Ordering of Energy Levels in Heisenberg Models and Applications

In a recent paper we conjectured that for ferromagnetic Heisenberg models the smallest eigenvalues in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin and called this property ferromagnetic ordering of energy levels (FOEL). We have proved this conjecture for the Heisenberg model with arbitrary spins and coupling constants on a chain. In this paper we give a pedagogical introduction to this result and also discuss some extensions and implications. The latter include the property that the relaxation time of symmetric simple exclusion processes on a graph for which FOEL can be proved, equals the relaxation time of a random walk on the same graph. This equality of relaxation times is known as Aldous' Conjecture.Comment: 20 pages, contribution for the proceedings of QMATH9, Giens, September 200

Selectivity control in Pt-catalyzed cinnamaldehyde hydrogenation

Chemoselectivity is a cornerstone of catalysis, permitting the targeted modification of specific functional groups within complex starting materials. Here we elucidate key structural and electronic factors controlling the liquid phase hydrogenation of cinnamaldehyde and related benzylic aldehydes over Pt nanoparticles. Mechanistic insight from kinetic mapping reveals cinnamaldehyde hydrogenation is structure-insensitive over metallic platinum, proceeding with a common Turnover Frequency independent of precursor, particle size or support architecture. In contrast, selectivity to the desired cinnamyl alcohol product is highly structure sensitive, with large nanoparticles and high hydrogen pressures favoring C=O over C=C hydrogenation, attributed to molecular surface crowding and suppression of sterically-demanding adsorption modes. In situ vibrational spectroscopies highlight the role of support polarity in enhancing C=O hydrogenation (through cinnamaldehyde reorientation), a general phenomenon extending to alkyl-substituted benzaldehydes. Tuning nanoparticle size and support polarity affords a flexible means to control the chemoselective hydrogenation of aromatic aldehydes

Safety of topical methimazole for the treatment of melasma. Transdermal absorption, the effect on thyroid function and cutaneous adverse effects

Methimazole is an oral antithyroid compound that exhibits a skin-depigmenting effect when used topically. However, the effect of topical methimazole on thyroid function has not been reported. This study was aimed at assessing the safety of topical methimazole used to treat pigmented lesions, without affecting thyroid hormones due to systemic delivery. The pharmacokinetics of methimazole, either applied in the form of a 5% topical formulation to facial skin or taken orally in the form of a 5-mg tablet by 6 volunteers, were determined. In addition, the effect of long-term topical applications of 5% methimazole on the function of the thyroid gland in 20 patients with epidermal melasma was determined following 6 weeks of once-daily application. Cutaneous adverse effects of topical methimazole were determined. From 15 min up to 24 h after application, methimazole was undetectable in the serum of the individuals receiving single topical methimazole dosing. Methimazole, however, was detected in serum after 15 min of oral administration and remained detectable in serum up to 24 h after administration. Long-term topical methimazole applications in melasma patients did not induce any significant changes in serum TSH, free thyroxine and free triiodothyronine levels. Topical methimazole was well tolerated by the patients and did not induce any significant cutaneous side effects. Present data together with the previously shown non-cytotoxic and non-mutagenic characteristics of methimazole indicate that this agent could be considered as a safe skin-depigmenting compound for topical treatment of skin hyperpigmentary disorders in humans