The Orthomodular Poset of Projections of A Symmetric Lattices

In a Hilbert space, there exists a natural correspondence between continuous projections and particular pairs of closed subspaces. In this paper, we generalize this situation and associate to a symmetric lattice L a subset P(L) of L× L, called its projection poset. If L is the lattice of closed subspaces of a topological vector space then elements of P(L) correspond to continuous projections and we prove that automorphisms of P(L) are determined by automorphisms of the lattice L when this lattice satisfies some basic properties of lattices of closed subspaces. Primary: 06C15, Secondary: 03G12 81P10.     

Mott transition and suppression of orbital fluctuations in orthorhombic 3d1 perovskites

Using t(2g) Wannier functions, a low-energy Hamiltonian is derived for orthorhombic 3d(1) transition-metal oxides. Electronic correlations are treated with a new implementation of dynamical mean-field theory for noncubic systems. Good agreement with photoemission data is obtained. The interplay of correlation effects and cation covalency (GdFeO3-type distortions) is found to suppress orbital fluctuations in LaTiO3 and even more in YTiO3, and to favor the transition to the insulating state.     

An efficient, stereoselective approach to syn-1,2-diols protected as cyclic carbonates

Enantioenriched 4-hydroxyalk-2-ynyl carbonates (or benzoates) have been prepared by stereoselective zinc-mediated addition of alkyl 2-propynyl carbonates (or their benzoate analogues) to aldehydes. Their partial reduction to Z-olefins followed by cyclization under mild Pd-catalyzed conditions allowed a straightforward access to enantioenriched syn-1,2-diols protected as cyclic carbonates.     

Flow linear dichroism to probe binding of aromatic molecules and DNA to single-walled carbon nanotubes

Structures of carbon nanotube/ligand complexes were studied by flow linear dichroism (the differential absorption of light polarized parallel and perpendicular to the flow orientation direction) with the aim of establishing linear dichroism as a technique to study such systems. Anthracene, naphthalene, and DNA were chosen as ligands, and the potential for flow linear dichroism to probe ligands noncovalently (as well as covalently) bound to single-walled nanotubes is reported. Linear dichroism enables the determination of approximate orientations of the ligands on the carbon nanotubes.     

Heterogeneity of the surface energy on unused C18-chromolith adsorbents in reversed-phase liquid chromatography

Single-component adsorption isotherm data were acquired by frontal analysis (FA) for phenol and caffeine on a new C18-Chromolith column (Merck, Darmstadt, Germany), using a water-rich mobile phase (methanol/water, 15/85, v/v). These data were modeled for best agreement between the experimental data points and the adsorption isotherm model. The adsorption-energy distributions, based on the expectation-maximization (EM) procedure, were also derived and used for the selection of the best isotherm model. The adsorption energy distributions (AEDs) for phenol and caffeine converged toward a trimodal and a quadrimodal distribution, respectively. Energy distributions with more than two modes had not been reported before for the adsorption of these compounds on packed columns. The third high energy mode observed for both phenol and caffeine seems to be specific of the surface of the monolithic column while the first and second low energy modes have the same physical origin as the two modes detected on packed columns. These results suggest significant differences between the structures of the porous silica in these different materials.     

Passively mode-locked diode-pumped Nd:YVO4 oscillator operating at an ultralow repetition rate

We demonstrate the operation of an ultralow-repetition-rate, high-peak-power, picosecond diode-pumped Nd:YVO4 passively mode-locked laser oscillator. Repetition rates lower than 1 MHz were achieved with the use of a new design for a multiple-pass cavity and a semiconductor saturable absorber. Long-term stable operation at 1.2 MHz with a pulse duration of 16.3 ps and an average output power of 470 mW, corresponding to 24-kW peak-power pulses, is reported. These are to our knowledge the lowest-repetition-rate high-peak-power pulses ever generated directly from apicosecond laser resonator without cavity dumping.     

Coherence scale of the kondo lattice

It is shown that the large- N approach yields two energy scales for the Kondo lattice model. The single-impurity Kondo temperature, T(K), signals the onset of local singlet formation, while Fermi-liquid coherence sets in only below a lower scale, T small star, filled. At low conduction electron density n(c) ("exhaustion" limit), the ratio T small star, filled/T(K) is much smaller than unity, and is shown to depend only on n(c) and not on the Kondo coupling. The physical meaning of these two scales is demonstrated by computing several quantities as a function of n(c) and temperature.     

Mean field theory of a quantum heisenberg spin glass

A full mean-field solution of a quantum Heisenberg spin-glass model is presented in a large- N limit. A spin-glass transition is found for all values of the spin S. The quantum critical regime associated with the quantum transition at S = 0 and the various regimes in the spin-glass phase at high spin are analyzed. The specific heat is shown to vanish linearly with temperature. In the spin-glass phase, intriguing connections between the equilibrium properties of the quantum problem and the out-of-equilibrium dynamics of classical models are pointed out.     

On Two Theorems about Symplectic Reflection Algebras

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl Algebra W, and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP (2n)) and, as a consequence, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg (Invent Math 147:243–348, 2002), which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones). Dedicated to my friend J.-C. Cortet.     

Influence of camphorsulfonic acid in nitroxide‐mediated styrene miniemulsion polymerization

The rate‐accelerating effects of camphorsulfonic acid (CSA) on nitroxide‐mediated styrene miniemulsion polymerization were studied. Polymerizations were initiated with benzoyl peroxide (BPO) as an initiator and mediated with either 2,2,6,6‐tetramethylpiperidinyloxy (TEMPO) or 4‐hydroxy‐2,2,6,6‐tetramethylpiperidinyloxy (OH‐TEMPO). Although CSA has been used to accelerate the rate in bulk nitroxide‐mediated polymerizations, it has not been well studied in emulsion/miniemulsion. With dispersed systems, the effectiveness of CSA is likely to be affected by partitioning between the aqueous and organic phases. In styrene miniemulsion experiments performed over a range of conditions, the effect of adding CSA varied from negligible to significantly increasing the final conversion and molecular weight, depending on the nitroxide:BPO ratio. At a ratio of nitroxide:BPO = 1.7, the effect of CSA addition is small, whereas the final conversion and molecular weight are dramatically enhanced by CSA addition when the nitroxide:BPO ratio is 3.6. CSA is most effective in enhancing the rate and molecular weight when the initial free‐nitroxide concentration is higher. The magnitude of the rate and molecular weight enhancement was similar for TEMPO and OH‐TEMPO despite their differences in water solubility. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2828–2841, 2002