Accurate calculation of the complex eigenvalues of the Schr\"{o}dinger equation with an exponential potential

We show that the Riccati--Pad\'{e} method is suitable for the calculation of the complex eigenvalues of the Schr\"{o}dinger equation with a repulsive exponential potential. The accuracy of the results is remarkable for realistic potential parameters

Irregular hypergeometric D-modules

We study the irregularity of hypergeometric D-modules $\mathcal{M}_A (\beta )$ via the explicit construction of Gevrey series solutions along coordinate subspaces in $X =\mathbb{C}^n$. As a consequence, we prove that along coordinate hyperplanes the combinatorial characterization of the slopes of $\mathcal{M}_A (\beta)$ given by M. Schulze and U. Walther in [21] still holds without any assumption on the matrix A. We also provide a lower bound for the dimensions of the spaces of Gevrey solutions along coordinate subspaces in terms of volumes of polytopes and prove the equality for very generic parameters. Holomorphic solutions outside the singular locus of $\mathcal{M}_A (\beta)$ can be understood as Gevrey solutions of order one along X at generic points and so they are included as a particular case.Comment: 41 pages; references, Remark 7.2. and 4 figures added; some comments changed; corrected typo

Comment on the numerical solutions of a new coupled MKdV system (2008 Phys. Scr. 78 045008)

In this comment we point out some wrong statements in the paper by Inc and Cavlak, Phys. Scr. 78 (2008) 04500

Wronskian formula for confluent second-order supersymmetric quantum mechanics

The confluent second-order supersymmetric quantum mechanics, for which the factorization energies tend to a single value, is studied. We show that the Wronskian formula remains valid if generalized eigenfunctions are taken as seed solutions. The confluent algorithm is used to generate SUSY partners of the Coulomb potential.Comment: 7 pages, 1 figure, to be published in Physics Letters

Formality of Donaldson submanifolds

We introduce the concept of s-formal minimal model as an extension of formality. We prove that any orientable compact manifold M, of dimension 2n or (2n-1), is formal if and only if M is (n-1)-formal. The formality and the hard Lefschetz property are studied for the symplectic manifolds constructed by Donaldson with asymptotically holomorphic techniques. This study permits us to show an example of a Donaldson symplectic manifold of dimension eight which is formal simply connected and does not satisfy the hard Lefschetz theorem.Comment: 24 pages, no figures, Latex2e; v3. statement of Lemma 2.7 correcte

Characteristic cycles and Gevrey series solutions of AA-hypergeometric systems

We compute the $L$-characteristic cycle of an $A$-hypergeometric system and higher Euler-Koszul homology modules of the toric ring. We also prove upper semicontinuity results about the multiplicities in these cycles and apply our results to analyze the behavior of Gevrey solution spaces of the system.Comment: 22 page