By Ice Risteski

The topic of advanced vector practical equations is a brand new quarter within the thought of practical equations. This monograph presents a scientific evaluate of the authors' lately got effects bearing on either linear and nonlinear advanced vector sensible equations, in all facets in their usage. it's meant for mathematicians, physicists and engineers who use useful equations of their investigations.

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Extra info for Complex Vector Functional Equations

Example text

18) into Eq. 11) and if we take into account the transformation Eq. 10). On the basis of the expression Eq. 11) is given by the following formulae / r ( X i , X 2 , . . , X p , Y i , Y 2 , . . , Yg) = 8-1 2_^{~ 1)' - F r i ( X j + i , X t + 2 , . . , X p , Y j + i , Y j + 2 , . . , Yq) 1=1 n—p i+l)Xj+2i • • • > i=q + k—T 2_^i ( ~ * ) ' i=n—p+1 + ( — 1) -^ri(Xj+i,Xj+2,.. , X p , X i , X 2 , . . ,Xj+p) _r r i r ^ + i _ r ( X f c + 2 _ r , X f c + 3 _ r , . . , X p , X i , X 2 , . . ,Xfc+i_ r + p ) ,-1 + 2^i ( _ I ) ' " ^ r t ( X i + i , X i + 2 i • • • >X p , Y j + i , Yj+2, .

I=max(n-q+l,n—r+1) ( l < r < * - g + l); / r ( X i , X 2 , . . ,Xp, Yi, Y 2 , . . , Yq) k-r = 2 l , ( —1)* ^ r i ( X j + i , X t + 2 , . . , X p , Y ; + 1 , Yj+2, . . , Yg) i=l 9-1 + 2^1 (~l)l~ i=n—r+1 n—p + •fr»(Xi+i,Xi+2,... ,Xp, Y i + i , Y j + 2 , . . , Yg) / ^ (— l ) t _ • F r i ( X i + l , X j + 2 , . . , X p ) i=max (g,n—r+1) p-1 • P i + r , n - i ( X i , X 2 , . . , X j + p , X j + i , Xj_|-2; • • • j X p ) i=max (n—p+l,n—r+1) n—q + 2~2 (-1)n" ' • F i + r , n - i ( X i , X 2 , .

X P , Y i , Y 2 ) . . 5) min (n—p,k—r) — 2^/ (~^y -Frt(Xj+i,Xj + 2, • • • , X p , Y j + i , Y j + 2 , . . , Y g ) 1=1 n—p + 2 _ , (~1Y~ i=n—r+1 • f r i ( X i + i , X j + 2 , • • • , X p , Y j + i , Y j + 2 , . . , Yq) min (k—r, q—1) + ]r (-lr^x^ -^•i+2) • • • > -*-p> i=n—p+1 X l , X 2 , . • , X j + p , Y j + i , Yj_)-2, . • , Yq) q-1 + 2_^ (—^)l_ ^rt(Xi+i,Xi+2,. • • ,Xp, «=max (n—p+1,n—r+1) X i , X 2 , . . , X j + p , Y i + i , Y j + 2 , . . , Yg) min (A—r,n—g) + ( - 1 ) ' _ • P , r i ( X i + i , X i + 2 , .