The Nicolas and Robin inequalities with sums of two squares

In 1984, G. Robin proved that the Riemann hypothesis is true if and only if the Robin inequality $\sigma(n)<e^\gamma n\log\log n$ holds for every integer $n>5040$, where $\sigma(n)$ is the sum of divisors function, and $\gamma$ is the Euler-Mascheroni constant. We exhibit a broad class of subsets \cS of the natural numbers such that the Robin inequality holds for all but finitely many n\in\cS. As a special case, we determine the finitely many numbers of the form $n=a^2+b^2$ that do not satisfy the Robin inequality. In fact, we prove our assertions with the Nicolas inequality $n/\phi(n)<e^{\gamma}\log \log n$; since $\sigma(n)/n1$ our results for the Robin inequality follow at once.Comment: 21 page

The Gribov Ambiguity for Maximal Abelian and Center Gauges in SU(2) Lattice Gauge Theory

We present results for the fundamental string tension in SU(2) lattice gauge theory after projection to maximal abelian and direct maximal center gauges. We generate 20 Gribov copies/configuration. Abelian and center projected string tensions slowly decrease as higher values of the gauge functionals are reached.Comment: 3 pages, latex, 1 postscript figure, presented at Lattice 2000(Topology and Vacuum

“One Percenters”: Black Atheists, Secular Humanists, and Naturalists

This essay explores an emergent black atheist, secular humanist, and naturalistic imagination. Based on a 2007 survey by the Pew Forum on Religion and Public Life that measured the percentage of African Americans holding such views, I refer to this group as “one percenters.” Broadly speaking, one percenters view human nature and destiny (necessity and historical contingency) through an anthropological rather than a theological lens. As three perspectives on the same phenomenon, they are the dialectical other of theism and conventional forms of religion. In all three cases, negating theism does “positive” productive and creative work, energizing a different kind of affirmation. Nuances in rhetoric, emotional color, and practical engagement with religious cultures and institutions create distinctions among atheists, secular humanists, and naturalists that are more than merely artful and stylized. These nuances reveal different understandings of what nonbelief entails in matters of conduct and whether the negative and epistemic category of “nonbelief” properly describes their difference from theists

What is Theory?

Believing and Acting (2012) is equally erudite and witty. Known for his good humor, Davis uses wit to make the medicine he dispenses go down more easily. For the patient—that is, scholars engaged in the study of religion who are concerned about proper “methods and approaches”—the prognosis is rather good. But Davis’s wit, I suspect, may also encourage us to move too quickly past some of the claims that he makes. I wish to explore one such claim, namely, his assertion that the study of religion does not need theory. I consider myself a critical theorist of religion, so my engagement with Davis’s argument is not merely business, it’s personal. Though heartfelt, I should hope that the last sentence is taken with a grain of humor. To preview my argument, I shall offer a negative assessment of Davis’s claim about the utility of theory in the study of religion

NATURALIZING CHRISTIAN ETHICS: A Critique of Charles Taylor's A Secular Age

This essay critically engages the concept of transcendence in Charles Taylor's A Secular Age. I explore his definition of transcendence, its role in holding a modernity-inspired nihilism at bay, and how it is crucial to the Christian antihumanist argument that he makes. In the process, I show how the critical power of this analysis depends heavily and paradoxically on the Nietzschean antihumanism that he otherwise rejects. Through an account of what I describe as naturalistic Christianity, I argue that transcendence need not be construed as supernatural, that all of the resources necessary for a meaningful life are immanent in the natural process, which includes the semiotic capacities of Homo sapiens. Finally, I triangulate Taylor's supernatural account of transcendence, naturalistic Christianity, and Dreyfus and Kelly's physis-based account of “going beyond” our normal normality in All Things Shining: Reading the Western Classics for Meaning in a Secular Age

Slaves, Fetuses, and Animals: Race and Ethical Rhetoric

This essay is an exploration in ethical rhetoric, specifically, the ethics of comparing the status of fetuses and animals to enslaved Africans. On the view of those who make such comparisons, the fetus is treated as a slave through abortion, reproductive technologies, and stem cell research, while animals are enslaved through factory farming, experimentation, and as laborers, circus performers, and the like. I explore how the apotheosis of the fetus and the humanization of animals represent the flipside of the subjugation and animalization of black people. At their ethical best, those who compare aborted fetuses and abused animals with enslaved black people have laudable ethical goals. The anti-abortion right and the animal rights left, respectively, wish to abolish abortion (and associated reproductive technologies that harm prenatal life) and the unethical treatment of animals. They seek, respectively, to reimagine the ethical-political status of the fetus and to criticize the animalization of animals, the practice of constructing them as beasts. While sympathetic to these goals, I worry about the comparative diminution of the historical, literal enslavement of black people. To what extent, I ask, does the comparative ethical rhetoric of fetal slaves and animal slaves affect historical constructions of black people as beastly and disposable

Introduction: Race as Euphemism and Shorthand

The essays in this focus on race and ethics approach the topic from a variety of perspectives. Yet they all advance a basic claim: race—a euphemism for white supremacy—is an ethical issue too often evaded. The essays demonstrate that the ethics of race is integrally bound up with religion, colonialism, and secularism

The Algorithm Theoretical Basis Document for the GLAS Atmospheric Data Products

The purpose of this document is to present a detailed description of the algorithm theoretical basis for each of the GLAS data products. This will be the final version of this document. The algorithms were initially designed and written based on the authors prior experience with high altitude lidar data on systems such as the Cloud and Aerosol Lidar System (CALS) and the Cloud Physics Lidar (CPL), both of which fly on the NASA ER-2 high altitude aircraft. These lidar systems have been employed in many field experiments around the world and algorithms have been developed to analyze these data for a number of atmospheric parameters. CALS data have been analyzed for cloud top height, thin cloud optical depth, cirrus cloud emittance (Spinhirne and Hart, 1990) and boundary layer depth (Palm and Spinhirne, 1987, 1998). The successor to CALS, the CPL, has also been extensively deployed in field missions since 2000 including the validation of GLAS and CALIPSO. The CALS and early CPL data sets also served as the basis for the construction of simulated GLAS data sets which were then used to develop and test the GLAS analysis algorithms