7. Malthus and the Problem of Population

One of the central beliefs of classical economic theory was that there is an inexorable tendency for population to press against the available natural resources, especially those providing the food supply. This doctrine, though not originating with him, was eloquently expressed by Thomas Robert Malthas (1766-1834) in an essay which first appeared in 1798. Malthus, a high-ranking graduate of Cambridge University, was a clergyman in the Church of England before he became a professor of history and political economy at the East India College, Haileybury, in 1805. This college had just been established by the British East India Company to train men for its service in Asia. Malthus, one of the first persons ever to hold a professorship in economics, continued in this post for the remainder of his life. [excerpt

Supersaturation Problem for the Bowtie

The Tur\'an function $ex(n,F)$ denotes the maximal number of edges in an $F$-free graph on $n$ vertices. We consider the function $h_F(n,q)$, the minimal number of copies of $F$ in a graph on $n$ vertices with $ex(n,F)+q$ edges. The value of $h_F(n,q)$ has been extensively studied when $F$ is bipartite or colour-critical. In this paper we investigate the simplest remaining graph $F$, namely, two triangles sharing a vertex, and establish the asymptotic value of $h_F(n,q)$ for $q=o(n^2)$.Comment: 23 pages, 1 figur

Problem Set 7

Problem Set 7https://digitalcommons.usu.edu/foundation_wave/1031/thumbnail.jp

A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem

We give a 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem.Comment: 6 figure

Possible solution to the 7^7Li problem by the long lived stau

Modification of standard big-bang nucleosynthesis is considered in the minimal supersymmetric standard model to resolve the excessive theoretical prediction of the abundance of primordial lithium 7. We focus on the stau as a next-lightest superparticle, which is long lived due to its small mass difference with the lightest superparticle. It provides a number of additional decay processes of $\mathrm{^{7}Li}$ and $\mathrm{^{7}Be}$. A particularly important process is the internal conversion in the stau-nucleus bound state, which destroys the $\mathrm{^{7}Li}$ and $\mathrm{^{7}Be}$ effectively. We show that the modification can lead to a prediction consistent with the observed abundance of $\mathrm{^{7}Li}$.Comment: 6 pages, 5 figure