Showing papers by "Université du Québec à Montréal published in 1977"

Turnpike Properties for the Optimal Use of a Natural Resource

Abstract: This paper is an attempt to deal rigorously with some fundamental mathematical problems arising from the consideration of natural resources in the neoclassical framework of optimal economic growth. The theory of optimal economic growth initiated by Ramsey [20] and developed by many others has benefited considerably from an optimal control formulation (see for example [1] and [22]). Incidentally it posed two interesting problems which seem to be typical of these economic models. The first one concerns the precise formulation of the Turnpike Property (see Cass [5]), the second one is the definition and the characterization of the optimality when the time interval considered is infinite and the formulation of existence conditions for such an optimal solution (see Koopmans [14]). It appeared that the two problems are linked together through the important role played in both problems by an optimal steady state suitably defined (see for example Gale [9] and McKenzie [17] for discrete time growth models and Haurie [11] for continuous time control systems). In the case of optimal exploitation of a natural resource, the Turnpike Property is well illustrated by the very simple model of optimal fish-harvesting studied by Cliff and Vincent [6] (this model is very close to the one proposed by Plourde [19]). Those authors showed that, for their particular model, any optimal trajectory on a sufficiently large interval would contain a singular arc where the fish population is maintained at its level of maximal yield, this singular arc being independent of the initial and terminal conditions. This result is similar to the turnpike property first presented in DOSSO [8] for efficient programmes of capital accumulation and then extended to the neoclassical optimal growth framework. However no formal proof has been given yet for an extension of the turnpike property to the case of an optimal growth model where both capital and natural resources enter into the production process. A first difference between capital and resource assets is that the former enter as stock inputs in the production process while the latter are often flow inputs. Another difference is that capital depreciates over time and is reproducible through investment while a natural resource is depleted by its use in the economic process and, when replenishable, reproduces itself according to a natural law. In Section 3 this extended turnpike property is proven for a continuous time model and expressed as a bound for the measure of the time spent away from the Von Neumann Set of the economy, a set which always contains the optimal steady state. This is essentially an adaptation of the classical result obtained by McKenzie in a discrete time setting without natural resources. When the Von Neumann set reduces to a

Clivages, régions et science politique: application d'un schéma d'analyse aux cas de la Suisse et de la Belgique

Abstract: The purpose of this article is to create a method for determining regions which is suitable for political science. The criteria proposed to define a “political region” are based on the concepts of political cleavages and party systems. Applying this framework of analysis to Belgium and Switzerland makes it possible to establish two very different kinds of regions. In the case of Switzerland, the proposed political regions do not correspond to linguistic areas but are instead combinations of religious and industrial factors. On the other hand, in the case of Belgium the suggested political regions reflect the tensions among the Flemings, Walloons, residents of Brussels, and German-speaking Belgians.

A proposed air quality index for urban areas

Abstract: A critical review of various air quality indices is made. Two shortcomings of these indices are indicated and remedied in a proposed urban air quality index (UAQI). A few computations on Canadian air pollution data show how this new index is an improvement over the past ones.

The Oil Crisis and the Emerging World Order

Abstract: The paper outlines a conceptual framework for understanding and analyzing the structuring of an institutional order. Particular attention is given to developments which make institution restructuri...

Stability, structural stability, and games: Toward a theory of differential hypergames

Abstract: Differential games (DG's) are investigated from a stability point of view. Several resemblances between the theory of optimal control and that of structural stability suggest a differential game approach in which the operators have conflicting interests regarding the stability of the system only. This qualitative approach adds several interesting new features. The solution of a differential game is defined to be the equilibrium position of a dynamical system in the framework of a given stability theory: this is the differential hypergame (DHG). Three types of DHG are discussed: abstract structural DHG, Liapunov DHG, and Popov DHG. The first makes the connection between DG and the catastrophe theory of Thom; the second makes the connection between the value function approach and Liapunov theory; and the third provides invariant properties for DG's. To illustrate the fact that the theory sketched here may find interesting applications, the up-to-date problem of the world economy is outlined.

A non-stationary two-variable operational calculus and its use in the synthesis of distributed parameter systems†

Abstract: A generalized operational two-variable calculus is proposed which uses algebraic properties of differential polynomials only and deals with partial differential equations with space- and time-dependent coefficients. The main result is an extension of the decomposition formula of Heaviside which provides a new approach to non-stationary distributed parameter systems. Two applications are given: a general method for solving linear partial differential equations with space-dependent coefficients; and an approach to the synthesis of non-stationary distributed parameter systems which may be considered as an extension of the Guillemin and Truxal's method for lumped parameter systems. The block-diagram of the compensating network so obtained is given and its feasibility is pointed out

Quatenus (de la contradiction en philosophie)

Abstract: Le principe de non-contradiction a depuis tres longtemps etereconnu comme le principe le plus fondamental de la pensee rationnelle. II est facile de l'enoncer sous sa forme symbolique: – (P.–P). Ce principe pose que quelqu'un ne saurait affirmer en meme temps une proposition et sa negation. Pour que ce principe ne demeure pas une exigence vide, il faut en outre que l'on puisse determiner avec precision quelles sont les conditions de son application. Cette determination des conditions d'application d'un principe commence par la recherche des moyens par lesquels il est possible de demarquer, dans le champ de son application, ce qui en respecte l'enonce de ce qui n'en respecte pas l'enonce. Or si rien n'est plus facile que de formuler un precepte, rien, appa-remment, n'est plus difficile que de tracer une ligne nette entre ce qui se conforme au precepte et ce qui le transgresse. Bien qu'il soit l'assise la plus profonde de nos raisonnements, le principe de non-contradiction ne fait pas exception a ce constat. Son enonce fait sans doute l'unanimite mais il est assez rare que l'on s'accorde, en dehors des disciplines formelles, sur ce qui constitue l'occurrence d'une contradiction. Cet accord sur ce qui constitue ou non l'exemple d'une contradiction m'apparait faire defaut d'une facon particulierement marquee en philosophic Cette situation pose un double probleme.