abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.

in this thesis, a new optically active poly(amide-imide) (pai) was synthesized by the indirect polycondensation reaction of the l-phenylalanine based diacid chloride and 4,4?-diaminodiphenylether in the presence of triethylamine in n-methyl-2-pyrrolidone. the formation of pai was confirmed by ftir, 1h nmr and elemental analysis. in next step, the surface of titanium dioxide (tio2) nanoparticles...