Back of the envelope estimates of environmental damage costs in Mexico

For developing countries, budget constraints help set the agenda on mitigating environmental damage, one of the indelible marks of our era. Political considerations often dictate the measures taken. There are no firm analytical formulas to help even environmentally conscious policymakers rank needs and remedies. A developing country such as Mexico - the focus of this paper - cannot afford an in-depth study of every environmental issue. Policymakers need to be provided with rough,"back-of-the envelope"estimates of the economic costs of various environmental problems. This allows them to rank the issues and act. In this paper the author applied existing methods to estimate the costs stemming from different environmental problems in Mexico. Although the examples are from Mexico, the method can be useful in other developing countries as well. The author how creative use of U.S. and other data can help provide simple estimates of the likely costs of soil erosion, air pollution, mining of underground waters, and estimates of the health effects of water and solid waste pollution, lack of sanitation, and the ingestion of food contaminated by polluted irrigation. The assumptions underlying all calculations are conservative. Some environmental damage issues, such as loss of biodiversity, were too complex to permit quantification.Water Conservation,Economic Theory&Research,Health Monitoring&Evaluation,Environmental Economics&Policies,Pollution Management&Control

Flows on homogeneous spaces and Diophantine approximation on manifolds

We present a new approach to metric Diophantine approximation on manifolds based on the correspondence between approximation properties of numbers and orbit properties of certain flows on homogeneous spaces. This approach yields a new proof of a conjecture of Mahler, originally settled by V. Sprindzhuk in 1964. We also prove several related hypotheses of A. Baker and V. Sprindzhuk formulated in 1970s. The core of the proof is a theorem which generalizes and sharpens earlier results on non-divergence of unipotent flows on the space of lattices.Comment: 19 pages. To appear in Annals of Mathematic

Locally Divergent Orbits on Hilbert Modular Spaces

We describe the closures of locally divergent orbitsunder the action of tori on Hilbert modular spaces of rank r = 2. In particular, we prove that if D is a maximal R-split torus acting on a real Hilbert modular space then every locally divergent non-closed orbit is dense for r > 2 and its closure is a finite union of tori orbits for r = 2. Our results confirm an orbit rigidity conjecture of Margulis in all cases except for (i) r = 2 and, (ii) r > 2 and the Hilbert modular space corresponds to a CM-field; in the cases (i) and (ii) our results contradict the conjecture. As an application, we describe the set of values at integral points of collections of non-proportional, split, binary, quadratic forms over number fields.Comment: The reason to replace the previous (second) version was a typo in the formulation of Conjecture A. In comparison with the first version the changes are the following: added references, corrected typos, added Corollary 1.4(a). In the present version I discuss only Margulis' orbit rigidity conjecture.The measure rigidity conjecture will be hopefully discussed elsewhere late

Quantitative Version of the Oppenheim Conjecture for Inhomogeneous Quadratic Forms

A quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms is proved. We also give an application to eigenvalue spacing on flat 2-tori with Aharonov-Bohm flux