Analytical potentials for triatomic molecules VIII. A two valued surface for the lowest 1A¢ surfaces of H2O

Ab initio calculations of the energy have been made at approximately 150 points on the two lowest singlet A' potential energy surfaces of the water molecule, 1A' and 1A', covering structures having D∞h, C∞v, C2v and Cs symmetries. The object was to obtain an ab initio surface of uniform accuracy over the whole three-dimensional coordinate space. Molecular orbitals were constructed from a double zeta plus Rydberg basis, and correlation was introduced by single and double excitations from multiconfiguration states which gave the correct dissociation behaviour. A two-valued analytical potential function has been constructed to fit these ab initio energy calculations. The adiabatic energies are given in our analytical function as the eigenvalues of a 2 2 matrix, whose diagonal elements define two diabatic surfaces. The off-diagonal element goes to zero for those configurations corresponding to surface intersections, so that our adiabatic surface exhibits the correct Σ/II conical intersections for linear configurations, and singlet/triplet intersections of the O + H2 dissociation fragments. The agreement between our analytical surface and experiment has been improved by using empirical diatomic potential curves in place of those derived from ab initio calculations.

Anodic polarization curves revisited

An experiment published in this Journal has been revisited and it is found that the curve pattern of the anodic polarization curve for iron repeats itself successively when the potential scan is repeated. It is surprising that this observation has not been reported previously in the literature because it immediately brings into question the long accepted and well-known explanations involving a passive film. A qualitative and plausible explanation is provided from surprisingly simple principles for this new finding. Some important pedagogic conclusions have been derived from this work. It is noteworthy that the somewhat complicated phenomenon can be simply explained, thus providing two important lessons to students. First, even well-accepted scientific work studying simple processes may be incomplete and worthy of further study, and second, such processes may be explained simply at the undergraduate level. The contents of the paper also confirm that presenting curricular contents in a new and more correct manner is beneficial, interesting, and that research in curricular contents represents one of the important forms of educational research.

MALDI MS profiling of post-DRE urine samples highlights the potential of b-Microseminoprotein as a marker for prostatic diseases

BACKGROUND. To use spectra acquired by matrix-assisted laser desorption/ionization (MALDI) mass spectrometry (MS) from pre- and post-digital rectal examination (DRE) urine samples to search for discriminating peaks that can adequately distinguish between benign and malignant prostate conditions, and identify the peaks’ underlying biomolecules. METHODS. Twenty-five participants with prostate cancer (PCa) and 27 participants with a variety of benign prostatic conditions as confirmed by a 10-core tissue biopsy were included. Pre- and post-DRE urine samples were prepared for MALDI MS profiling using an automated clean-up procedure. Following mass spectra collection and processing, peak mass and intensity were extracted and subjected to statistical analysis to identify peaks capable of distinguishing between benign and cancer. Logistic regression was used to combine markers to create a sensitive and specific test. RESULTS. A peak at m/z 10,760 was identified as b-microseminoprotein (b-MSMB) and found to be statistically lower in urine from PCa participants using the peak’s average areas. By combining serum prostate-specific antigen (PSA) levels with MALDI MS-measured b-MSMB levels, optimum threshold values obtained from Receiver Operator characteristics curves gave an increased sensitivity of 96% at a specificity of 26%. CONCLUSIONS. These results demonstrate that with a simple sample clean-up followed by MALDI MS profiling, significant differences of MSMB abundance were found in post-DRE urine samples. In combination with PSA serum levels, obtained from a classic clinical assay led to high classification accuracy for PCa in the studied sample set. Our results need to be validated in a larger multicenter prospective randomized clinical trial.

Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.