538,159 research outputs found
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 via the explicit construction of Gevrey series solutions along coordinate
subspaces in . As a consequence, we prove that along
coordinate hyperplanes the combinatorial characterization of the slopes of
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 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 -hypergeometric systems
We compute the -characteristic cycle of an -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
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