Run-down room, a table and two chairs.Von Neumann enters and finds himself alone.Takes a seat

This note gives five applications of the eater-food interaction model (Garding 2005) where cycle length is a function of the eater average birth rate defined as the inverse of average life span. The model extends to an analysis of predator-prey-food cycles (Garding 2000). Here the cycle length is the same as that of en eater-food interaction whose average 'birth rate' is the sum of the average birth rates of the predator-prey and prey-food interactions.

The cyclicity of Arctic populations of small rodents is a subject with a long history and a large literature (Batzli, 1992) in which the question What drives the cycle? has received many answers, among them that the source of the cycle is either rodent interaction with food or the interaction with predators or both. Another question concerns the confinement of the cycle to Arctic conditions. The paper by Garding (2000) presented a simple mathematical model of the combined predator-prey-food interaction based on a general eater-food interaction in which cycle length is an explicit decreasing function of the average birth rate of eaters. In the combined interaction, the cycle length is the same function of the sum of the average birth rates of predators and preys Numerical fits of these models make it possible to answer the questions above. The results are that the short 3-5 year cycles of the Arctic rodents: lemming (Lemmus lemmus) and vole (Microtus agrestis) are mainly driven by interaction with food while the ten year cycle of the Canadian snowshoe hare (Lepus americanus), is driven by interaction with its predator - lynx. Rodents in the Arctic live and breed in burrows and experience predation pressure when surfacing. This explains their interaction with food. The greater variety and easier availability of food in a temperate climate accounts for a missing rodent interaction with food. The paper starts with a presentation of the eater-food interaction model itself, its simple but unfamiliar mathematics and its points of credibility. At the end of the paper sonic current hypotheses about the nature of the rodent cycle are seen in the light of the model used here. (Less)

This paper presents a simple mathematical model for multiannual population cycles, in particular the periods, for the triple of small rodents and their predators and food. The parameters used are average birth rates of rodents and predators. The period lengths fit observations of lemmings and voles rather well and the model explains why the observed periods cluster around 4 years and around 10 years.

The aim of this paper is to give an elementary construction of global parametrices for fundamental solutions of first order pseudo-differential operators. It is a simplified and corrected version of the construction given in my lectures 1985 at the Nankai university in Tianjin, China (Garding [3]) and reported on in (Garding [4])

In the year of the Lord 1957 there appeared in volume 24 of Duke Journal a short paper by Peter Lax with the title ‘Asymptotic solutions of oscillatory initial value problems’. It was one of the first signs that the aera of microlocal analysis was approaching. In this lecture I will try to look at Lax’s paper in the context of what was before and what came after.

An extension of the theorem of Hunziker-van Winter-Zhislin on the location of the essential spectrum of many-body Hamiltonians.