The Fractal Theory of Central Place Geometry: A Diophantine Analysis of Fractal Generators for Arbitrary Löschian Numbers

We develop material to determine whether or not an arbitrary number is Löschian; the procedure embodied in the theorems achieves the desired result more swiftly than do previous solutions to this problem. The correspondence between a partition of the central place lattice and a quadratic form permits the rapid determination of the lattice coordinates of an arbitrary Löschian number and of the exact shape of a single fractal generator used to form an entire central place hierarchy associated with an arbitrary Löschian number. Central place hierarchies may be generated geometrically using a single shape applied initially to a hexagon and subsequently, scaled appropriately, to resultant polygons. Fractional dimensions of arbitrary central place hierarchies, measuring their “space-filling” characteristics, follow naturally from this general procedure.     

A Location-Allocation Model of Lösch's Central Place Theory: Testing on a Uniform Lattice Network

This paper develops a location-allocation model of Lösch's central place theory that maximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. F.o.b. costs, economies of scale, and elastic demand are included. Consumer behavior postulates concerning the “nearest center hypothesis” and the “indifference principle” are formulated as nonlinear constraints but not used during solution. Methods are developed for simulating the continuous, infinite plain with a discrete, bounded network by use of an outer overflow network and a symmetrical market area constraint. The model is tested by applying it to a uniform lattice network and comparing the results to the expected pattern of nested hexagons. Solutions consistent with the k = 3, 4, and 7 patterns are generated by changing threshold values. However, remaining inconsistencies appear to be due to the inability to express the consumer behavior laws as linear constraints, to the bounded and discrete nature of the network, and to the objective function being the sum of integer variables. The long-run purpose of developing and validating a location-allocation model of a location theory is to use it to relax the theory's restrictive assumptions and to apply the theory to nonuniform regions.     

The Lösch System of Market Areas: Derivation and Extension

Certain aspects of Lösch's classic work on the network of markets and the system of networks have not yet been clearly explained in the literature. Lösch did not describe his derivation procedures in full, and apparent printing errors in certain förmulae confuse the issue further, with the result that several recent texts reproduce Lösch's diagrams but offer no explanation of how they are constructed. Accepting the network of hexagonal market areas for a continuous system of markets, given an even but discrete distribution of population, the derivation from first principles of the complete system of different market areas is presented. Apparent errors in the translated text of Lösch's work are corrected. Limitations in some other authors' work and accordance with earlier empirically derived formulae are mentioned. The production of “city-rich” and “city-poor” sectors is shown to be a constraint on, rather than a result of, the system, and Lösch's statement that the coincidence of centers is maximized is clarified. The extension of the Lösch system to the internal tertiary structure of the city is presented and attention drawn to the empirical attractiveness of this approach.     

The "Return of the Subject" As a Historico-Intellectual Problem

Recently, a call for the “return of the subject” has gained increasing influence. The power of this call is intimately linked to the assumption that there is a necessary connection between “the subject” and politics (and ultimately, history). Without a subject, it is alleged, there can be no agency, and therefore no emancipatory projects—and, thus, no history. This paper discusses the precise epistemological foundations for this claim. It shows that the idea of a necessary link between “the subject” and agency, and therefore between the subject and politics (and history) is only one among many different ones that appeared in the course of the four centuries that modernity spans. It has precise historico‐intellectual premises, ones that cannot be traced back in time before the end of the nineteenth century. Failing to observe the historicity of the notion of the subject, and projecting it as a kind of universal category, results, as we shall see, in serious incongruence and anachronisms. The essay outlines a definite view of intellectual history aimed at recovering the radically contingent nature of conceptual formations, which, it alleges, is the still‐valid core of Foucault's archeological project. Regardless of the inconsistencies in his own archeological endeavors, his archeological approach intended to establish in intellectual history a principle of temporal irreversibility immanent in it. Following his lead, the essay attempts to discern the different meanings the category of the subject has historically acquired, referring them back to the broader epistemic reconfigurations that have occurred in Western thought. This reveals a richness of meanings in this category that are obliterated under the general label of the “modern subject”; at the same time, it illuminates some of the methodological problems that mar current debates on the topic.     

The Misuse of Area in Mapping Census-Type Numbers

Abstract

Polish lands in 19th century are usually located in the economic peripheries of Europe. However there are no usable datasets of Polish GDP for this period to verify this hypothesis. The main problem is lack of reliable and comparable macroeconomic data from country divided between Russia, Austria and Prussia. The main goal of this research was to propose the method based on the urbanization data set to estimate the GDP of Polish territories and to verify the hypothesis on the peripheral development of Polish lands. In result the new estimates on GDP per capita were established, that allowed to confirm the hypothesis of semi-peripheral development of Polish territories in 19th century and slow process of catching-up with the core economies.     

欧洲整体的历史与整体的阐述——评《欧洲的分与合》

《欧洲的分与合》这部著作具有重大的学术价值：这是中国史学界第一次真正把欧洲作为一个整体来阐述它的历史发展,论证了当代欧洲发生巨变的必然性;标志着中国史学界在欧洲史研究领域取得了突破性进展。《欧洲的分与合》以其对欧洲整体的历史作出整体阐述的风格,超越了以往众多的欧洲史著作。     

The Price Theory of Thünen's Theory of Rent: Assumptions and Implications of a Familiar Model

Economic forces in the Thünen rent diagram and the equivalence of certain Thünian and Ricardian land rent concepts are shown diagrammatically. The usual, linear rent line requires fixed production coefficients in agriculture and constant costs in transportation. The ability to substitute among land and other inputs in agriculture makes the rent line convex to the origin, as do decreasing costs in transportation. Increasing cost transportation makes the rent line concave. Traditional, subsistence agriculture is likely to produce a more strongly convex rent line than modern, large-scale agriculture.
Les forces économiques dans le diagramme de rente de Thünen et l'equivalence de certains concepts de rente foncier Thünien et Ricardien sont exposés graphiquement. La courbe de rente linéaire exige des coëfficients de production fixes en agriculture et des coûts de transport fixes. La capacitéà substituer entre la terre et d'autres facteurs de production en agriculture, ainsi que des coûts de transport décroissants, donnent une courbe de rente convexe par rapport à 1'origine. Des coûts de transport accroissants donnent une courbe de rente concave. Une agriculture à petite échelle, traditionnelle, donnera probablement une courbe de rente plus convexe qu'une agriculture moderne, à grande échelle.     

The p‐Regions Problem. p‐区域问题

The p‐regions problem involves the aggregation or clustering of n small areas into p spatially contiguous regions while optimizing some criteria. The main objective of this article is to explore possible avenues for formulating this problem as a mixed integer‐programming (MIP) problem. The critical issue in formulating this problem is to ensure that each region is a spatially contiguous cluster of small areas. We introduce three MIP models for solving the p regions problem. Each model minimizes the sum of dissimilarities between all pairs of areas within each region while guaranteeing contiguity. Three strategies designed to ensure contiguity are presented: (1) an adaptation of the Miller, Tucker, and Zemlin tour‐breaking constraints developed for the traveling salesman problem; (2) the use of ordered‐area assignment variables based upon an extension of an approach by Cova and Church for the geographical site design problem; and (3) the use of flow constraints based upon an extension of work by Shirabe. We test the efficacy of each formulation as well as specify a strategy to reduce overall problem size.