The Distance 4-Sector of Two Points Is Unique
نویسندگان
چکیده
The (distance) k-sector is a generalization of the concept of bisectors proposed by Asano, Matoušek and Tokuyama. We prove the uniqueness of the 4-sector of two points in the Euclidean plane. Despite the simplicity of the unique 4-sector (which consists of a line and two parabolas), our proof is quite non-trivial. We begin by establishing uniqueness in a small region of the plane, which we show may be perpetually expanded afterward.
منابع مشابه
New spatial clustering-based models for optimal urban facility location considering geographical obstacles
The problems of facility location and the allocation of demand points to facilities are crucial research issues in spatial data analysis and urban planning. It is very important for an organization or governments to best locate its resources and facilities and efficiently manage resources to ensure that all demand points are covered and all the needs are met. Most of the recent studies, which f...
متن کاملSOME POINTS ON CASIMIR FORCES
Casimir forces of massive ferrnionic Dirac fields are calculated for parallel plates geometry in spatial space with dimension d and imposing bag model boundary conditions. It is shown that in the range of ma>>l where m is mass of fields quanta and a is the separation distance of the plates, it is equal to massive bosonic fields Casimir force for each degree of freedom. We argue this equalit...
متن کاملOn the Structure of Metric-like Spaces
The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...
متن کاملIdentifying and Prioritizing Entrepreneurship Development Strategies in the Agricultural Sector of Khuzestan Province
Agricultural Entrepreneurship One of the areas of entrepreneurship is the acceptance of the risks of a production, service, and business unit related to agricultural activities. The purpose of this study was to analyze the strengths, weaknesses, opportunities and threats of entrepreneurship development in the agricultural sector of Khuzestan province using AHP-SWOT integrated approach. The res...
متن کاملMeasuring the Similarity of Trajectories Using Fuzzy Theory
In recent years, with the advancement of positioning systems, access to a large amount of movement data is provided. Among the methods of discovering knowledge from this type of data is to measure the similarity of trajectories resulting from the movement of objects. Similarity measurement has also been used in other data mining methods such as classification and clustering and is currently, an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013