Gravity-Type Interactive Markov Models—Part II: Lyapunov Stability of Steady States

In Part I of this paper (Smith and Hsieh, 1997) a programming formulation of steady states was developed for gravity-type interactive Markov chains in terms of their associated spatial-flow chains. These results are here applied to analyze the stability properties of interactive Markov chains. In particular, the objective function for this programming formulation is shown to constitute a Lyapunov function for an appropriately defined continuous-time version of spatial-flow chains. The Lyapunov stability properties of these spatial flows are then shown to yield corresponding stability properties for the continuous-time versions of interactive Markov chains. In particular, these processes always exhibit global convergence to steady states. Finally, it is shown that when steady states are unique, these convergence results are inherited by those interactive Markov chains that are 'sufficiently close' to their continuous-time versions.     

Global firms in local information societies: Work and employment issues for Europe

The strategies of large firms have a major influence on the evolution of the global information society because they dominate the markets for information and communication technologies. This paper examines the user rather than the producer role of large firms, and focuses on the surrounding issues relating to evolving patterns of work and employment. Its discussion of these issues and their policy significance reflects the perspective of the EU on what is effectively a global agenda on the future of work in the information society.     

CENTER POINTS, EQUILIBRIUM POSITIONS, AND THE OBNOXIOUS LOCATION PROBLEM

ABSTRACT. Real variable analysis has een used to great benefit in a variety of classical problems in location theory. In this paper we explore basic complex variable techniques in one formulation of the obnoxious location problem. A general definition of center points is first given and used to formulate several alternate versions of the obnoxious location problem. A logarithmic transformation is then used to demonstrate some equivalences between these families of distinct location problems (defined via center points). A prototype logarithmic potential function which results from this formulation is then investigated, and it is demonstrated that the extremal solutions with this objective reside on the boundary of its domain of definition. An application using zero- and one-dimensional centers is discussed, and a generalization to the spatial obnoxious problem is also briefly examined. We define a zero-dimensional center as a critical point of the logarithmic potential function, and it is shown that these centers are equivalent to the solutions of the Complex Moment Problem.     

A tale of two towns: Buntingford and Standon in the later middle ages

The controversy over the fortunes of English towns in the later middle ages has tended to generate more heat than light. Much of the evidence employed in this debate has been drawn from the larger English towns, but this essay suggests a widening of the research agenda to include a more systematic assessment of small towns and village markets. Although weakened by the reduced demand for grain after the Black Death, these places competed for the growing local trade in basic consumer goods. Evidence from northeast Hertfordshire reveals that this competition resulted in a significant restructuring of the hierarchy of local marketing centres, and a decline in the ability of seigneurial and urban authorities to regulate trading activity.