The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

A Historical-Institutional Study of the Welfare Systems in the United States and Sweden: Net Social Wage Approach

In this study I first look at the historical developments of the welfare systems in Sweden and the United States to understand why these countries have produced two distinct systems over the years. After understanding their historical context I turn to the question of the relationship between the welfare system and economic growth. Policy makers and the mainstream media commonly cite the critique that through government deficit and public debt, welfare systems are a drag on the economy. By calculating the net social wage, the difference in taxes paid and benefits received by workers, I test this hypothesis to see if welfare systems are self-financed by the workers. My findings demonstrate that the net social wage has been negative in the U.S. from 1962 to the early 2000s and in Sweden from 1965 to 2012. This shows that the welfare systems are entirely self-financed by the workers for the full period in Sweden and until the recent financial crisis in the U.S.