Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.

Doubly-charged ethane ions: Solution to the dilemma of stability predicted by theory and instability observed in experiment

Potential energy curves have been computed for [C2H6]2+ ions and the results used to interpret the conspicuous absence of these ions in 2E mass spectra and in charge-stripping experiments. The energies and structures of geometry-optimized ground-state singlet and excited-state triplet [C2H6]2+ ions have been determined along with energies for different decomposition barriers and dissociation asymptotes. Although singlet and triplet [C2H6]2+ ions can exist as stable entities, they possess low energy barriers to decomposition. Vertical Franck-Condon transitions, involving electron impact ionization of ethane as well as charge-stripping collisions of [C2H6]+ ions, produce [C2H6]2+ ions which promptly dissociate since they are formed with energies in excess of various decomposition barriers. Appearance energies computed for doubly-charged ethane fragment ions are in accordance with experimental values.

Microscopic and Spectroscopic Methods for Probing the Clay Water Interface

Clay minerals have a fundamental importance in many processes in soils and sediments such as the bioavailability of nutrients, water retention, the adsorption of common pollutants, and the formation of an impermeable barrier upon swelling. Many of the properties of clay minerals are due to the unique environment present at the clay mineral/water interface. Traditional techniques such as X-ray diffraction (XRD) and absorption isotherms have provided a wealth of information about this interface but have suffered from limitations. The methods and results presented herein are designed to yield new experimental information about the clay mineral/water interface.A new method of studying the swelling dynamics of clay minerals was developed using in situ atomic force microscopy (AFM). The preliminary results presented here demonstrate that this technique allows one to study individual clay mineral unit layers, explore the natural heterogeneities of samples, and monitor swelling dynamics of clay minerals in real time. Cation exchange experiments were conducted monitoring the swelling change of individual nontronite quasi-crystals as the chemical composition of the surrounding environment was manipulated several times. A proof of concept study has shown that the changes in swelling are from the exchange of interlayer cations and not from the mechanical force of replacing the solution in the fluid cell. A series of attenuated total internal reflection Fourier transform infrared spectroscopy (ATR-FTIR) experiments were performed to gain a better understanding of the organization of water within the interlayer region of two Fe-bearing clay minerals. These experiments made use of the Subtractive Kramers-Kronig (SKK) Transform and the calculation of difference spectra to obtain information about interfacial water hidden within the absorption bands of bulk water. The results indicate that the reduction of structural iron disrupts the organization of water around a strongly hydrated cation such as sodium as the cation transitions from an outer-sphere complex with the mineral surface to an inner-sphere complex. In the case of a less strongly hydrated cation such as potassium, reduction of structural iron actually increases the ordering of water molecules at the mineral surface. These effects were only noticed with the reduction of iron in the tetrahedral sheet close to the basal surface where the increased charge density is localized closer to the cations in the interlayer.

Mental Health and Mental Illness in Later Life: The Ecology of Theory and Practice

Theoretical and practical concerns shape our conceptualizations of mental health and mental illness later in life. Together, these concerns form an ecology of theory and practice, shaping our expectations of later life and our efforts with an din behalf of older adults. Introduces a series of article which highlights several aspects of mental health and mental illness in later life to provide an understanding of the challenges faced by the aged in maintaining mental health.