Convergence and Stability of the Inverse Scattering Series for Diffuse Waves

We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence, stability and approximation error of the serie

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page

Continuity of the measure of the spectrum for quasiperiodic Schrodinger operators with rough potentials

We study discrete quasiperiodic Schr\"odinger operators on \ell^2(\zee) with potentials defined by $\gamma$-H\"older functions. We prove a general statement that for $\gamma >1/2$ and under the condition of positive Lyapunov exponents, measure of the spectrum at irrational frequencies is the limit of measures of spectra of periodic approximants. An important ingredient in our analysis is a general result on uniformity of the upper Lyapunov exponent of strictly ergodic cocycles.Comment: 15 page

A Bishop-Phelps-Bollobas Type Theorem for uniform algegras

This paper is devoted to showing that Asplund operators with range in a uniform Banach algebra have the Bishop¿Phelps¿Bollobas property, i.e., they are approximated by norm attaining Asplund operators at the same time that a point where the approximated operator almost attains its norm is approximated by a point at which the approximating operator attains it. To prove this result we use the weak*-to-norm fragmentability of weak*-compact subsets of the dual of Asplund spaces and we need to observe a Urysohn type result producing peak complex-valued functions in uniform algebras that are small outside a given open set and whose image is inside a Stolz region.This research was partially supported by MEC and FEDER projects MTM2008-05396 and MTM2011-25377. The research of the second author was also partially supported by Generalitat Valenciana (GV/2010/036), and by Universidad Politecnica de Valencia (project PAID-06-09-2829).Cascales, B.; Guirao Sánchez, AJ.; Kadets, V. (2013). A Bishop-Phelps-Bollobas Type Theorem for uniform algegras. Advances in Mathematics. 240:370-382. https://doi.org/10.1016/j.aim.2013.03.005S37038224

Time Asymmetric Quantum Physics

Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.Comment: Tex file with 2 figure

Revisiting the ‘Great Levelling’: the limits of Piketty’s Capital and Ideology for understanding the rise of late 20th century inequality

In Capital and Ideology, Thomas Piketty returns to questions of historical inequality, not merely to fill in the gaps in the earlier, widely circulated and impactful Capital in the 21st Century, but to undertake a far more ambitious and nuanced project. Critics (Bhambra and Holmwood 2017; Moeller 2015) pointed out that in the previous book, Piketty’s consideration of the role of high concentrations wealth on inequality focused largely on a handful of relatively wealthy countries (the US, UK, France, Germany and Japan). More importantly, it did not consider the political and economic relationships, forged by European colonization and the trans-Atlantic slave trade, that helped create lasting inequalities in wealth, status, education and life expectancy around the globe. These oversights corresponded to significant methodological gaps, in which inequalities defined by social status and identity, including gender, race and caste, were largely left out of considerations that centred around economic and material disparities. Yet these different forms of inequalities are intimately connected, as gender wage gaps and racial wealth gaps in different parts of the world attest

Schooling and Poor Children in 19th-Century America

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68138/2/10.1177_000276429203500307.pd

The theory and method of comparative area studies

Though many now downplay the tension between area studies and disciplinary political science, there has been little substantive guidance on how to accomplish complementarity between their respective approaches. This article seeks to develop the idea of comparative area studies (CAS) as a rubric that maintains the importance of regional knowledge while contributing to general theory building using inductive intra-regional, cross-regional, inter-regional comparison. Treating regions as theoretically-grounded analytical categories, rather than inert or innate geographical entities, can help inform both quantitative and qualitative attempts to build general theory.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline