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Equivalence conditions of two systems of vectors in the taxicab plane and its applications to taxicab polygons

Yıl 2020, Cilt: 69 Sayı: 1, 413 - 430, 30.06.2020
https://doi.org/10.31801/cfsuasmas.666357

Öz

This study presents the conditions of M_{T}(2)-equivalence for two systems of vectors {x₁,x₂,x₃} and {y₁,y₂,y₃} in R_{T}², where M_{T}(2) is the group of all isometries of the 2-dimensional taxicab space R_{T}². Firstly a minimal complete system of M_{T}(2)-invariants of {x₁,x₂,x₃} is obtained. Then, using the conditions of M_{T}(2)-equivalence, an answer is given to the open problem posed in sch. Furthermore, an algorithm is given for constructing taxicab regular polygons in terms of M_{T}(2)-invariants. This algorithm is general and useful to construct the taxicab regular 2n-gons and gives a tool to solve special cases of the open problem posed in col. Besides, both the conditions of the taxicab regularity of Euclidean regular polygons and Euclidean regularity of taxicab regular polygons are given in terms of M_{T}(2)-invariants.

Kaynakça

  • Abrams, P., Some comments on measuring niche overlap, Ecology, 61(1) (1980), 44-49.
  • Çolakoğlu, H. B., Kaya, R., Regular polygons in the taxicab plane, KoG, 12 (2008), 27-33.
  • Ekici, Kocayusufoğlu, İ., Akça, Z. The norm in taxicab geometry, Turk. J. Math, 22(3) (1998), 295-307.
  • Goulson, D., Darvill, B., Niche overlap and diet breadth in bumblebees; are rare species more specialized in their choice of flowers?, Apidologie, 35 (2004), 55-63.
  • Greub, W., Linear algebra, Berlin-Heidelberg-New York:Springer-Verlag, 1967.
  • Hanson, J. R., Regular polygons in taxicab geometry, Int. J. Math. Educ. Sci. Technol., 45(7) (2014), 1084-1095.
  • Legendre, P., Gallagher, E., Ecologically meaningful transformations for ordination of species data, Oecologia, 129 (2001), 271-280.
  • Ören, İ, Çoban, H. A., Some invariant properties of curves in the taxicab geometry, Missouri J. Math. Sci., 26 (2014), 107-114.
  • Ören,İ., Equivalence conditions of two Bézier Curves in the Euclidean geometry, Iran. J. Technol. A. Sci., 42(3) (2018), 1563-1577.
  • Schattschneider, D. J., The taxicab group, Am. Math. Mon., 91 (1984), 423-428.
  • Slobodchikoff, C. N., Schulz, W. C. Measures of niche overlap, Ecology, 61(7) (1980), 1051-1055.
  • Sohn, M. W., Distance and cosine measures of niche overlap, Soc. Networks, 23 (2001), 141-165.
  • Struble, R. A., Non-Linear differential equations, New York:Mc Graw-Hill, 1962.
  • Sturmfels, B. Algorithms in invariant theory, Wien:Springer, 2008.
  • Yüksel, S., Özcan, M., Some regular polygons in the taxicab 3-space, KoG, 19 (2005), 32-41.
  • Warren, D. L., Glor, R. E., Turelli, M., Environmental niche equivalency versus conservatism: quantitative approaches to niche evolution, Evolution, 62(11) (2008), 2868-2883.
  • Weyl, H., The classical groups, their invariants and representations, New Delhi: Princeton University Press, 2013.
Yıl 2020, Cilt: 69 Sayı: 1, 413 - 430, 30.06.2020
https://doi.org/10.31801/cfsuasmas.666357

Öz

Kaynakça

  • Abrams, P., Some comments on measuring niche overlap, Ecology, 61(1) (1980), 44-49.
  • Çolakoğlu, H. B., Kaya, R., Regular polygons in the taxicab plane, KoG, 12 (2008), 27-33.
  • Ekici, Kocayusufoğlu, İ., Akça, Z. The norm in taxicab geometry, Turk. J. Math, 22(3) (1998), 295-307.
  • Goulson, D., Darvill, B., Niche overlap and diet breadth in bumblebees; are rare species more specialized in their choice of flowers?, Apidologie, 35 (2004), 55-63.
  • Greub, W., Linear algebra, Berlin-Heidelberg-New York:Springer-Verlag, 1967.
  • Hanson, J. R., Regular polygons in taxicab geometry, Int. J. Math. Educ. Sci. Technol., 45(7) (2014), 1084-1095.
  • Legendre, P., Gallagher, E., Ecologically meaningful transformations for ordination of species data, Oecologia, 129 (2001), 271-280.
  • Ören, İ, Çoban, H. A., Some invariant properties of curves in the taxicab geometry, Missouri J. Math. Sci., 26 (2014), 107-114.
  • Ören,İ., Equivalence conditions of two Bézier Curves in the Euclidean geometry, Iran. J. Technol. A. Sci., 42(3) (2018), 1563-1577.
  • Schattschneider, D. J., The taxicab group, Am. Math. Mon., 91 (1984), 423-428.
  • Slobodchikoff, C. N., Schulz, W. C. Measures of niche overlap, Ecology, 61(7) (1980), 1051-1055.
  • Sohn, M. W., Distance and cosine measures of niche overlap, Soc. Networks, 23 (2001), 141-165.
  • Struble, R. A., Non-Linear differential equations, New York:Mc Graw-Hill, 1962.
  • Sturmfels, B. Algorithms in invariant theory, Wien:Springer, 2008.
  • Yüksel, S., Özcan, M., Some regular polygons in the taxicab 3-space, KoG, 19 (2005), 32-41.
  • Warren, D. L., Glor, R. E., Turelli, M., Environmental niche equivalency versus conservatism: quantitative approaches to niche evolution, Evolution, 62(11) (2008), 2868-2883.
  • Weyl, H., The classical groups, their invariants and representations, New Delhi: Princeton University Press, 2013.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

İdris Ören 0000-0003-2716-3945

Hüsnü Anıl Çoban 0000-0001-8175-4960

Yayımlanma Tarihi 30 Haziran 2020
Gönderilme Tarihi 10 Ekim 2017
Kabul Tarihi 23 Aralık 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 1

Kaynak Göster

APA Ören, İ., & Çoban, H. A. (2020). Equivalence conditions of two systems of vectors in the taxicab plane and its applications to taxicab polygons. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 413-430. https://doi.org/10.31801/cfsuasmas.666357
AMA Ören İ, Çoban HA. Equivalence conditions of two systems of vectors in the taxicab plane and its applications to taxicab polygons. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2020;69(1):413-430. doi:10.31801/cfsuasmas.666357
Chicago Ören, İdris, ve Hüsnü Anıl Çoban. “Equivalence Conditions of Two Systems of Vectors in the Taxicab Plane and Its Applications to Taxicab Polygons”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 1 (Haziran 2020): 413-30. https://doi.org/10.31801/cfsuasmas.666357.
EndNote Ören İ, Çoban HA (01 Haziran 2020) Equivalence conditions of two systems of vectors in the taxicab plane and its applications to taxicab polygons. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 413–430.
IEEE İ. Ören ve H. A. Çoban, “Equivalence conditions of two systems of vectors in the taxicab plane and its applications to taxicab polygons”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 1, ss. 413–430, 2020, doi: 10.31801/cfsuasmas.666357.
ISNAD Ören, İdris - Çoban, Hüsnü Anıl. “Equivalence Conditions of Two Systems of Vectors in the Taxicab Plane and Its Applications to Taxicab Polygons”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (Haziran 2020), 413-430. https://doi.org/10.31801/cfsuasmas.666357.
JAMA Ören İ, Çoban HA. Equivalence conditions of two systems of vectors in the taxicab plane and its applications to taxicab polygons. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:413–430.
MLA Ören, İdris ve Hüsnü Anıl Çoban. “Equivalence Conditions of Two Systems of Vectors in the Taxicab Plane and Its Applications to Taxicab Polygons”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 1, 2020, ss. 413-30, doi:10.31801/cfsuasmas.666357.
Vancouver Ören İ, Çoban HA. Equivalence conditions of two systems of vectors in the taxicab plane and its applications to taxicab polygons. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):413-30.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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