On the number of zeros of Abelian integrals for a kind of quartic Hamiltonians

An explicit upper bound B(n) is derived for the number of zeros of Abelian integrals I(h)=@?"@C"""hg(x,y)dx-f(x,y)dy on the open interval (0,1/4), where @C"h is an oval lying on the algebraic curve...