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ySEOtextz0. General Formulation, 'Rn(R4;Rn(R4),R), '(x;,0)=Ӄ(x), '(,)={x|y,x=x'*(y;)}, x'R4(R4;R), x'(x;0)=x, Conclusion, If I()/ƒӃ(x)=0 then: (/x)T(x;)=0, (d/dt)Q(t;)=0 where: TR4(R4;Rn(R4)), QR(R;Rn(R4)), T(x;)=x'(x;)/݃|=0L(*(x);**(x))+݃'(x;,)/݃|=0L(*(x);**(x))/[݃ʃӃ(x)], Q(t;)=d3xT0(t,x;) d. Local Complex Field, Consider the special case: n=2, L(x;y)=Lc(z(x1,x2),z(x1,x2);z(y01,y02),EEE,z(y31,y32);z(y01,y02),EEE,z(y31,y32)) where: xR2, yR4~2, LcC(C10), Lc(a,a;b,c,d,e;b,c,d,e)R, 1. Euler-Lagrange Equation, I()/ƒӃ(x)=0{Lc((x),Ӂ(x);݃(x),݃Ӂ(x))/݃(x)-/xʁLc(EEEEE)/[݃ʃ(x)]=0, Lc((x),Ӂ(x);݃(x),݃Ӂ(x))/݃Ӂ(x)-/xʁLc(EEEEE)/[݃ʃӁ(x)]=0 where: (x)=z(1(x),2(x))

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