Towards a Model Theory for Transseries

The differential field of transseries extends the field of real Laurent series, and occurs in various context: asymptotic expansions, analytic vector fields, o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field, and report on our efforts to understand its first-order theory.Comment: Notre Dame J. Form. Log., to appear; 33 p

Dimension in the realm of transseries

Let $\mathbb T$ be the differential field of transseries. We establish some basic properties of the dimension of a definable subset of ${\mathbb T}^n$, also in relation to its codimension in the ambient space ${\mathbb T}^n$. The case of dimension $0$ is of special interest, and can be characterized both in topological terms (discreteness) and in terms of the Herwig-Hrushovski-Macpherson notion of co-analyzability. The proofs use results by the authors from "Asymptotic Differential Algebra and Model Theory of Transseries", the axiomatic framework for "dimension" in [L. van den Dries, "Dimension of definable sets, algebraic boundedness and Henselian fields", Ann. Pure Appl. Logic 45 (1989), no. 2, 189-209], and facts about co-analyzability from [B. Herwig, E. Hrushovski, D. Macpherson, "Interpretable groups, stably embedded sets, and Vaughtian pairs", J. London Math. Soc. (2003) 68, no. 1, 1-11].Comment: 16 pp; version 2, taking into account comments by the refere

Teaching functional programming to first-year students

In the period 1986-1991, experiments have been carried out with an introductory course in computer programming, based on functional programming. Due to thorough educational design and evaluation, a successful course has been developed. This has led to a revision of the computer programming education in the first year of the computer science curriculum at the University of Twente. This article describes the approach, the aim of the computer programming course, the outline and subject matter of the course and the evaluation. Educational research has been done to assess the quality of the course. Contents 1 Introduction 50 1.1 Motivation 50 1.2 The students 51 2 The computer programming course 51 2.1 Functional Programming 52 2.2 Imperative Programming 53 2.3 Programming techniques 53 2.4 Instructional material 54 3 Evaluations 55 3.1 Observations 55 3.2 Problems 56 3.3 Functional versus imperative programming 58 4 Programming project 60 4.1 Organisation 61 4.2 Railway information sys..

Filling gaps in Hardy fields

We show how to fill "countable" gaps in Hardy fields. We use this to prove that any two maximal Hardy fields are back-and-forth equivalent.Comment: 57 p

Maximal Hardy Fields

We show that all maximal Hardy fields are elementarily equivalent as differential fields, and give various applications of this result and its proof. We also answer some questions on Hardy fields posed by Boshernitzan.Comment: 470 pp. This document is not intended for publication in its current for

Using satellite imagery analysis to redesign provincial parks for a better cooling effect on cities

The purpose of this research is to analyse the thermal behaviour of South Holland provincial parks during heat waves, in order to provide design adaptation guidelines to increase their cooling capacity over the hotspots present in their urban surroundings. This research analyses the thermal behaviour of different land use patches (forests, cropland, grassland, water surfaces, built areas and greenhouse areas) present in the six South Holland provincial parks during heat waves. It studies their average night land surface temperature (LST) (with Modis 11A1), day LST (with Landsat 5TM), NDVI, imperviousness, patch size and patch shape index, and analyses through a multiple regression analysis the impact of each of these last four parameters in the night and day LST for each land use. Based on these conclusions, a set of design guidelines are provided to improve the cooling capacity of Midden-Delfland park areas which are adjacent to hotspots with day LST above 41°C and with day LST between 36°C and 41°C. The average day LST within South Holland provincial parks varies from 25.9°C for water surfaces, to 31.4°C for forests, 33°C for cropland, 33.1°C for greenhouse areas, 34.9°C for grassland patches and 37.9°C for built areas. Within each land use category, NDVI, imperviousness and patch shape index influence differently the thermal behaviour of the patches. NDVI is inversely correlated to day LST for all categories, imperviousness is correlated to day LST for all areas which do not comprise a significant presence of greenhouses (grassland and built patches) and inversely correlated to LST for areas with a high presence of greenhouses (cropland and warehouses). Finally, the shape index varies depending on the nature of the surrounding patches, especially for small patches (built areas, forests and greenhouse areas). Most of the hotspots surrounding the Midden-Delfland park are adjacent to grassland patches. The measure to increase the cooling capacity of those patches would consist in a change of land use and or an increase of the NDVI of the existing grassland patches. These suggestions to increase the cooling potential of the parks remain deliberately open in order to allow combining these measures with other spatial planning priorities