Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Beam steering due to displaced slots

Using a two-dimensional algorithm, steering of triode slots was investigated for the first time with a reasonable accounting of the ion extraction sheath

2D accelerator design for SITEX negative ion source

Solving the Poisson-Vlasov equations where the magnetic field, B, is assumed constant, we optimize the optical system of a SITEX negative ion source in infinite slot geometry. Algorithms designed to solve the above equations were modified to include the curved emitter boundary data appropriate to a negative ion source. Other configurations relevant to negative ion sources are examined

Why aren't countries rich?: Weak states and bad neighbourhoods

This article challenges a common viewpoint that the policy choices made by state leaders are central to explanations of economic growth. It argues that there are two possible flaws in this viewpoint. First, that state leaders have a free choice in policy decisions; second, that it is policies that in large part determine growth rates. Using a set of variables designed to capture the weakness of the policy autonomy of the state and possible non-policy influences on growth rates, the article concludes that initial conditions are a better determinant of wealth and growth than free policy choice.