Bishop Lightfoot as an Historian

Paolo Sylos Labini as a historian of economics

An Austrian (Mis)Reads Adam Smith: A Critique of Rothbard as Intellectual Historian

A Bishop surface with a vanishing Bishop invariant

We derive a complete set of invariants for a formal Bishop surface near a point of complex tangent with a vanishing Bishop invariant under the action of formal transformations. We prove that the modular space of Bishop surfaces with a vanishing Bishop invariant and with a fixed Moser invariant s < ∞ is of infinite dimension. We also prove that the equivalence class of the germ of a generic real...

The Mergelyan-Bishop Theorem

We define the differential operator ∂ ∂z on infinitely differentiable functions (also called smooth or C∞ functions) on some open set in C by ∂ ∂z = 1 2 ( ∂ ∂x + i ∂ ∂y ). A quick calculation shows that ∂ ∂z obeys the product rule. Recall that a function f is holomorphic if and only if ∂ ∂z (f) = 0. A function is biholomorphic, or an analytic isomorphism, if it is holomorphic and has holomorphi...

Mapping an ancient historian in a digital age

HESTIA (the Herodotus Encoded Space-Text-Imaging Archive) employs the latest digital technology to develop an innovative methodology to the study of spatial data in Herodotus’ Histories. Using a digital text of Herodotus, freely available from the Perseus on-line library, to capture all the place-names mentioned in the narrative, we construct a database to house that information and represent i...