Dual Parametrik Eğrilerin Denklik Problemi
reel sayılar cismi ve * * * 2 ( , ) , , , 0 D a a a a a a dual cebir olsun. D nin
The Equivalence Problem Of Dual Parametric Curves
Let be the field of real numbers and * * * 2 D (a,a ) a a ,a,a , 0 be the algebra of dual numbers.The subset * *1 ( , ), 0, , D a a a a a of D is an abelian group with respect to the multiplication operationin the algebra D . For an element *1 A a a D and a transformation 2 2 S : where S A Sa a , we define the sets *1 *0, 0, , AaID S a a aa a and*1 *0 1 0, 0, ,0 1aID a a aa a . Let us denote 1 1 1 ID ID ID . Moreover, we denote the setℳ 1ID ℳ 1ID ℳ 1ID whereℳ 2 2 21 1 : , ( ) , , , A ID F F B S B C A D B C andℳ 2 2 21 11 0: , ( ) ( ) , , , ,0 1 A ID F F B S W B C A D B C W . Let ( , ) T a b be an openinterval of . A (2) C -function 2 :T for tT where, ( ) ( ( ), ( )) t x t y t is called a parametrized curve(path) on the plane. Let G be a group. Two parametric curves (paths) ()t and ()t are called G - equivalentif the equality ( ) ( ) t Ft is satisfied for an element FG and all tT . Then, it is denoted by ( ) ( )GttThis work is devoted to the solutions of problems of G-equivalence of parametric curves in Euclidean space2 for the groups G ℳ 1ID , ℳ 1ID .
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