We give a explicit computation of the pointed harmonic volumes of hyperelliptic curves with Weierstrass base points, which are paraphrased into a combinatorial formula.

The potential function of Lippincott and Schroeder for linear hydrogen bond has been re-examined and extended to nonlinear hydrogen bond. The parameters originally introduced to the potential function by Lippincott and Schroeder have been determined from the structural parameters such as 0.. .Odistance 0-H bond distance, H.. .O distance and HOO angle. Thevalidity of harmonic oscillator appr...

We prove a Fourier restriction result for general polynomial curves in Rd . Measuring the Fourier restriction with respect to the affine arclength measure of the curve, we obtain a universal estimate for the class of all polynomial curves of bounded degree. Our method relies on establishing a geometric inequality for general polynomial curves which is of interest in its own right. Applications ...

Consider oriented surfaces immersed in R. Associated to them, here are studied pairs of transversal foliations with singularities, defined on the Elliptic region, where the Gaussian curvature K, given by the product of the principal curvatures k1, k2 is positive. The leaves of the foliations are the lines of harmonic mean curvature, also called characteristic or diagonal lines, along which the ...