Araştırma Makalesi
Yıl 2018,
Cilt: 8 Sayı: 2, 348 - 357, 31.07.2018
Öz
Bu çalışmada {x_1,x_2,...,x_m} parametrik eğrileriyle oluşturulan R<x_1,x_2,...,x_m>^GL(n,R) kümesinin üreteç kümesi bulunmuştur. Herhangi
iki eğri ailesinin GL(n,R)-denklik koşulları, bu üreteç diferansiyel
invaryantlar kullanılarak elde edilmiştir. Ayrıca üreteç sisteminin minimal
olduğu gösterilmiştir.
Anahtar Kelimeler
Kaynakça
- Gardner, R.B., ve Wilkens, G.R., 1997. The fundamental theorems of curves and hypersurfaces in centro-affine geometry. Bull. Belg. Math. Soc., 4, 379-401.
- Giblin, P.J., ve Sano, T., 2012. Generic equi-centro-affine differential geometry of plane curves. Topology Appl., 159, 476-483.
- Izumiya, S., ve Sano, T., 2000. Generic affine differential geometry of space curves. Proceedings of the Royal Soc. of Edinburgh, 128A, 301-314.
- İncesu, M., ve Gürsoy, O., 2017. LS(2)-Equivalence conditions of control points and application to planar Bezier curves. NTMSCI, 5(3), 70-84.
- Khadjiev, Dj., ve Pekşen, Ö., 2004. The complete system of global differential and integral invariants for equi-affine curves. Diff. Geom. Appl., 20, 167-175.
- Nadjafikhah, M., 2002. Affine differential invariants for planar curves. Balk. J. Geom. Appl., 7, 69-78.
- Olver, P.J., 2010. Moving frames and differential invariants in centro-affine geometry. Lobachevskii J. Math., 31, 77-89.
- Pekşen, Ö., ve Khadjiev, D., 2004. On invariants of curves in centro-affine geometry. J. Math. Kyoto Univ., 44(3), 603-613.
- Sağıroğlu, Y., 2012. Affine Differential Invariants of Curves. LAP, Saarbrücken, 128p.
- Sağıroğlu, Y., 2016. Centro-equiaffine differential invariants of curve families. IEJG, 9, 23-29.
- Sağıroğlu, Y., 2015. Equi-affine differential invariants of a pair of curves. TWMS J. Pure. Appl. Math., 6, 238-245.
- Sağıroğlu, Y., ve Pekşen, Ö., 2010. The equivalence of equi-affine curves. Turk. J. Math., 34, 95-104.
- Sağıroğlu, Y., ve Yapar, Z. 2016. GL(n,R)-Equivalence of a pair of curves in terms of invariants. Journal of Mathematics and System Science, 6, 16-22.
- Sibirskii, K.S., 1976. Algebraic invariants of differential equations and matrices, Kishinev, Stiintsa, 268p.
Yıl 2018,
Cilt: 8 Sayı: 2, 348 - 357, 31.07.2018
Öz
In this study, the generating system of the set R<x_1,x_2,...,x_m>^GL(n,R) formed by the parametric curves {x_1,x_2,...,x_m} is obtained. The conditions of GL(n,R)-equivalence of two curve families are given by means of the differential
invariants. It is also shown that the generating system is minimal.
Anahtar Kelimeler
Kaynakça
- Gardner, R.B., ve Wilkens, G.R., 1997. The fundamental theorems of curves and hypersurfaces in centro-affine geometry. Bull. Belg. Math. Soc., 4, 379-401.
- Giblin, P.J., ve Sano, T., 2012. Generic equi-centro-affine differential geometry of plane curves. Topology Appl., 159, 476-483.
- Izumiya, S., ve Sano, T., 2000. Generic affine differential geometry of space curves. Proceedings of the Royal Soc. of Edinburgh, 128A, 301-314.
- İncesu, M., ve Gürsoy, O., 2017. LS(2)-Equivalence conditions of control points and application to planar Bezier curves. NTMSCI, 5(3), 70-84.
- Khadjiev, Dj., ve Pekşen, Ö., 2004. The complete system of global differential and integral invariants for equi-affine curves. Diff. Geom. Appl., 20, 167-175.
- Nadjafikhah, M., 2002. Affine differential invariants for planar curves. Balk. J. Geom. Appl., 7, 69-78.
- Olver, P.J., 2010. Moving frames and differential invariants in centro-affine geometry. Lobachevskii J. Math., 31, 77-89.
- Pekşen, Ö., ve Khadjiev, D., 2004. On invariants of curves in centro-affine geometry. J. Math. Kyoto Univ., 44(3), 603-613.
- Sağıroğlu, Y., 2012. Affine Differential Invariants of Curves. LAP, Saarbrücken, 128p.
- Sağıroğlu, Y., 2016. Centro-equiaffine differential invariants of curve families. IEJG, 9, 23-29.
- Sağıroğlu, Y., 2015. Equi-affine differential invariants of a pair of curves. TWMS J. Pure. Appl. Math., 6, 238-245.
- Sağıroğlu, Y., ve Pekşen, Ö., 2010. The equivalence of equi-affine curves. Turk. J. Math., 34, 95-104.
- Sağıroğlu, Y., ve Yapar, Z. 2016. GL(n,R)-Equivalence of a pair of curves in terms of invariants. Journal of Mathematics and System Science, 6, 16-22.
- Sibirskii, K.S., 1976. Algebraic invariants of differential equations and matrices, Kishinev, Stiintsa, 268p.
Toplam 14 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Temmuz 2018 |
| Gönderilme Tarihi | 24 Şubat 2018 |
| Kabul Tarihi | 17 Nisan 2018 |
| Yayımlandığı Sayı | Yıl 2018 Cilt: 8 Sayı: 2 |
