Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

Philosophers and practical men: Charles Babbage, Irish merchants and the economics of information

Before the emergence of coordination of production by firms, manufacturers and merchants traded in markets with asymmetric information. Evidence suggests that the practical knowledge thus gained by these agents was well in advance of contemporary political economists and anticipates twentieth-century developments in the economics of information. Charles Babbage, who regarded merchants and manufacturers as the chief sources of reliable economic data, drew on this knowledge as revealed in the evidence of manufacturers and merchants presented to House of Commons select committees to make an important pioneering contribution to the theory of production and exchange with information asymmetries.