetic Hecke triangle groups are discussed. It is demonstrated both numerically and analytically that at least for certain groups the mean multiplicity of periodic orbits with exactly the same length increases exponentially with the length. The main ingredient used is the construction of joint distribution of periodic orbits when group matrices are transformed by field isomorphisms. The method can be generalized to other groups for which traces of group matrices are integers of an algebraic field of finite degree