A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

A mantle plume origin for the Palaeoproterozoic Circum-Superior Large Igneous Province

The Circum-Superior Large Igneous Province (LIP) consists predominantly of ultramafic-mafic lavas and sills with minor felsic components, distributed as various segments along the margins of the Superior Province craton. Ultramafic-mafic dykes and carbonatite complexes of the LIP also intrude the more central parts of the craton. Most of this magmatism occurred ∼1880 Ma. Previously a wide range of models have been proposed for the different segments of the CSLIP with the upper mantle as the source of magmatism. New major and trace element and Nd-Hf isotopic data reveal that the segments of the CSLIP can be treated as a single entity formed in a single tectonomagmatic environment. In contrast to most previous studies that have proposed a variety of geodynamic settings, the CSLIP is interpreted to have formed from a single mantle plume. Such an origin is consistent with the high MgO and Ni contents of the magmatic rocks, trace element signatures that similar to oceanic-plateaus and ocean island basalts and εNd-εHf isotopic signatures which are each more negative than those of the estimated depleted upper mantle at ∼1880 Ma. Further support for a mantle plume origin comes from calculated high degrees of partial melting, mantle potential temperatures significantly greater than estimated ambient Proterozoic mantle and the presence of a radiating dyke swarm. The location of most of the magmatic rocks along the Superior Province margins probably represents the deflection of plume material by the thick cratonic keel towards regions of thinner lithosphere at the craton margins. The primary magmas, generated by melting of the heterogeneous plume head, fractionated in magma chambers within the crust, and assimilated varying amounts of crustal material in the process

Who’s to Blame?: An Analysis of Agricultural Subsidies and Their Effects on Development

This essay aims to reveal the complex landscape of the hindrances to development that developing countries themselves and developed nations’ agricultural subsidies pose. It discusses developing countries’ objectives and desires to see trade as a tool for development and then considers the potential for trade to contribute to development by examining how different international organizations use trade to aid developing countries. It examines China’s use of the green box as a case study of the potential that certain agricultural subsidies hold for development. Then, it looks at the limitations of trade as a means to make development progress, citing both agricultural subsidies and faulty development models. The essay lays out a brief structure of the different boxes of subsidies under the Agreement on Agriculture in the WTO with a focus on the green box and the complaints being mounted against its use by developed countries. It studies the effects of U.S. agricultural subsidies, both on the U.S. and developing countries, and it concludes by looking to the current political landscape of the Doha round and the U.S. to gain a sense of the prospects for agricultural subsidies. This essay seeks to show how both the agricultural subsidies of rich, developed countries and the domestic inadequacies of developing countries are to blame for the lack of development that we see in the world today