Systems of Inclusions Involving Fredholm Operators of Nonnegative Index and Nonconvex-Valued Maps

We study the existence of solutions to a system of two inclusions involving Fredholm operators of nonnegative (Fredholm) index and the so-called c-admissible maps: upper semicontinuous maps with values being continuous images of cell-like sets. The presented approach resembles the substitution technique, i.e. applies the so-called solution map. The appearance of the ‘dimension defect’ reflecting the nonnegativity of Fredholm indices requires the use of algebraic tools based on the cohomotopy theory, different from the usual homological ones present in the fixed point theory. An application to boundary value problems is provided as well as the brief exposition of basic facts from the cohomotopy theory. Mathematics Subject Classifications (2000) 47H04, 47A53, 55M20, 55Q55, 34A60.     

Probing the 3d spin momentum with X-ray emission spectroscopy: the case of molecular-spin transitions

We report X-ray emission spectra of Fe(III), Fe(II), and Co(II) spin-crossover compounds in their high-spin and low-spin forms. It is shown that all X-ray emission features are sensitive to the spin state. Variations of the Kbeta and the Kalpha emission line shapes, which are in agreement with theory, can be used as quantitative probes of the spin state; it is suggested that with appropriate reference experiments one can extract the spin momentum for a general case. Resonant X-ray emission spectra unveil details of the redistribution of electrons on the 3d levels associated with the spin-state change by revealing features at the X-ray absorption preedge not accessible through standard absorption measurements.     

In situ sum frequency generation vibrational spectroscopy observation of a reactive surface intermediate during high-pressure benzene hydrogenation

Sum frequency generation surface vibrational spectroscopy and kinetic measurements using gas chromatography have been used to identify a reactive surface intermediate in situ during hydrogenation of benzene on a Pt(111) single crystal surface at Torr pressures. Upon adsorption at 310 K, both chemisorbed and physisorbed benzene coexist on the surface, a result which has not previously been observed. Kinetic measurements show a linear compensation effect for the production of both cyclohexane and cyclohexene. From these data the isokinetic temperature was identified and correlated to the chemisorbed benzene species, which were probed by means of vibrational spectroscopy. Additionally, chemisorbed benzene was determined to be a reactive intermediate, which is critical for hydrogenation.     

Characteristic Numbers of Multiple-Point Manifolds

We give a general method for expressing various characteristicnumbers of the multiple-point manifolds of an immersion. 2000Mathematics Subject Classification 57R42 (primary), 57R20, 57R75(secondary).