Boundaries of Coxeter Matroids

The purpose of this paper is to introduce, for a finite Coxeter groupW, the mod 2 boundary operator on the space of all Coxeter matroids (also known asWP-matroids) forWandP, wherePvaries through all the proper standard parabolic subgroups ofW(Theorem 3 of the paper). A remarkably simple interpretation of Coxeter matroids as certain sets of faces of the generalized permutahedron associated with the Coxeter groupW(Theorem 1) yields a natural definition of the boundary of a Coxeter matroid. The latter happens to be a union of Coxeter matroids for maximal standard parabolic subgroupsQ_iofP(Theorem 2). These results have very natural interpretations in the case of ordinary matroids and flag-matroids (Section 3).     

Second Order Integrability Conditions for Difference Equations: An Integrable Equation

Integrability conditions for difference equations admitting a second order formal recursion operator are presented and the derivation of symmetries and canonical conservation laws are discussed. In a generic case, some of these conditions yield nonlocal conservation laws. A new integrable equation satisfying the second order integrability conditions is presented and its integrability is established by the construction of symmetries, conservation laws and a 3 × 3 Lax representation. Finally, via the relation of the symmetries of this equation to the Bogoyavlensky lattice, an integrable asymmetric quad equation and a consistent pair of difference equations are derived.     

Effect of aerosil dispersions on the nematic-to-isotropic interface

The effect of silica aerosils on the kinetics of the first-order nematic-isotropic (NI) phase transition is phenomenologically described in the framework of the time-dependent Landau-Ginzburg equation. A steady-state solution to the equation is presented such that the NI interface may propagate with a solitary-like wave profile under constant quenching. The results provide a plausible basis for the interpretation of the dynamical effects of quenched disorder in the liquid-crystal systems, caused by randomly interconnected porous media, such as aerosils. In the low silica aerosil ρ_s ( ≤0.1 g/cm^3) regime, the calculated values of the interface velocity v(T,ρ_s), the interface thickness κ(T,ρ_s), and the critical radius of a spherical nucleus of new nematic phase in a bulk isotropic environment, composed of polar molecules, such as 4-n-octyl- 4^′- cyanobiphenyl and 4-n-heptyl- 4^′- cyanobiphenyl shows that the effect of silica aerosils on the kinetics is reflected in a shifting of the set of temperature-dependent curves to lower temperature values.-1     

Tunable coupling of superconducting qubits

We study an LC circuit implemented using a current-biased Josephson junction (CBJJ) as a tunable coupler for superconducting qubits. By modulating the bias current, the junction can be tuned in and out of resonance and entangled with the qubits coupled to it. One can thus implement two-qubit operations by mediating entanglement. We consider the examples of CBJJ and charge-phase qubits. A simple recoupling scheme leads to a generalization to arbitrary qubit designs.     

Solubility and Raman Spectroscopic Study of As(III) Speciation in Organic Compound-Water Solutions. A Hydration Approach for Aqueous Arsenic in Complex Solutions

Solubilities of arsenolite (As₂O₃, cub.) were measured from 22 to 90°C in water–acetone, water–acetic acid, and water—formic acid solutions of compositions ranging from the pure organic compound to pure water. Raman spectra were obtained at ambient temperature on As-containing water–acetic acid and water–acetone solutions. Results show that arsenic solvation by these organic compounds is negligible and hydroxide species dominate As speciation over a wide range of water activity (a_{H 2 O}> 0.01). The solubility data were analyzed using an approach based on stoichiometric hydration reactions. Results show that As₂O₃ solubility can be described as a function of water activity, independently of the nature of the organic compound, by involving two neutral As hydroxide complexes: As(OH)₃ and As(OH)₃·4H₂O. Stability constants derived for these species indicate that hydration weakens with increasing temperature. Calculations using these constants show that at low temperatures the tetrahydrate As(OH)₃·4H₂O is dominant in water-rich solutions; by contrast, in high-temperature crustal fluids, As(OH)₃ becomes the major As species. The proposed hydration model can be used to analyze solubility of arsenic-bearing minerals and arsenic transport in complex H₂O–CO₂—electrolyte solutions encountered in natural and industrial environments.     

High diversity on simple substrates: 1,4-dihalo-2-butenes and other difunctionalized allylic halides for copper-catalyzed S(N)2' reactions

Enantioselective allylic alkylation with an organomagnesium reagent catalyzed by copper thiophene carboxylate (CuTC) was carried out on difunctionalized substrates, such as commercially available 1,4-dichloro-2-butene and 1,4-dibromo-2-butene, and on similar compounds of higher substitution pattern of the olefin for the formation of all-carbon chiral quaternary centers. The high regioselectivity obtained throughout the reactions favored good regiocontrol for the addition of phenyl Grignard reagents. Other difunctionalized substrates (allylic ethers and allylic alcohols) also underwent asymmetric S(N)2' substitution.     

Electron density redistribution accounts for half the cooperativity of alpha helix formation

The energy of alpha helix formation is well known to be highly cooperative, but the origin and relative importance of the contributions to helical cooperativity have been unclear. Here we separate the energy of helix formation into short range and long range components by using two series of helical dimers of variable length. In one dimer series two monomeric helices interact by forming hydrogen bonds, while in the other they are coupled only through long range, primarily electrostatic interactions. Using Density Functional Theory, we find that approximately half of the cooperativity of helix formation is due to electrostatic interactions between residues, while the other half is due to nonadditive many-body effects brought about by redistribution of electron density with helix length.     

Copper acetylacetonate anchored onto amine-functionalised clays

Copper (II) acetylacetonate was immobilised directly onto two clays, laponite (Lap) and K10-montmorillonite (K10), and after their amine functionalisation with (3-aminopropyl)triethoxysilane (APTES). All the materials were characterised by nitrogen adsorption isotherms at -196 degrees C, elemental analysis, TG-DSC, XRD, and IR spectroscopy. The K10-based materials were also characterised by XPS. The APTES-functionalised K10 showed higher copper loading than K10, indicating that the clay functionalisation enhanced the complex immobilisation; on the contrary, in Lap-based materials higher metal content was obtained by direct complex anchoring, probably due to the delaminated nature of Lap which induced the particles aggregation on functionalisation with APTES. All the results pointed out that the Cu complex was anchored onto the amine-functionalised clays by Schiff condensation between the amine groups of anchored APTES and the carbonyl groups of the acetylacetonate ligand, whereas direct immobilisation proceeded mostly through interaction between the metal centre and the clay surface hydroxyl groups.     

Studies on the Eschenmoser coupling reaction and insights on its mechanism. Application in the synthesis of Norallosedamine and other alkaloids

The conditions of the Eschenmoser coupling reaction were studied. The formation of the α-thioiminium ion was achieved faster in the presence of an additive (NaI) and dry chloroform as the preferred solvent. The developed conditions were used for the second part of the reaction (the sulfur extrusion itself). The present protocol avoids the formation of byproducts, which were previously described as a major drawback to be overcome. Electrospray ionization tandem mass spectrometry was used to characterize some aspects (intermediates) of the first step of the reaction mechanism. Some reduction conditions were properly tested and the selected conditions were applied to the synthesis of the natural alkaloid Norallosedamine and other derivatives.