The Apollonius Circle Problem dates to Greek antiquity, circa 250 b.c. Given three circles in the plane, find or construct a circle tangent to all three. This was generalized by replacing some circles with straight lines. Viéte [Canon mathematicus seu Ad triangula cum adpendicibus, Lutetiae:...

The Bezout–Dixon resultant method for solving systems of polynomial equations lends itself to various heuristic acceleration techniques, previously reported by the present author, which can be extraordinarily effective. In this paper we will discuss how well these techniques apply to the...

The Dixon resultant method solves a system of polynomial equations by computing its resultant. It constructs a square matrix whose determinant (det) is a multiple of the resultant (res). The naïve way to proceed is to compute det, factor it, and identify res. But often det is too large to...

This paper deals with error correction models (ECM's) and cointegrated systems that are formulated in continuous time. Problems of representation, identification, estimation and time aggregation are discussed. It is shown that every ECM in continuous time has a discrete time equivalent model in...

This paper considers the evaluation of the average treatment effect (ATE) in a triangular system with binary dependent variables. I impose a threshold crossing model on both endogenous regressor and the outcome. No parametric functional form or distributional assumptions are imposed. Shaikh and...