Benford's Law, Values of L-functions and the 3x+1 Problem

We show the leading digits of a variety of systems satisfying certain conditions follow Benford's Law. For each system proving this involves two main ingredients. One is a structure theorem of the limiting distribution, specific to the system. The other is a general technique of applying Poisson Summation to the limiting distribution. We show the distribution of values of L-functions near the central line and (in some sense) the iterates of the 3x+1 Problem are Benford.Comment: 25 pages, 1 figure; replacement of earlier draft (corrected some typos, added more exposition, added results for characteristic polynomials of unitary matrices

A Sociological Analysis of Crimes of Honor: Examining the Effects of Higher Education on the Concepts of Honor and Notions of Gender Equality in Jordan

The study analyzes the ever present traditional notions of patriarchy in Jordan, and the contexts by which they are surviving in the milieu of democratization. By way of 12 interviews with academics, legal professionals, judges, and tribal sheikhs, it specifically looks to legislation, concepts of honor, and gender notions as exemplified by the traditional exercise of honor killings in Jordan. The conclusion of this research critically assesses that, despite a wealth of political rhetoric promising the ideals of egalitarianism, Jordan still harbors a patriarchal society that does not apply benefits of equality (especially sexual equality) to all of its citizens (especially women in traditional areas of the country). Furthermore, the study conducts a survey which examines the influence of higher education (in the College of Law at the University of Jordan) on the cultural mindset which perpetuates these crimes in traditional societies. The survey analyzed 39 students from a fourth year level class at the university and 35 students who had not yet completed an introductory level class in the college of law. The researcher examined nineteen pertinent questions which inspect notions of gender equality and sentiments surrounding family honor and mitigation legislation with reference to honor killings. After conducting two tailed, independent t tests and crosstabulational analyses on all nineteen questions, it seemed only one question retained a significant difference between the answers of the introductory and advanced courses which would support a hypothesis stating education is changing students’ mindsets. Thus, despite literature and public discourse from academics, political leaders, and human rights activists which advocates the use of education to steer social change, the results of a survey at the University of Jordan do not reveal any significant difference in introductory level and advanced level students’ traditional notions of gender equality and family honor

Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues

We present two graph quantities Psi(G,S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, lambda(G,S) and lambda_2(G), respectively. Our techniques make use of a discrete Hardy-type inequality due to Muckenhoupt

An Evaluation of Nutrient Trading Options in Virginia: A Role for Agriculture?

Water Quality Trading, offsets, nutrients, agriculture, BMPs, Environmental Economics and Policy,