Invariant polynomials on truncated multicurrent algebras

We construct invariant polynomials on truncated multicurrent algebras, which are Lie algebras of the form $\mathfrak{g}{?}_{\mathbb{F}}\mathbb{F}[t_1,\dots ,t_{?}]/I$, where $\mathfrak{g}$ is a finite-dimensional Lie algebra over a field $\mathbb{F}$ of characteristic zero, and I is a finite-codimensional ideal of $\mathbb{F}[t_1,\dots ,t_{?}]$ generated by monomials. In particular, when $\mathfrak{g}$ is semisimple and $\mathbb{F}$ is algebraically closed, we construct a set of algebraically independent generators for the algebra of invariant polynomials. In addition, we describe a transversal slice to the space of regular orbits in $\mathfrak{g}{?}_{\mathbb{F}}\mathbb{F}[t_1,\dots ,t_{?}]/I$. As an application of our main result, we show that the center of the universal enveloping algebra of $\mathfrak{g}{?}_{\mathbb{F}}\mathbb{F}[t_1,\dots ,t_{?}]/I$ acts trivially on all irreducible finite-dimensional representations provided I has codimension at least two.     

Catechol Thioesters: Ligands for Hierarchically Formed Lithium-Bridged Titanium(IV) Helicates and Helicate-Based Switches

The thioester moiety is introduced as a lithium binding unit for the hierarchical formation of titanium(IV) catecholate-based lithium-bridged helicates. In solution, the coordination compounds show a monomer–dimer equilibrium which —in comparison to the oxo esters— is significantly shifted towards the monomers. In addition, the influence of the thioester side chain on the dimerization behavior is investigated and an expansible/compressible molecular switch is synthesized. In the latter case expansion and compression are performed reversibly in methanol, whereas in DMSO spontaneous expansion occurs.     

Measurement of iron self-diffusion in hematite single crystals by secondary ion-mass spectrometry (SIMS) and comparison with cation self-diffusion in corundum-structure oxides

Iron bulk self-diffusion coefficients were measured in Fe₂O₃ single crystals using original methodology based on the utilization of ⁵⁷Fe stable isotope as iron tracer and depth profiling by secondary ion-mass spectrometry (SIMS). The iron self-diffusion coefficients were measured along and perpendicular to the c-axis, between 900 and 1100°C, in an oxygen atmosphere. Along the c-axis, the coefficients can be described by D _{∥ c} (cm²/s)?=?5.2?×?10⁶?exp[?510 (kJ/mol)/RT], and are close to reliable data, available in the literature, obtained by means of radioactive techniques. Perpendicular to the c-axis, D _⊥c (cm²/s)?= 83?exp[?430 (kJ/mol)/RT], and the coefficients are smaller than coefficients along the c-axis. The data are compared with previously results of cation bulk self-diffusion in Cr₂O₃ and Al₂O₃ single crystals.     

Regioselectivity in the acylation of methylhydroquinone dimethyl ether: an unprecedented case of indirect steric hindrance

The origin of the highly regioselective acylation of methylhydroquinone dimethyl ether was investigated using geometry minimization (ab initio and DFT) and NOE spectroscopic measurements. The theoretical and experimental results were consistent with the indirect participation of the aromatic methyl group in blocking the electrophile attack at position 3 of the aromatic ring.     

Thermodynamic behavior of lipid nanoparticles upon delivery of Vitamin E derivatives into the skin: in vitro studies

This article reports the thermodynamic changes of lipid nanoparticles (LN) upon delivery of lipophilic vitamin E derivatives to the skin. Skin penetration of α-tocopherol (α-T) and α-tocopherol acetate (α-Ta) into and across porcine ear skin was investigated in vitro using tape-stripping test in modified Franz diffusion cells. Wide angle X-ray scattering (WAXS) and differential scanning calorimetry (DSC) have been used to characterize the polymorphism of the solid matrix of LN before and after in vitro skin penetration assay. Cetyl palmitate LN with a loading capacity of 20% of vitamin E derivatives (with regard to the lipid matrix) have shown the typical β’ modification of waxes, with a crystallinity index (%CI) between 30 and 40%. Mean particle size and shelf life stability was assessed by static (laser diffractometry, LD) and dynamic (photon correlation spectroscopy, PCS) light scattering techniques. Submicron-sized LN were produced, i.e., 99% of LN showed a size below 600 nm immediately after production. A mean size between 180 and 350 nm (polydispersity index < 0.25) was obtained for LN stored at both 8 and 22 °C, and this size range was kept constant for at least 20 days of shelf life. Quantification of α-T and α-Ta in the skin using tape-stripping provided a 3.4-fold increase in the level of actives within the stratum corneum (SC) and 1.3-fold increase in the viable epidermis (VE). LN increased skin penetration of both actives, following a cumulative release during 8 h in modified Franz diffusion cells. The differences in the distribution levels observed between α-T and α-Ta when delivered via LN was due to the different thermodynamic activity of both actives, i.e., following increased partition coefficient of α-Ta into SC and VE, in comparison to α-T.     

Ethanol Production from Cashew Apple Bagasse: Improvement of Enzymatic Hydrolysis by Microwave-Assisted Alkali Pretreatment

In this work, the potential of microwave-assisted alkali pretreatment in order to improve the rupture of the recalcitrant structures of the cashew able bagasse (CAB), lignocellulosic by-product in Brazil with no commercial value, is obtained from cashew apple process to juice production, was studied. First, biomass composition of CAB was determined, and the percentage of glucan and lignin was 20.54 ± 0.70% and 33.80 ± 1.30%, respectively. CAB content in terms of cellulose, hemicelluloses, and lignin, 19.21 ± 0.35%, 12.05 ± 0.37%, and 38.11 ± 0.08%, respectively, was also determined. Results showed that, after enzymatic hydrolysis, alkali concentration exerted influence on glucose formation, after pretreatment with 0.2 and 1.0 mo L⁻¹ of NaOH (372 ± 12 and 355 ± 37 mg g_glucan⁻¹) when 2% (w/v) of cashew apple bagasse pretreated by microwave-assisted alkali pretreatment (CAB-M) was used. On the other hand, pretreatment time (15–30 min) and microwave power (600–900 W) exerted no significant effect on hydrolysis. On enzymatic hydrolysis step, improvement on solid percentage (16% w/v) and enzyme load (30 FPU g_CAB-M⁻¹) increased glucose concentration to 15 g L⁻¹. The fermentation of the hydrolyzate by Saccharomyces cerevesiae resulted in ethanol concentration and productivity of 5.6 g L⁻¹ and 1.41 g L⁻¹ h⁻¹, respectively.     

Study of the Alkyl Chain Length on Laccase Stability and Enzymatic Kinetic with Imidazolium Ionic Liquids

The activity and stability of laccase and their kinetic mechanisms in water soluble ionic liquids (ILs): 1-butyl-3-methyl imidazolium chloride [C₄mim][Cl], 1-octyl-3-methyl imidazolium chloride [C₈mim][Cl], and 1-decyl-3-methyl imidazolium chloride [C₁₀mim][Cl] were investigated. The results show that an IL concentration up to 10% is satisfactory for initial laccase activity at pH 9.0. The laccase stability was well maintained in [C₄mim][Cl] IL when compared to the control. The inactivation of laccase increases with the length of the alkyl chain in the IL: [C₁₀mim][Cl] > [C₈mim][Cl] > [C₄mim][Cl]. The kinetic studies in the presence of ABTS as substrate allowed calculating the Michaelis–Menten parameters. Among the ILs, [C₄mim][Cl] was the suitable choice attending to laccase activity and stability. Alkyl chains in the ions of ILs have a deactivating effect on laccase, which increases strongly with the length of the alkyl chain.     

Determination and modelling of osmotic coefficients and vapour pressures of binary systems 1- and 2-propanol with CnMimNTf2 ionic liquids (n = 2, 3, and 4) at T = 323.15 K

The osmotic and activity coefficients and vapour pressures of binary mixtures containing 1-propanol, or 2-propanol and imidazolium-based ionic liquids with bis(trifluoromethylsulfonyl)imide as anion (1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, C₂MimNTf₂, 1-methyl-3-propylimidazolium bis(trifluoromethylsulfonyl)imide, C₃MimNTf₂, and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, C₄MimNTf₂) were determined at T = 323.15 K using the vapour pressure osmometry technique. The experimental osmotic coefficients were correlated using the extended Pitzer model modified by Archer and the MNRTL model, obtaining standard deviations lower than 0.033 and 0.064, respectively. The mean molal activity coefficients and the excess Gibbs free energy for the mixtures studied were calculated from the parameters of the extended Pitzer model modified by Archer. Besides the effect of the alkyl-chain of the cation, the effect of the anion can be assessed comparing the experimental results with those previously obtained for imidazolium ionic liquids with sulphate anions.