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Proceedings in pdf format. - Sociotechnical Systems Engineering ...

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MagMag0, m , m , m1 2 31, m , m , m1 2 3= m= mm1 m2m3p2 2 2m l( − ) 1 2 3 4 1F∑∑∑i= 0 j= 0 l=0 i j l p m1 i m2 j m3l2 p m1 −2i m2−2j 3−221 p! x x x x Ge( p, wx )( ) ( − ) ( − ) ( − )! ! ! 2 ! 2 ! 2 ! 2 !m1 m2m3p2 2 2m l( − ) 1 2 3 4+1Fi= 0 j= 0 l=0 i j l ( p + ) ( m1 − i) ( m2 − j) ( m3− l)2 p+1 m1 −2i m2−2j 3−221 p! x x x x Ge( p 1, wx )∑∑∑ (33),where p = i + j + l , mFm1 ! m2 ! m3!! ! ! 2 1 ! 2 ! 2 ! 2 != .The recurrent form of the record for four measurements is:Mag0,m1 / 2 m2/ 2 m3/ 21 2 3m , m , m = ∑ ∑ ∑ ai,j,l x x x x Ge(i + j +1a 0 = 1a,0,0i,j,l− a− ai,j−1,li,j,l−12= −a3i−1,j,li= 0 j=0l=02i+2 j+2l1( m2− 2 j + 2)( m2− 2 j + 1)−(2i+ 2 j + 2l)(2i+ 2 j + 2l− 1)( m3− 2l+ 2)( m3− 2l+ 1)(2i+ 2 j + 2l)(2i+ 2 j + 2l− 1)m2−2i( m1− 2i+ 2)( m1− 2i+ 1)−(2i+ 2i+ 2l)(2i+ 2 j + 2l− 1)m3−2jm4−2l(34)l,wx21)Mag1,m1 / 2 m2/ 2 m3/ 21 2 3m , m , m = ∑ ∑ ∑ ai,j,l x x x x Ge(i + j + l + 1, wx1a 0 = 1a,0,0i,j,l− a− ai,j−1,li,j,l−12= −a3i−1,j,li = 0 j=0l = 0( m3− 2l+ 2)( m3− 2l+ 1)(2i+ 2 j + 2l)(2i+ 2 j + 2l+ 1)2i+ 2 j+2l+ 11( m1− 2i+ 2)( m1− 2i+ 1)−(2i+ 2i+ 2l)(2i+ 2 j + 2l+ 1)( m2− 2 j + 2)( m2− 2 j + 1)−(2i+ 2 j + 2l)(2i+ 2 j + 2l+ 1)And the more general version will be exam<strong>in</strong>ed for equation (31):m2−2im3−2jm4−2l21)2 2 2 2∂ u ∂ u ∂ u ∂ u+ b + b + b + wu =∂x ∂x ∂x ∂x2 2 2 3 2 4 21 2 3 40Annual <strong>Proceed<strong>in</strong>gs</strong> of Vidzeme University College “ICTE <strong>in</strong> Regional Development”, 2006147

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