Synchronization and Non-Smooth Dynamical Systems

In this article we establish an interaction between non-smooth systems, geometric singular perturbation theory and synchronization phenomena. We find conditions for a non-smooth vector fields be locally synchronized. Moreover its regularization provide a singular perturbation problem with attracting critical manifold. We also state a result about the synchronization which occurs in the regularization of the fold-fold case. We restrict ourselves to the 3-dimensional systems (ℓ = 3) and consider the case known as a T-singularity.     

On the dynamics of the Szekeres system

The gravitational Szekeres differential system is completely integrable with two rational first integrals and an additional analytical first integral. We describe the dynamics of the Szekeres system when one of these two rational first integrals is negative, showing that all the orbits come from the infinity of ${\mathbb{R}}^4$ and go to infinity.     

Access to Enantiopure Advanced Intermediates en Route to Madangamines

The synthesis of enantiopure ABCE and ABCD tetracyclic advanced intermediates en route to madangamine alkaloids and studies for the construction of the triunsaturated 15-membered D ring of madangamine B and the saturated 13-membered D ring of madangamine E are reported.     

Self‐Assembled Tetragonal Prismatic Molecular Cage Highly Selective for Anionic π Guests

The metal‐directed supramolecular synthetic approach has paved the way for the development of functional nanosized molecules. In this work, we report the preparation of the new nanocapsule 3? (CF₃SO₃)₈ with a A₄B₂ tetragonal prismatic geometry, where A corresponds to the dipalladium hexaazamacrocyclic complex Pd‐1 , and B corresponds to the tetraanionic form of palladium 5,10,15,20‐tetrakis(4‐carboxyphenyl)porphyrin ( 2 ). The large void space of the inner cavity and the supramolecular affinity for guest molecules towards porphyrin‐based hosts converts this nanoscale molecular 3D structure into a good candidate for host–guest chemistry. The interaction between this nanocage and different guest molecules has been studied by means of NMR, UV/Vis, ESI‐MS, and DOSY experiments, from which highly selective molecular recognition has been found for anionic, planar‐shaped π guests with association constants (K_a) higher than 10⁹ M ^?1, in front of non‐interacting aromatic neutral or cationic substrates. DFT theoretical calculations provided insights to further understand this strong interaction. Nanocage 3? (CF₃SO₃)₈ can not only strongly host one single molecule of M(dithiolene)₂ complexes (M=Au, Pt, Pd, and Ni), but also can finely tune their optical and redox properties. The very simple synthesis of both the supramolecular cage and the building blocks represents a step forward for the development of polyfunctional supramolecular nanovessels, which offer multiple applications as sensors or nanoreactors.     

Synthesis of amphidinolide Y precursors

The Negishi coupling between a chiral C3 synthon and an iodoalkene arising from 3-butyn-1-ol, which gave the C3–C9 fragment of amphidinolide Y, was the starting point of a formal total synthesis of this marine natural product. By means of Sharpless ADH and TADDOL-mediated crotylation, the full western fragment (C1–C11) was obtained, which was coupled with the eastern fragment (3-hydroxyoxolane derivative). The penultimate step (ring-closing metathesis, with G-II, H–G-II, or Nitro-Grela reagents, under several conditions) posed great difficulties. The cyclization was achieved with 15c (7,9-bis-O-TES) and 15d (7-O-TES, 9-O-TBS); more than stoichiometric amounts of the H–G-II Ru complex were required for complete conversion.