This is a geometric approach to spatial involute gearing which has recently been developed by Jack Phillips (2003). After recalling Phillips' fundamental theorems and other properties, some geometric questions around this interesting type of gearing are discussed.

We study the simultaneous approximation properties of the Bézier variant of the well known Phillips operators and estimate the rate of convergence of the Phillips-Bézier operators in simultaneous approximation, for functions of bounded variation.

There are at least two broad categories of interpretation to consider when examining observations on a country’s output-inflation relationship (a country’s Phillips curve). On the one hand is the traditional interpretation, which emphasizes how such a relationship mainly reflects a country’s wageand price-setting institutions. In this case, the Phillips curve is viewed primarily as a structural...

We discuss some of the experimental motivation for the need for semigroup decay laws, and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the...

This paper presents three new systematic approaches for computing coefficient matrices of the Heffron-Phillips multi-machine model (K1, …, K6). The amount of computations needed for conventional and three new approaches are compared by counting number of multiplications and divisions. The advantages of new approaches are: (1) their computation burdens are less than 73 percent of that of convent...

At the core of modern macroeconomics is some version or another of the famous Phillips curve relationship between inflation and unemployment. The Phillips curve, both in itspriginal and more recently reformulated expectations-augmented versions, has two main uses. In theoretical models of inflation, it provides the so-called “missing equation” that explains how changes in nominal income divide ...

This paper studies optimal monetary policy in a model where inflation is persistent. Two types of price setters are assumed to exist. One acts rationally given Calvo-type constraints on price setting. The other type sets prices according to a rule-of-thumb. This results in a Phillips curve with both a forward-looking term and a backward-looking term. The Phillips curve nests a standard purely f...

We establish that the Phillips curve is persistence-dependent: inflation responds differently to persistent versus moderately (or transient) fluctuations in unemployment rate gap. This persistence-dependent relationship appears align with business-cycle stages and thus consistent existing theory. Previous work fails model this dependence, thereby finding numerous "inflation puzzles" – e.g., mis...

We use a Bayesian Markov Chain Monte Carlo algorithm jointly to estimate the parameters of a ‘true’ data generating mechanism and those of a sequence of approximating models that a monetary authority uses to guide its decisions. Gaps between a true expectational Phillips curve and the monetary authority’s approximating non-expectational Phillips curve models unleash inflation that a monetary au...