?? de k- Vektör İçin R(x1,x2,…,xk)S(3) Cisminin Üreteçleri
k- bilinmeyenli reel kaysayılı tüm G- invaryant rasyonel fonksiyonların kümesi ?(x1 ,x2,…,xk)?ile gösterilir. Üç boyutlu ℝ3Öklid uzayında benzerlik dönüşümleri grubu G = S(3) olmak üzere, bu çalışmada ℝ3 de verilen ve k vektörden oluşan ? ={?1, ?2 , … , ?? } kümesinin rasyonel S(3)-invaryantlarını tam olarak belirleyebilmek için G grubuna göre invaryant rasyonelfonksiyonlar cismi olan R(x1,x2,…,xk)G cisminin üreteç kümesi ifade edilmiştir. Böylece A kümesinin herhangi bir S(3)invaryantı bu üreteç kümenin elemanlarının bir fonksiyonu olarak ifade edilebilecektir.
The generators of the field R(x1,x2,…,xk)S(3) for k- vectors given in ?3
The field of the G-invariant rational functions with k- variables ?1 , ?2, … , ?? is denoted by?(x1 ,x2,…,xk) ? . In this paper the generator set of the field of G-invariant rational functions denoted by R(x1,x2,…,xk)G is obtained to determine completely all S(3)-invariants of the set ? = {?1 , ?2 , … , ?? } consisted of k- vector variables in ℝ3 where G = S(3) which is the similarity transformations' group in 3 dimensional Euclidean space ℝ3. So any S(3)-invariant of the set A can be stated by the functions of the generator set of the field R(x1,x2,…,xk)G .
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- Yayın Aralığı: Yılda 4 Sayı
- Yayıncı: Marmara Üniversitesi
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