Paul Deguire

Approachability and Fixed Points for Non-convex Set-Valued Maps*

This paper studies the approachability of upper semicontinuous nonconvex set-valued maps by single-valued continuous functions and its applications to fixed point theory. The use of “approximate selections” was initiated by J. von Neumann [41] in the proof of his well-known minimax principle. This remarkable property was extended to the normed space setting by Cellina [S] and Cellina and Lasota [9] in the context of a degree theory for upper semicontinuous convex compact-valued maps. It also holds for maps with compact contractible values defined on finite polyhedra of Iw” (Ma+Cole11 [40]) and more generally defined on compact ANRs (McLennan [39]). It was recently taken up by Gbrniewicz, Granas, and Kryszewski [22-241 in the context of an index theory for non-convex maps defined on compact ANRs. The content of this paper is divided into three parts. The first part is devoted to background material concerning the types of spaces and set-valued maps studied herein. In the second part we define the abstract class d of approachable set-valued maps; that is, the class of maps A: X+ Y

The competencies demonstrated by farmers while adapting to climate change

World population growth, overconsumption of resources, competition among countries and climate change are putting significant pressure on agriculture. In Canada, changes in precipitation, the appearance of new pests and poor soil quality are threatening the prosperity of small farmers. What human competencies could facilitate citizens’ adaptation to climate change? The competencies displayed by six Canadian farmers were observed as they tried to improve the quality of their soil in order to increase its climate resilience. The farmers in the case study demonstrated a wide array of skills while adapting to climate change. Used to adjusting their farming practices to bad weather, the participants predicted that their already declining soil was very vulnerable to extreme events. They implemented some adaptations: planting forage radish and practicing more crop rotations. During the adaptation process, the farmers showed in-depth local and agricultural knowledge, critical thinking (which they used to assess the solutions), futures thinking and hindsight, identification and control of the variables affecting the crops, openness to novelty, collaboration, optimism and self-efficacy. The research, which results in the identification of competencies conducive to adaptation, leads to the recommendation of a few educational strategies to strengthen adaptive competencies when supporting citizens in a climate change adaptation process.

Human competences that facilitate adaptation to climate change: a research in progress

Purpose – For communities threatened by current or impending climate change, adaptation is becoming a necessity. Although little research has been done on human competences so far, this research shows that some appear to facilitate the adaptation process. The purpose of this multiple‐case study is to identify adaptive competences demonstrated by two groups of Canadian citizens: municipal employees in a coastal community and farmers.Design/methodology/approach – As part of workshops based on a problem solving process, the two groups analyzed the impacts of climate change in their field of work and geographical area, chose a problem related to these impacts, suggested and then implemented adaptation measures. The municipal employees worked on sea level rise, whereas the farmers focused on poor soil quality, which makes it vulnerable to bad weather.Findings – By thematically analyzing the verbatim transcripts of the workshops and by building narratives, the authors were able to identify similar adaptive comp...

Competencies Demonstrated by Municipal Employees During Adaptation to Climate Change: A Pilot Study

Since coastal communities are already subjected to the impacts of climate change, adaptation has become a necessity. This article presents competencies demonstrated by Canadian municipal employees during an adaptation process to sea level rise. To adapt, the participants demonstrated the following competencies: problem solving (highlighting components of the problem and identifying constraints), futures thinking, risk prediction, vulnerability analysis, local knowledge, planning, and communication. However, some competencies that could be potentially useful in adaptation were used less frequently by participants: developing solutions, knowledge of adaptation, math skills, hope, and self-efficacy.

Generalized Fixed-Points and Systems of Minimax Inequalities

To begin, we recall the notion of selecting families, introduced by Deguire and Lassonde in [4] . We also recall a selection theorem and a generalized fixed-point theorem for Ky Fan families of set valued maps. Applications of those results are then presented: a generalization of the Tychonoff fixed-point theorem and a version of the KyFan intersection theorem for families of maps together with it’s analytical formulation, a very general system of minimax inequalities.