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�ySEOtext�z0. General Formulation, ƒÓ'�¸Rn(R4;Rn(R4),R), ƒÓ'ƒ¿(x;ƒÓ,0)=ƒÓƒ¿(x), ƒ¶'(ƒ¶,ƒÃ)={x|�Îy�¸ƒ¶,x=x'*(y;ƒÃ)}, x'�¸R4(R4;R), x'ƒÊ(x;0)=xƒÊ, Conclusion, If ƒÂI(ƒÓ)/ƒÂƒÓƒ¿(x)=0 then: (�Ý/�ÝxƒÊ)TƒÊ(x;ƒÓ)=0, (d/dt)Q(t;ƒÓ)=0 where: T�¸R4(R4;Rn(R4)), Q�¸R(R;Rn(R4)), TƒÊ(x;ƒÓ)=�Ýx'ƒÊ(x;ƒÃ)/�݃Ã|ƒÃ=0L(ƒÓ*(x);�Ý*ƒÓ*(x))+�݃Ó'ƒ¿(x;ƒÓ,ƒÃ)/�݃Ã|ƒÃ=0�ÝL(ƒÓ*(x);�Ý*ƒÓ*(x))/�Ý[�݃ʃӃ¿(x)], Q(t;ƒÓ)=�çd3xT0(t,x;ƒÓ) d. Local Complex Field, Consider the special case: n=2, L(x;y)=Lc(z(x1,x2),z�õ(x1,x2);z(y01,y02),�E�E�E,z(y31,y32);z�õ(y01,y02),�E�E�E,z�õ(y31,y32)) where: x�¸R2, y�¸R4�~2, Lc�¸C(C10), Lc(a,a�õ;b,c,d,e;b�õ,c�õ,d�õ,e�õ)�¸R, 1. Euler-Lagrange Equation, ƒÂI(ƒÓ)/ƒÂƒÓƒ¿(x)=0�Ì{�ÝLc(ƒÓ(x),ƒÓ�õ(x);�݃Ó(x),�݃Ó�õ(x))/�݃Ó(x)-�Ý/�ÝxƒÊ�ÝLc(�E�E�E�E�E)/�Ý[�݃ʃÓ(x)]=0, �ÝLc(ƒÓ(x),ƒÓ�õ(x);�݃Ó(x),�݃Ó�õ(x))/�݃Ó�õ(x)-�Ý/�ÝxƒÊ�ÝLc(�E�E�E�E�E)/�Ý[�݃ʃÓ�õ(x)]=0 where: ƒÓ(x)=z(ƒÓ1(x),ƒÓ2(x))

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