ar X iv : d g - ga / 9 60 80 02 v 1 8 A ug 1 99 6 Higher Spectral Flow ∗

ar X iv : a lg - g eo m / 9 60 80 25 v 1 2 2 A ug 1 99 6 COUNTING PLANE CURVES OF ANY GENUS

ar X iv : d g - ga / 9 50 80 01 v 1 3 A ug 1 99 5 On the L n 2 - norm of Scalar Curvature

Comparisons on L n 2-norms of scalar curvatures between Riemannian metrics and standard metrics are obtained. The metrics are restricted to conformal classes or under certain curvature conditions.

ar X iv : c on d - m at / 9 60 80 14 v 1 5 A ug 1 99 6 Why DNA ?

A small collection of general facts related to DNA is presented.

ar X iv : q - a lg / 9 60 80 20 v 1 2 3 A ug 1 99 6 SHIFTED JACK POLYNOMIALS , BINOMIAL FORMULA , AND APPLICATIONS

In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [

ar X iv : c on d - m at / 9 60 80 07 v 1 2 A ug 1 99 6 The Edge Currents and Edge Potentials in IQHE

It is shown that an observed length in the potential drops across IQHE samples is a universal length for a given value of magnetic field which results from the quantum mechanical uncertainty relation.