We consider permutations of {1, 2, . . . , n} in which each integer is given a direction; such permutations are called directed permutations. An integer k in a directed permutation is called mobile of its arrow points to a smaller integer adjacent to it. For example, for → 3 → 2 ← 5 → 4 → 6 → 1 , the integers 3, 5, and 6 are mobile. It follows that 1 can never be mobile since there is no intege...

We prove the existence of general equilibrium for continuous-time overlappinggenerations models. Previous theorems exclude all non-linear C.E.S. and von Neumann Morgenstern preferences and exclude production. Our primitive assumptions are satisfied by such preferences and by all Markovian production technologies satisfying Bewley's assumptions for Arrow Debreu models provided that storage is po...

This paper reports results of a qualitative study of sixteen students enrolled in a second year organic chemistry course for chemistry and chemical engineering majors. The focus of the study was student use of the arrow-pushing formalism that plays a central role in both the teaching and practice of organic chemistry. The goal of the study was to probe how students made sense of the arrow-pushi...

In this article we propose a calculus of qualitative geographic coordinates which allows reasoning about cardinal directions on grid-based reference systems in maps. Grids in maps can be considered as absolute reference systems. The analysis reveals that the basic information coded in these reference systems is ordering information. Therefore, no metric information is required. We show that it ...

It is well known that an equilibrium in the Arrow-Debreu model may fail to exist if a very restrictive condition called the survival assumption is not satisfied. We study two approaches that allow for the relaxation of this condition. Danilov and Sotskov (1990), and Florig (2001) developed a concept of a generalized equilibrium based on a notion of hierarchic prices. Marakulin (1990) proposed a...