By Ice Risteski

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

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**Sample text**

K). We can write the above equalities in a general form / r ( X i , X 2 , . . , Xp, Y i , Y2,. . 19) min (q—l,fc+l—r) = 2_^ (— I ) * •Pri(Xi+i,Xi_(-2, . . ,Xp) -fri(Xi+i,Xi+2,. . , X p , X i , X 2 , • . ,Xj+p) 44 General Classes of Cyclic Functional Equations 9-1 + ( _ I)'" 2^i -^rt(Xj + i,Xj+2,- . , X p , Y j + i , Y j + 2 , . . , Yq) i—n—r+1 n—p + (_1)' 2^, i=max _ ^r»(Xi+i,Xj+2, •.. ,Xp) (q,n—r+1) p-1 + ^ ^ (""I)" ' • P ' » + r , n - i ( X i , X 2 , . . ,Xj_|_p, t=max (n—p+l,n—r+1) Xj+i, Xj+2 > • • •j Xp) n—q + 2 ^ (—1)" *-Fi+r,n-i(Xi,X2,.

Y j + , ) 2^ i=max(n—

Y,) i=n—r+1 n—p + 2__, { — 1)* i=max (q,n—r+1) -Fr«(X{+i,X;+2, • • • , X p ) p-1 + ^_, ( — 1)™ ' • F i + r , n - i ( X i , X 2 , . . , X i + p , X j + i , X i + 2 , . . , X p ) i=max (n—p+l,n—r+1) n—g + E (*"•'•)" i=max (p,n—r+1) l -^i+r,n-i(Xi,X2,. ,Xj+p) n-1 i Fi+r,n-i(X\, X 2 , . . ,Xj_|_p, Y i , Y 2 , . . , X p ) (r = k + p - n + 1,... ,k - q + 1); Paracyclic Functional Equation 43 / r ( X 1 , X 2 , . . ,Xp, Y i , Y2, . . , Yg) k—r ^ ( — I ) = 1 •PVt(Xi+i,Xi+2,... , X P , Yj+i, Y j + 2 , .