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  • 1
    Electronic Resource
    Electronic Resource
    Boston, USA and Oxford, UK : Blackwell Publishers Inc
    Journal of regional science 42 (2002), S. 0 
    ISSN: 1467-9787
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: An explanation for the rank-size distribution for human settlements based on simple stochastic models of settlement formation and growth is presented. Not only does the analysis of the model explain the rank-size phenomenon in the upper tail, it also predicts a reverse rank-size phenomenon in the lower tail. Furthermore it yields a parametric form (the double Pareto-lognormal distribution) for the complete distribution of settlement sizes. Settlement-size data for four regions (two in Spain and two in the U.S.) are used as examples. For these regions the lower tail rank-size property is seen to hold and the double Pareto-lognormal distribution shown to provide an excellent fit, lending support to the model and to the explanation for the rank-size law.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 52 (1990), S. 583-596 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 53 (1991), S. 215-229 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 54 (1992), S. 185-207 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The maximum principle of deterministic optimal control, which has proved to be a very useful tool in theoretical bioeconomics, is extended in this article to cover the optimal exploitation of a biological resource vulnerable to catastrophic collapse, the probability of which may depend in general on the state of the resource, the current control and time. A general formulation of the maximum principle for such stochastic problems is presented and a number of applications are outlined. These include: optimal harvesting of a fishery vulnerable to catastrophic collapse; optimal thinning of a forest vulnerable to fire; optimal expenditure and investment in forest fire protection and optimal consumption-pollution tradeoffs in an ecosystem vulnerable to pollution-related collapse. In addition an application of the method to a highly stylized behavioral ecology model is given.
    Type of Medium: Electronic Resource
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