A Theoretical Framework for Modeling Asymmetric, Nonpositive Definite and Nonuniform Distance Functions on Rn
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| Natura: | Artículo científico |
| Lingua: | en |
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Universidad Nacional Autónoma de México
2010
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| _version_ | 1876461784244682752 |
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| author | Herica Sánchez-Larios |
| author_facet | Herica Sánchez-Larios |
| contents | A Theoretical Framework for Modeling Asymmetric, Nonpositive Definite and Nonuniform Distance Functions on Rn Herica Sánchez-Larios Servio Tulio Guillén-Burguete Ingeniería non norm isotropy asymmetry uniformity In this paper, we give theoretical foundations for modeling distance functions on the usual Euclidean space Rn, where distance may refer to physical kilometers, liters of fuel consumed, time spent in traveling, or transportation cost. In our approach, a distance function d is derived from a function F0 called the fundamental function of d. Our distance functions, unlike metrics, can be asymmetric and non-positive definite, and unlike the Lp norms, they can be nonuniform. We illustrate our theoretical framework by modeling an asymmetric and non-uniform distance function on R2 which can take negative values. 2010 artículo científico 1665-6423 https://www.redalyc.org/articulo.oa?id=47415823010 en http://www.redalyc.org/revista.oa?id=474 Journal of Applied Research and Technology application/pdf Universidad Nacional Autónoma de México Journal of Applied Research and Technology (México) Num.3 Vol.8 |
| format | Artículo científico |
| id | redalyc_47415823010 |
| institution | Redalyc |
| language | en |
| publishDate | 2010 |
| publisher | Universidad Nacional Autónoma de México |
| spellingShingle | A Theoretical Framework for Modeling Asymmetric, Nonpositive Definite and Nonuniform Distance Functions on Rn Herica Sánchez-Larios Ingeniería non norm isotropy asymmetry uniformity A Theoretical Framework for Modeling Asymmetric, Nonpositive Definite and Nonuniform Distance Functions on Rn Herica Sánchez-Larios Servio Tulio Guillén-Burguete Ingeniería non norm isotropy asymmetry uniformity In this paper, we give theoretical foundations for modeling distance functions on the usual Euclidean space Rn, where distance may refer to physical kilometers, liters of fuel consumed, time spent in traveling, or transportation cost. In our approach, a distance function d is derived from a function F0 called the fundamental function of d. Our distance functions, unlike metrics, can be asymmetric and non-positive definite, and unlike the Lp norms, they can be nonuniform. We illustrate our theoretical framework by modeling an asymmetric and non-uniform distance function on R2 which can take negative values. 2010 artículo científico 1665-6423 https://www.redalyc.org/articulo.oa?id=47415823010 en http://www.redalyc.org/revista.oa?id=474 Journal of Applied Research and Technology application/pdf Universidad Nacional Autónoma de México Journal of Applied Research and Technology (México) Num.3 Vol.8 |
| title | A Theoretical Framework for Modeling Asymmetric, Nonpositive Definite and Nonuniform Distance Functions on Rn |
| topic | Ingeniería non norm isotropy asymmetry uniformity |
| url | https://www.redalyc.org/articulo.oa?id=47415823010 |