Highly enantioselective synthesis of tetrahydro-beta-carbolines and tetrahydro-gamma-carbolines via Pd-catalyzed intramolecular allylic alkylation

A novel Pd-catalyzed intramolecular allylic alkylation of indoles allows THBCs and THGCs to be effectively synthesized in high yields and excellent enantiomeric excesses (ee up to 97%).     

Microbial transformation of two 15α-hydroxy-ent-kaur-16-ene diterpenes by Mucor plumbeus

The microbiological transformation of candidiol (15α,18-dihydroxy-ent-kaur-16-ene) by Mucor plumbeus led to 3β,15α,18-trihydroxy-ent-kaur-16-ene, 6α,15α,18-trihydroxy-ent-kaur-16-ene, 3α,15α,18-trihydroxy-ent-kaur-16-ene, 11β,15α,18-trihydroxy-ent-kaur-16-ene and 15α,17,18-trihydroxy-11β,16β-epoxy-ent-kaurane, whilst the incubation of 15α,19-dihydroxy-ent-kaur-16-ene gave 9β,15α,19-trihydroxy-ent-kaur-16-ene, 3α,15α,19-trihydroxy-ent-kaur-16-ene, 11β,15α,19-trihydroxy-ent-kaur-16-ene, 6α,15α,19-trihydroxy-ent-kaur-16-ene, 15α,17,19-trihydroxy-11β,16β-epoxy-ent-kaurane, 19-(β-d-glucopyranosyl)-15α-hydroxy-ent-kaur-16-ene and 19-(β-d-glucopyranosyl)-15-oxo-ent-kaur-16-ene. An interesting rearrangement in dilute acid medium of 9β,15α,19-trihydroxy-ent-kaur-16-ene into 16-oxo-19-hydroxy-ent-abiet-8(9),15-diene, is also described in this work.     

Restricting the versatile metal-binding behaviour of adenine by using deaza-purine ligands in mixed-ligand copper(II) complexes

In order to deepen our understanding of the versatile behaviour of adenine (Hade) as ligand, we have synthesized four novel ternary copper(II) complexes having two deazaadenine ligands, namely 4-azabenzimidazole (H4abim) or 7-azaindole (H7azain) as N1,N6-dideazaadenine or N1,N6,N7-trideazaadenine, respectively. The related compounds were studied by thermal, spectral and single crystal X-ray diffraction methods. In [Cu(NBzIDA)(H4abim)]_n (1) the recognition between H4abim and the (N-benzyliminodiacetate)-copper(II) chelate only displays the formation of the Cu–N7(purine-like) bond, in contrast to Hade behaviour in [Cu(NBzIDA-like)(Hade)(H₂O)]·H₂O (Cu–N3(Hade) bond reinforced by N9–H···O(IDA-like) interaction). In [Cu(EIDA)(H7azain)(H₂O)] (2, EIDA = N-ethyliminodiacetate ligand), [Cu(NBzIDA)(H7azain)(H₂O)] (3) and [Cu(μ₂-SO₄)(H7azain)₂(H₂O)₂]_n (4), H7azain binds Cu(II) centre by the Cu–N3(purine-like) bond, reinforced by a N9–H···O(IDA-like or sulfate) intra-molecular interligand interaction.     

On the index and the order of quasi-regular implicit systems of differential equations

This paper is mainly devoted to the study of the differentiation index and the order for quasi-regular implicit ordinary differential algebraic equation (DAE) systems. We give an algebraic definition of the differentiation index and prove a Jacobi-type upper bound for the sum of the order and the differentiation index. Our techniques also enable us to obtain an alternative proof of a combinatorial bound proposed by Jacobi for the order.As a consequence of our approach we deduce an upper bound for the Hilbert–Kolchin regularity and an effective ideal membership test for quasi-regular implicit systems. Finally, we prove a theorem of existence and uniqueness of solutions for implicit differential systems.     

Spectral theory of Volterra-composition operators

Given a Lebesgue measurable self-map of the interval [0, 1], the Volterra- composition operator is defined as We develop the spectral theory of these operators. In particular, for a class of natural symbols , finiteness of the spectrum is characterized and formulae for the trace and the convergence exponent of eigenvalues are provided. The positivity of the spectrum as well as the analyticity of the eigenfunctions are also treated. The theory of entire functions as well as solving some Cauchy Problems will play a fundamental role in this theory. We also supply some examples of symbols to which the theory can be applied and, in particular, eigenvalues and eigenfunctions are computed explicitly. Partially supported by Plan Nacional I+D+I grant no. MTM2006-09060, Junta de Andalucía FQM-260 and P06-FQM-02225.     

Local product structure for expansive homeomorphisms

Let be an expansive homeomorphism with dense topologically hyperbolic periodic points, M a closed manifold. We prove that there is a local product structure in an open and dense subset of M. Moreover, if some topologically hyperbolic periodic point has codimension one, then this local product structure is uniform. In particular, we conclude that the homeomorphism is conjugated to a linear Anosov diffeomorphism of a torus.     

Carbon Quantum Dot Optical Properties for potential infiltration into Hollow Core Photonic Crystal Fibers

Carbon quantum dots (CQD) have received significant attention in recent years due to their potential applications in optics and sensing. In this study, the authors report on the first characterization of the optical activity and broad absorption spectrum covering from short-wave ultraviolet, at 200 nm, to mid-infrared, at 1600 nm, of CQD synthesized using the “low-molecular-weight alcohols electrochemical carbonization” method. The CQD are analyzed using spectroscopic techniques, optical activity in the infrared, and high-resolution transmission electron microscopy. Results show a CQD size distribution of 5±3 nm and spherical morphology. The absorption spectra show increased absorption at both, high and low frequency. Additionally, the specific rotation of the CQD solution is significantly higher than that of pure ethanol, by three orders of magnitude. These findings suggest that CQD may have potential applications in polarized infrared filters and/or sensors due to their ability to rotate the polarization state of light at 1550 nm. The results of this study provide valuable insights into the optical properties of CQD and their potential for infiltration into hollow core photonic crystal fibers, making them a promising material for future research and development in the field of optics and sensing.     

A simple model of flow-induced crystallization memory

Flow induced crystallization of polymer systems exhibits strong memory effects. Crystalline structures gradually change when the flow is switched off and the polymer is relaxed prior to crystallization. A simple model based on the multidimensional theory of crystal nucleation^[1] is proposed. Steady, potential flow applied to a polymer fluid above melting temperature (T_p > T_m) results in molecular orientation of crystallizing units. The flow controls formation of molecular clusters which convert into athermal nuclei when the system is cooled down to crystallization temperature, T_c < T_m. Orientation effects gradually disappear when the melt is relaxed above T_m in the absence of flow or stress.