Mg,n ψ1 1 · · ·ψ dn n . Witten-Kontsevich theorem [9, 4] provides a recursive way to compute all these intersection numbers. However explicit and effective recursion formulae for computing intersection indices are still very rare and very welcome. Our n-point function formula [5] computes intersection indices recursively by decreasing the number of marked points. So it is natural to ask whether...

In this paper, a generic intersection theorem in projective differential algebraic geometry is presented. Precisely, the intersection of an irreducible projective differential variety of dimension d > 0 and order h with a generic projective differential hyperplane is shown to be an irreducible projective differential variety of dimension d − 1 and order h. Based on the generic intersection theo...

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the...

In 1893 J. J. Sylvester [8] posed the following celebrated problem: Given a finite collection of points in the affine plane, not all lying on a line, show that there exists a line which passes through precisely two of the points. Sylvester’s problem was reposed by Erdős in 1944 [4] and later that year a proof was given by Gallai [6]. Since then, many proofs of the Sylvester-Gallai Theorem have ...