In this paper we investigate the operator H=??(??) in L2 (R2), where> 0 and? is a closed C4 Jordan curve in R2. We obtain the asymptotic form of each eigenvalue of H as tends to in nity. We also get the asymptotic form of the number of negative eigenvalues of H in the strong coupling asymptotic regime. MSC: 35J10, 35P15

The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the framework gives an efficient algorithm to calculate all tautological equations using only finite dimensional linear algebra. Other applications are also indicated.

In this paper, we prove that the degree of regularity of the family of Square systems, an HFE type of systems, over a prime finite field of odd characteristics q is exactly q, and therefore prove that \begin{itemize} \item inverting Square systems algebraically is exponential, when q=O(n), where n is the number of variables of the system. \end{itemize}

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