Tandem Michael addition–Claisen-type condensation of anions of O-ethyl carbonates of cyanohydrins to cyclohex-2-en-1-one

A one pot method for the synthesis of ethyl 2-acetoxy-6-aroylcyclohex-1-ene-1-carboxylates and ethyl 2-acetoxy-6-heterocarbonylcyclohex-1-ene-1-carboxylates through Michael addition of the anions of ethyl carbonates of cyanohydrins to cyclohex-2-en-1-one and subsequent reaction with acetic anhydride is described. These compounds are potential intermediates for the synthesis of 9,10-anthraquinone and heterofused 1,4-naphthoquinone derivatives.     

Enantioselective addition of Et2Zn to seven‐membered cyclic imines catalyzed by a (R)-VAPOL-Zn(II) complex

Various substituted dibenzo[b,f][1,4]oxazepines underwent an enantioselective alkylation with Et₂Zn catalyzed by a (R)-VAPOL-Zn(II) complex. The corresponding chiral 11-ethyl-10,11-dihydrodibenzo[b,f][1,4]oxazepine derivatives were obtained with good yields and moderate enantioselectivities. This represents the first example of enantioselective addition of Et₂Zn to cyclic aldimines.     

Synthesis of 3-substituted 2-cyclohexenones through umpoled functionalization

A new protocol to obtain 3-substituted 2-cyclohexenones, was developed by reversing the chemical reactivity of 2-cyclohexenone. One-pot synthesis of 3-substituted 2-cyclohexenones can be achieved by treatment of 3-phenylthiosilyl enol ether with a mixture of t-BuLi/HMPA that allows hydrogen-selective exchange in presence of reactive electrophiles such as aldehydes, ketones and alkyl halides. This affords the corresponding product in moderate overall yield, after silyl enol ether cleavage and concomitant thiophenol elimination initiated with TBAF.     

Theoretical investigation of the molecular structure and spectroscopic properties of oxicams

Nonsteroidal anti-inflammatory drugs (NSAIDs) are among the most frequently prescribed drugs and have multiple therapeutic uses. These drugs are predominantly used for the treatment of musculoskeletal diseases because of their analgesic, antipyretic, and antiplatelet activities. Oxicams constitute an interesting class of organic compounds and have been investigated in the search for new analgesic and anti-inflammatory drugs. In the present work, a theoretical investigation of the molecular structure and spectroscopic properties of a series of five oxicams in different solvents was performed using density functional theory (DFT) methods. The geometric optimizations of the oxicams were carried out using the M06 density functional and the CBSB7 basis set. The infrared data were all obtained at the same theoretical level. The UV-Vis absorption and NMR data of some oxicams were calculated using the DFT and CBSB3 basis sets. The analysis of structural parameters, particularly the bond length and spectroscopic data, indicated that interactions occurred between the hydrogen bond types for 4-meloxicam, isoxicam, and normeloxicam. Stereoelectronic interactions caused by the substitution of alkyl groups caused the bond lengths to elongate. Similarly, the substitution of heteroatoms, such as nitrogen, sulfur, or oxygen, increased the bond lengths and angular stresses.     

Application of thermal analysis for evaluating the digestion of microwave pre-treated sewage sludge

The effect of microwave pre-treatment (MwP) on anaerobic digestion of sewage sludge was studied by means of thermal analysis and evolved gas analysis. The effect of the pre-treatment at low energy input (<1000 kJ L^?1) on sludge solubilisation was studied with the aid of response surface methodology. The pre-treatment process was subsequently studied at energies of 488–2700 kJ L^?1 to evaluate the improvement in biogas production under mesophilic conditions. Organic matter modifications were studied using a Setaram TGA92 analyser at atmospheric pressure coupled to an MSC200 quadrupole mass spectrometer from Balzers. Particle size analysis was carried out using a Laser Diffraction Particle Size Analyser LS 13 320 Beckmann Coulter for evaluating the effect of MwP on sludge particles. Results showed an increase in organic matter solubilisation with the increase in the energy applied. Modifications in the specific surface area of the organic matter due to the MwP resulted in increments in methane yields. However, an accumulation of complex compounds was observed in thermal profiles at the maximum energy input (2700 kJ L^?1). Semi-continuous digestion experiments were evaluated using as substrate pre-treated sludge at the optimum energy value (975 kJ L^?1). Results showed a significant increase in methane yield (43 %) when evaluating the process at hydraulic retention times (HRTs) of 25–10 days.     

Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts.     

Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.     

Lattices with Defining Relations Close to Distributivity

We consider the 3-generated lattices whose generators enjoy the defining relations of the type a∨(b∧c) = (a∨b)∧(a∨c). Moreover, if the lattice is finite then we obtain its diagram; otherwise, we prove that the corresponding lattice is infinite.