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

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

Application of the Asymptotic Iteration Method to a Perturbed Coulomb Model

We show that the asymptotic iteration method converges and yields accurate energies for a perturbed Coulomb model. We also discuss alternative perturbation approaches to that model.Comment: 9 pages, 2 figures, 1 tabl

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

Accurate calculation of resonances in multiple-well oscillators

Quantum--mechanical multiple--well oscillators exhibit curious complex eigenvalues that resemble resonances in models with continuum spectra. We discuss a method for the accurate calculation of their real and imaginary parts

Natural and laser-induced cavitation in corn stems: On the mechanisms of acoustic emissions

Water in plant xylem is often superheated, and therefore in a meta-stable state. Under certain conditions, it may suddenly turn from the liquid to the vapor state. This cavitation process produces acoustic emissions. We report the measurement of ultrasonic acoustic emissions (UAE) produced by natural and induced cavitation in corn stems. We induced cavitation and UAE in vivo, in well controlled and reproducible experiments, by irradiating the bare stem of the plants with a continuous-wave laser beam. By tracing the source of UAE, we were able to detect absorption and frequency filtering of the UAE propagating through the stem. This technique allows the unique possibility of studying localized embolism of plant conduits, and thus to test hypotheses on the hydraulic architecture of plants. Based on our results, we postulate that the source of UAE is a transient "cavity oscillation" triggered by the disruptive effect of cavitation inception.Comment: 8 pages, 5 figure