Balls, Segments, Convex Sets in Metric Spaces and Structures with Heredity

Козин, И.В., Нарзуллаев, У.Х.

Рақамли технологияларнинг назарий ва амалий масалалари · 2022-yil

Annotatsiya

The article considers the extension of such concepts as a ball, a segment, a convex set to an arbitrary metric space. In particular, along with the Euclidean metric, the Manhattan metric and the supremal metric in a multidimensional vector space are considered. The Hamming metric in binary space and a number of metrics in the space of permutations are also considered. Segments are formally described in the binary space with the Hamming metric and in the space of permutations with the Kendall metric. It is shown that the interval in the Hamming metric coincides with the concept of a skhema (shim), which is used in the theory of genetic algorithms in the Holland model. It is proved that the segment between two permutations in the space of permutations with the Kendall metric consists of all permutations that preserve the relative orders induced by these permutations. The concept of structures with heredity is introduced, examples and properties of these structures are described. It is shown that the sets of segments in a metric space form a structure with heredity.

Maqola ma’lumotlari
MualliflarКозин, И.В., Нарзуллаев, У.Х.
JurnalРақамли технологияларнинг назарий ва амалий масалалари
NashriyotТАТУ Самарқанд филиали
ISSN2181-3086, 2181-3094
Nashr sanasi2022-09-10
Jild1
Son1
Betlar7-15
TilIngliz
Ilmiy sohaTexnika
Indeksga qo‘shilgan2026-08-26

Maqolaning asl sahifasi

Kalit so‘zlar

metric space, ball, segment, convex set, Hamming metric, Kendall metric, structures with heredity, метрическое пространство, шар, отрезок, выпуклое множество, метрика Хемминга, метрика Кэндалла, структуры с наследственностью

Ilmiy soha

Texnika

Iqtibos keltirish

APAКозин, И.В., & Нарзуллаев, У.Х. (2022). Balls, Segments, Convex Sets in Metric Spaces and Structures with Heredity. Рақамли технологияларнинг назарий ва амалий масалалари, 1(1), 7-15. https://ijdt.uz/index.php/ijdt/article/view/24
GOST (OAK)Козин, И.В., Нарзуллаев, У.Х. Balls, Segments, Convex Sets in Metric Spaces and Structures with Heredity // Рақамли технологияларнинг назарий ва амалий масалалари. – 2022. – T. 1, № 1. – P. 7-15.
MLAКозин, И.В., and Нарзуллаев, У.Х. “Balls, Segments, Convex Sets in Metric Spaces and Structures with Heredity.” Рақамли технологияларнинг назарий ва амалий масалалари, 1(1), 7-15, 2022. https://ijdt.uz/index.php/ijdt/article/view/24
ChicagoКозин, И.В., and Нарзуллаев, У.Х. “Balls, Segments, Convex Sets in Metric Spaces and Structures with Heredity.” Рақамли технологияларнинг назарий ва амалий масалалари, 1(1), 7-15 (2022). https://ijdt.uz/index.php/ijdt/article/view/24
HarvardКозин, И.В., and Нарзуллаев, У.Х (2022) ‘Balls, Segments, Convex Sets in Metric Spaces and Structures with Heredity’, Рақамли технологияларнинг назарий ва амалий масалалари, 1(1), 7-15. https://ijdt.uz/index.php/ijdt/article/view/24
BibTeX
@article{article2022,
  title = {Balls, Segments, Convex Sets in Metric Spaces and Structures with Heredity},
  author = {Козин, И.В. and Нарзуллаев, У.Х.},
  journal = {Рақамли технологияларнинг назарий ва амалий масалалари},
  year = {2022},
  volume = {1},
  number = {1},
  pages = {7-15},
  url = {https://ijdt.uz/index.php/ijdt/article/view/24}
}

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