MARKET CAPTURE BY TWO COMPETITORS: THE PREEMPTIVE LOCATION PROBLEM*

ABSTRACT. We consider a location and allocation game for two competitor firms, A and B, that each seek to locate p facilities in a network. A market is captured by a particular firm if that market's closest facility belongs to that firm rather than a competitor. The question is as follows: Firm A wants to locate its p facilities so that B, which enters also with p facilities after Firm A has located its facilities, will capture the minimum market value possible. That is, Firm A wishes to preempt Firm B in its bid to capture market share to the maximum extent possible. A model is presented that addresses this issue, together with solution methods and computing times.     

THE MAXIMUM CAPTURE PROBLEM IN A WEIGHTED NETWORK*

ABSTRACT. In this paper, a conditional location problem on a weighted network is examined. Attraction functions are defined and the problem is formulated as a mixed integer program. A method which simultaneously locates an additional facility on the given network and optimizes its weight is then described. A numerical example is provided.     

旅游吸引物空间结构分析——以中国首批国家4A级旅游区(点)为例

本文利用地理数学方法中的空间分析手段,通过对首批国家4A级旅游区(点)在不同地域范围的空间分布规律进行研究,以及对各旅游区(点)与非农业人口在20万以上的城市之间的空间关系分析,揭示了国家首批4A级旅游区(点)的空间结构整体特征,以及与不同规模客源市场之间的距离分异特征,为旅游目的地空间结构理论研究提供了基础方法。     

The Experiment in Archaeology: A Comparison of Two Case Studies

Abstract

A critical comparison is made between two recent case studies in American archaeology, The Dynamics of Stylistic Change in Arikara Ceramics by James Deetz and “Archaeology as Anthropology: A Case Study” by William A. Longacre. The notion of experiment is introduced as a standard of comparison which results in a lesson about archaeology as a science.     

Nonlinear Modeling and Mitigation of Seismic Pounding between R/C Frame Buildings

A multi-link finite element contact model reproducing Jankowski’s nonlinear viscoelastic relationships is devised and implemented for a time-history analysis of seismic pounding. The mechanical and algorithmic parameters are calibrated with a numerical test case study, represented by two single-story R/C frames. A real case study, concerning two adjacent buildings representative of a stock of R/C multi-story frame structures with insufficient separation joints at rest, is then examined. A damped interconnection-based mitigation solution consisting in linking the two structures with fluid-viscous dissipaters is proposed. The benefits of this retrofit strategy are discussed by comparison with the response in original conditions.     

Rewriting the end of the Early Bronze Age in the United Arab Emirates through the anthropological and artefactual evaluation of two collective Umm an-Nar graves at Hili (eastern region of Abu Dhabi)

The Hili archaeological complex in Al Ain (U.A.E.) is important for its wealth of third-millennium BC Umm an-Nar burial and settlement sites. Two of the most significant burial sites are Tomb N at Hili and Tomb A Hili North. The latter is a classic circular Umm an-Nar monumental grave, while Hili N is a pit-grave, one of only two Umm an-Nar period pit-graves discovered so far in the U.A.E. Both of these tombs contained the remains of hundreds of individuals, in the case of Tomb A Hili North, more than 300, while around 600 people had been deposited in Hili N. Both population groups have been the subject of anthropological and artefactual analyses and a comparison of the findings help to shed light on the chronology of the end of the Umm an-Nar period.     

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.     

COMPETITIVE FACILITIES: MARKET SHARE AND LOCATION WITH RANDOM UTILITY*

ABSTRACT. A new approach is proposed for calculating the expected market share. It is assumed that consumers patronize a facility according to a utility function, selecting the facility with the highest utility value. However, consumers'ratings of the utility components are stochastic by some random distribution. Therefore, the buying power of customers located at the same point is divided among several facilities. A probability that a consumer patronizes a certain facility can be calculated. Consequently, the expected market share by competing facilities can be estimated. This calculation is more than 1,000 times faster than repeating a simulation enough times to achieve a reasonable accuracy. The distance decay calculated using the new approach is approximately exponential. A procedure for finding the optimal location anywhere in the plane for a new facility that maximizes the market share is also introduced.     

Zones of Influence of Middle-Size Cities,Their Boundaries and Passenger Flows

A modified gravity model is used to describe the flows of commuters between a central city and concentric zones around it. A multiplier-type model of a central-place system (after Christaller) is then used to calculate the number of residents for service centers at each level of the hierarchy within the system. The rank-size rule (Zipf's formula) is also considered as a criterion of a true system of urban places. Results are presented for the urban network of the Ukraine.     

ELASTIC EARTH PRESSURES ON RIGID WALLS UNDER EARTHQUAKE LOADING

Elastic dynamic earth pressures induced by earthquakes are computed by analyzing a wall-foundation-backfill system. Both foundation and backfill are considered viscoelastic; the foundation is a semi-infinite space and the backfill, a uniform layer of constant thickness. A simple analytical solution is developed by assuming an approximate backfill-foundation interface condition and adopting the least squares method. The response functions computed indicate the large influence of the various system parameters on earth pressure, including the foundation characteristics,as well as wall geometry and mass. The transient response of the system is also studied by obtaining spectra for base shear. A large number of seismic records are analyzed to obtain average spectra and a total of three correction functions are used to take into account the foundation stiffness and density as well as wall inertia. A simple design method is proposed to estimate the maximum base shear.     

Shackleton Limestone archaeocyaths

A new monotypic genus of cheirurine trilobite, Azyptyx, is described based on the new species A. toongabbiensis from Early Devonian (late Lochkovian) limestones of the Wurutwun Formation near Toongabbie, Victoria. A feature of the genus that is unusual for the subfamily is a continuous basal glabellar furrow (S1) that does not normally meet the occipital furrow medially.     

Parameterization of the radiative flux divergence in the 9.6 μm O3 band

A parameterization of the cooling rate of the Earth's atmosphere in the height region of approximately 20–75 km due to radiation transfer in the 9.6 μm O₃ band is proposed. A general random band model is used to calculate the radiation transmission. The parameterization takes into consideration a peculiar feature of the radiative transfer—the height step increases with growing distance from the level for which cooling is calculated. A simple method of accounting for the variation of the vertical profile of the absorbing gas is proposed and utilized. The procedure proposed is multiparametric: 22 parameters are prescribed for calculating cooling at a given level. The procedure can be recommended for calculating radiative cooling for any temperature and ozone profile not having a small- or meso-scale structure. It can be used, in particular, for modelling of the middle atmospheric circulation.     

SPATIAL ASYMMETRIC DUOPOLY WITH AN APPLICATION TO BRUSSELS' AIRPORTS*

ABSTRACT In this paper, the problem of a city with access to two firms or facilities (shopping malls, airports, commercial districts) selling a differentiated product (shopping, flights) and/or offering a differentiated workplace is studied. Transport connections to one facility are congested. A model is presented for this asymmetric duopoly game that can be solved for a Nash equilibrium in prices and wages. A comparative statics analysis is used to illustrate the properties of the equilibrium. A numerical model is then applied to the two Brussels airports. Three stylized policies are implemented to address the congestion problem: expansion of transport capacity, congestion pricing, and a direct subsidy to the uncongested facility. Our results indicate that the degree of intrinsic differentiation between the two firms is crucial in determining the difference in profit and market share. Price and wage differences also depend on trip frequency and consumer preferences for diversity. Congestion pricing is the most effective policy tool but all three options are shown to have attractive attributes.     

Building a GIScience Community in Cyberspace: reflections on GIScOnline

In this paper, distance learning is defined not as the physical separation of students from a tutor but by the need to facilitate group learning, interaction and a sense of community amongst course participants. A critical review of an established distance-learning course is made reflecting on the team's experiences of building a learning community in cyberspace. The successes and failures are recorded, as are the barriers to engendering a sense of kinship on the course. A survey of students' own experiences with and feeling towards various communication technologies is also presented.     

Using AMOEBA to Create a Spatial Weights Matrix and Identify Spatial Clusters

The creation of a spatial weights matrix by a procedure called AMOEBA, A Multidirectional Optimum Ecotope-Based Algorithm , is dependent on the use of a local spatial autocorrelation statistic. The result is (1) a vector that identifies those spatial units that are related and unrelated to contiguous spatial units and (2) a matrix of weights whose values are a function of the relationship of the ith spatial unit with all other nearby spatial units for which there is a spatial association. In addition, the AMOEBA procedure aids in the demarcation of clusters, called ecotopes, of related spatial units. Experimentation reveals that AMOEBA is an effective tool for the identification of clusters. A comparison with a scan statistic procedure (SaTScan) gives evidence of the value of AMOEBA. Total fertility rates in enumeration districts in Amman, Jordan, are used to show a real-world example of the use of AMOEBA for the construction of a spatial weights matrix and for the identification of clusters. Again, comparisons reveal the effectiveness of the AMOEBA procedure.     

The Information—Gradient Method in Geographical Regionalization

In terms of information theory, homogeneous regions are viewed as areas in which an observer is likely to gain little new information in terms of a selected parameter or set of parameters as he moves about the region. The values of the parameter would be significantly different in an adjoining region. Adjoining points with significantly different parametric values would lie in different regions. The boundary between regions would be drawn in places where the observer would gain a maximum of new information within a unit distance. A mathematical procedure is developed to measure the gain of information along a set of profile lines drawn through a study area. A maximum information increment within a given interval is interpreted as marking a regional boundary. A minimum gain is interpreted as designating the regional core. The technique is illustrated with particular reference to the delimitation of landscape regions. Landscape boundaries identified by the information—gradient technique are found to come close to boundaries delimited by conventional means on the basis of photo interpretation.     

ON THE INTERPRETATION OF FIXED INPUT COEFFICIENTS UNDER AGGREGATION*

ABSTRACT A fixed input coefficient is traditionally interpreted as the additional input from one sector that is required for an additional unit of output in another sector. It is shown that this ratio of increments is, in general, not fixed under aggregation. A tight upper and lower bound for its variation are derived. A necessary and sufficient condition for the ratio to be fixed is obtained. As a consequence, adopting the common assumption of fixed input coefficients implies that additional assumptions at any subaggregate level are required. Similar results are given for the Leontief inverse, whose typical element is usually interpreted as the additional output in one sector that is required for an additional unit of final demand in another sector.     

Secondary cancer in an Anglo-Saxon female

A mature/elderly female skeleton from the Anglo-Saxon cemetery at Eccles, Kent, is described. A diagnosis of Paget's disease of the left tibia is made. The macroscopic radiological features of perforating and non-perforating osteolytic lesions in the cranium and femora are described. The differential diagnosis is discussed. The lesions are considered to be due to metastatic carcinoma, possibly from a primary carcinoma of the breast. There is a brief resumé of other recorded examples of metastatic carcinoma in early skeletons.     

Eine unvollendete sabäische Urkunde

A certificate concerning a transaction in cereal, inscribed in wood, and in Sabaean language is discussed here. The text was never completed. At the beginning of the text at least two words are missing. The reason was probably a mistake in line 2. Of particular interest is the dating. An eponym is mentioned, who was a contemporary of Šā'irum Awtar. It can be assumed that the text was written in the early 3^rd ct. A.D.