References

cheb

Чебышевский сборник

Chebyshevskii Sbornik

2226-8383

Tula State Lev Tolstoy Pedagogical University

10.22405/2226-8383-2019-20-2-140-155

cheb-600

Research Article

Статьи

Article

Конусы и многогранники обобщенных метрик

Cones and polytopes of geleralized metrics

Деза

Елена Ивановна

Deza

Elena Ivanovna

elena.deza@gmail.com

2019

21012020

202140155

2019

Деза Е.И.

Deza E.I.

Данная работа распространяется под лицензией Creative Commons Attribution 4.0.

This work is licensed under a Creative Commons Attribution 4.0 License.

https://www.chebsbornik.ru/jour/article/view/600

References1

Деза М. М., Деза Е. И., Дютур Сикирич М. Полиэдральные конструкции, связанные с квазиметриками // Чебышевский сборник. 2015. Т. 16, выпуск 2. С. 79–92.

Deza, M. M., Deza, E. I., Dutour Sikirić, М. 2015, “Polyhedral structures associated with quasimetrics”, Chebyshevskii sbornik, Vol. 16 (2), P. 79–92.

Кудряшов Б. Д. Теория информации: Учебник для вузов. – СПб.: Петир, 2009.

Kudryashov, B. D. 2009, “Information Theory”, StPb.: Petir.

Лидовский В. В. Теория информации: Учебное пособие. – М.: Компания Спутник, 2004.

Lidovskii, V. V. 2004, “Information Theory”, M.: Sputnik.

Шеннон К. Математическая теория связи. – М.: ИЛ, 1963.

Shannon, C. E. 1948, “A Mathematical Theory of Communication”, M.: IL.

Charikar M., Makarychev K., Makarychev V. Directed metrics and directed graph partitioning problem // Proc. of 11-th ACM-SIAM Symp. on Discrete Algorithms. 2006. P. 51–60.

Charikar, M., Makarychev, K., Makarychev, V. 2006, “Directed metrics and directed graph partitioning problem”, Proc. of 11-th ACM-SIAM Symp. on Discrete Algorithms, P. 51–60.

Chebotarev P. Studying new classes of graph metrics // Proceedings of the SEE Conference “Geometric Science of Information” (GSI-2013), Lecture Notes in Computer Science, LNCS 8085. 2013. P. 207–214.

Chebotarev, P. 2013, “Studying new classes of graph metrics”, Proceedings of the SEE Conference “Geometric Science of Information” (GSI-2013), Lecture Notes in Computer Science, LNCS 8085, P. 207–214.

Chebotarev P., Agaev R. Forest matrices around the Laplacian matrix // Linear Algebra and its Applications. 2002. No 356. P. 253–274.

Chebotarev, P., Agaev, R. 2002, “Forest matrices around the Laplacian matrix”, Linear Algebra and its Applications, No 356, P. 253–274.

Chebotarev P., Deza E. Hitting time quasi-metric and its forest representation // Optimization Letters. 2018. URL: https://link.springer.com/article/10.1007%2Fs11590-018-1314-2.

Chebotarev, P., Deza, E. 2018, “Hitting time quasi-metric and its forest representation”, Optimization Letters, URL: https://link.springer.com/article/10.1007%2Fs11590-018-1314-2.

Chebotarev P., Shamis Е. The forest metric for graph verticies // arXiv:060257v1. 2006.

Chebotarev, P., Shamis, Е. 2006, “The forest metric for graph verticies”, arXiv:060257v1.

Chebotarev P., Shamis E. Matrix forest theorems // arXiv:0602575v1. 2006.

Chebotarev, P., Shamis, E. 2006, “Matrix forest theorems”, arXiv:0602575v1.

Chebotarev P., Shamis E. On proximity measures for graph vertices // Automation and Remote Control. 1998. No 59. P. 1443–1459.

Chebotarev, P., Shamis, E. 1998, “On proximity measures for graph vertices”, Automation and Remote Control, No 59, P. 1443–1459.

Chebotarev P., Shamis E. The matrix-forest theorem and measuring relations in small social groups // Automation and Remote Control. 1997. No 58. P. 1505–1514.

Chebotarev, P., Shamis, E. 1997, “The matrix-forest theorem and measuring relations in small social groups”, Automation and Remote Control, No 58, P. 1505–1514.

Deza M. M., Deza E. I. Encyclopedia of Distances, 4-rd edition. – Springer-Verlag, Berlin, 2016.

Deza, M. M., Deza, E. I. 2016, “Encyclopedia of Distances”, 4-rd edition, Springer-Verlag, Berlin.

Deza M.M., Deza E.I. Cones of partial metrics // Contrib. Discrete Math. 2011. No 6(1). P. 26–47.

Deza, M. M., Deza, E. I. 2011, “Cones of partial metrics”, Contrib. Discrete Math., No 6(1), P. 26–47.

Deza M. M., Deza E. I., Vidali J. Cones of weighted and partial metrics // Proceedings of the International Conference on Algebra. 2010. P. 177–197.

Deza, M. M., Deza, E. I., Vidali, J. 2010, “Cones of weighted and partial metrics”, Proceedings of the International Conference on Algebra, P. 177–197.

Deza M. M., Dutour M., Deza E. I. Generalizations of finite metrics and cuts. –World Scientific, 2016.

Deza, M. M., Dutour, M., Deza, E. I. 2016, “Generalizations of finite metrics and cuts”, World Scientific.

Deza M. M., Dutour M., Panteleeva E. I. Small cones of oriented semi-metrics // Forum for Interdisciplinary Mathematics Proceedings on Statistics, Combinatorics and Related Areas. 2002. Vol. 22. P. 199–225.

Deza, M. M., Dutour, M., Panteleeva, E. I. 2002, “Small cones of oriented semi-metrics”, Forum for Interdisciplinary Mathematics Proceedings on Statistics, Combinatorics and Related Areas, Vol. 22, P. 199–225.

Deza M. M., Grishukhin V. P., Deza E. I. Cones of weighted quasi-metrics, weighted quasihypermetrics and of oriented cuts // Mathematics of Distances and Applications, ITEA, Sofia. 2012. P. 31–53.

Deza, M. M., Grishukhin, V. P., Deza, E. I. 2012, “Cones of weighted quasi-metrics, weighted quasi-hypermetrics and of oriented cuts”, Mathematics of Distances and Applications, ITEA, Sofia, P. 31–53.

Deza M. M., Laurent M. Geometry of cuts and metrics. - Springer-Verlag, Berlin, 1997.

Deza, M. M., Laurent, M. 1997, “Geometry of cuts and metrics”, Springer-Verlag, Berlin.

Deza M. M., Panteleeva E. I. Quasi-semi-metrics, oriented multi-cuts and related polyhedra // European Journal of Combinatorics. 2000. No 21(6). P. 777–795.

Deza, M. M., Panteleeva, E. I. 2000, “Quasi-semi-metrics, oriented multi-cuts and related polyhedral”, European Journal of Combinatorics, No 21(6), P. 777–795.

Deza M. M., Rosenberg I. G. n-semimetrics // European Journal of Combinatorics, Special Issue Discrete Metric Spaces. 2000. No 21(6). P. 797–806.

Deza, M. M., Rosenberg, I. G. 2000, “n-semimetrics”, European Journal of Combinatorics, Special Issue Discrete Metric Spaces, No 21(6), P. 797–806.

Doyle P. G., Snell J. L. Random Walks and Electric Networks. - Mathematical Association of America, Washington D.C., 1984.

Doyle, P. G., Snell, J. L. 1984, “Random Walks and Electric Networks”, Mathematical Association of America, Washington D.C..

Fréchet M. Sur quelques points du calcul fonctionnel // Rend. Circolo mat. Palermo. 1906. Vol. 22. P. 1–74.

Fréchet, M. 1906, “Sur quelques points du calcul fonctionnel”, Rend. Circolo mat. Palermo, Vol. 22, P. 1–74.

Gvishiani A. D., Gurvich V. A. Metric and ultrametric spaces of resistances // Russian Mathematical Surveys. 1987. No 42. P. 235–236.

Gvishiani, A. D., Gurvich, V. A. 1987, “Metric and ultrametric spaces of resistances”, Russian Mathematical Surveys, No 42, P. 235–236.

Hausdorff F. Grundzüge der Mengenlehre. – Leipzig, 1914.

Hausdorff, F. 1914, “Grundzüge der Mengenlehre”, Leipzig.

Klein D. J., Randic M. Resistance distance // Journal of Mathematical Chemistry. 1993. No 12. P. 81–95.

Klein, D. J., Randic, M. 1993, “Resistance distance”, Journal of Mathematical Chemistry, No 12, P. 81–95.

Seda A.K. Quasi-metrics and the semantic of logic programs // Fundamenta Informaticaem. 1997. Vol. 29. P. 97–117.

Seda, A. K. 1997, “Quasi-metrics and the semantic of logic programs”, Fundamenta Informaticaem, Vol. 29, P. 97–117.

Sharpe G. E. Solution of the (m + 1)-terminal resistive network problem by means of metric geometry // Proceedings of the First Asilomar Conference on Circuits and Systems, Pacific Grove, CA. 1967. P. 319–328.

Sharpe, G. E. 1967, “Solution of the (m + 1)-terminal resistive network problem by means of metric geometry”, Proceedings of the First Asilomar Conference on Circuits and Systems, Pacific Grove, CA, P. 319–328.

Wilson W.A. On quasi-metric spaces // American J. of Math. 1931. Vol. 53. P. 575–681.

Wilson, W. A. 1931, “On quasi-metric spaces”, American J. of Math., Vol. 53, P. 575–681.

The authors declare that there are no conflicts of interest present.