Short Total Synthesis of Ajoene, (E,Z)-4,5,9-Trithiadodeca-1,6,11-triene 9-oxide,in Batch and (E,Z)-4,5,9-Trithiadodeca-1,7,11-triene in Continuous Flow

A short total synthesis of ajoene, (E,Z)-4,5,9-trithiadodeca-1,6,11-triene 9-oxide, has been achieved over six steps. In addition, a continuous flow synthesis under mild reaction conditions to (E,Z)-4,5,9-trithiadodeca-1,7,11-triene is described starting from simple and easily accessible starting materials. Over four steps including propargylation, radical addition of thioacetate, deprotection, and disulfide formation/ allylation, the target product can be obtained at a rate of 0.26 g h⁻¹ in an overall yield of 12 %.     

Strategies for 1H-Detected Dynamic Nuclear Polarization Magic-Angle Spinning NMR Spectroscopy

Combining dynamic nuclear polarization with proton detection significantly enhances the sensitivity of magic-angle spinning NMR spectroscopy. Herein, the feasibility of proton-detected experiments with slow (10 kHz) magic angle spinning was demonstrated. The improvement in sensitivity permits the acquisition of indirectly detected ¹⁴N NMR spectra allowing biomolecular structures to be characterized without recourse to isotope labelling. This provides a new tool for the structural characterization of environmental and medical samples, in which isotope labelling is frequently intractable.     

Compressing Double [7]Helicene by Successive Charging with Electrons

Chemical reduction of a benzo‐fused double [7]helicene ( 1 ) with two alkali metals, K and Rb, provided access to three different reduced states of 1 . The doubly‐reduced helicene 1 ^2? has been characterized by single‐crystal X‐ray diffraction as a solvent‐separated ion triplet with two potassium counterions. The triply‐ and tetra‐reduced helicenes, 1 ^3? and 1 ^4?, have been crystallized together in an equimolar ratio and both form the contact‐ion complexes with two Rb⁺ ions each, leaving three remaining Rb⁺ ions wrapped by crown ether and THF molecules. As structural consequence of the stepwise reduction of 1 , the central axis of helicene becomes more compressed upon electron addition (1.42 Å in 1 ^4? vs. 2.09 Å in 1 ). This is accompanied by an extra core twist, as the peripheral dihedral angle increases from 16.5° in 1 to 20.7° in 1 ^4?. Theoretical calculations provided the pattern of negative charge build‐up and distribution over the contorted helicene framework upon each electron addition, and the results are consistent with the X‐ray crystallographic and NMR spectroscopic data.     

Congruences of small degree in G(1,4)

We give the list of all possible congruences in G(1,4) of degree d ≤10 and we explicitely construct most of them.     

Congruences on near-Heyting algebras

A near-Heyting algebra is a join-semilattice with a top element such that every principal upset is a Heyting algebra. We establish a one-to-one correspondence between the lattices of filters and congruences of a near-Heyting algebra. To attain this aim, we first show an embedding from the lattice of filters to the lattice of congruences of a distributive nearlattice. Then, we describe the subdirectly irreducible and simple near-Heyting algebras. Finally, we fully characterize the principal congruences of distributive nearlattices and near-Heyting algebras. We conclude that the varieties of distributive nearlattices and near-Heyting algebras have equationally definable principal congruences.     

Platinum(II)-Based Optical Probes for Imaging Quadruplex DNA Structures via Phosphorescence Lifetime Imaging Microscopy

G-quadruplex DNA is a non-canonical structure that forms in guanine-rich regions of the genome. There is increasing evidence showing that G-quadruplexes have important biological functions, and therefore molecular tools to visualise these structures are important. Herein we report on a series of new cyclometallated platinum(II) complexes which, upon binding to G-quadruplex DNA, display an increase in their phosphorescence, acting as switch-on probes. More importantly, upon binding to G-quadruplexes they display a selective and distinct lengthening of their emission lifetime. We show that this effect can be used to selectively visualise these structures in cells using Phosphorescence Lifetime Imaging Microscopy (PLIM).     

Non-maturing deposits modelling in a Ornstein-Uhlenbeck framework

This paper builds a multivariate Lévy-driven Ornstein-Uhlenbeck process for the management of non-maturing deposits, that are a major source of funding for banks. The contribution of the paper is both theoretical and operational. On the theoretical side, the novelty of this model is to include three independent sources of randomness in a Lévy framework: market interest rates, deposit rates and deposit volumes. The choice of a Lévy background driving process allows us to model rare but severe events. On the operational side, we propose a procedure to include severe volume outflows with positive probability in future scenarios simulation, explaining its implementation with an illustrative example using Italian banking sector data.     

Solitons generated by self-organization in bismuth germanium oxide single crystals during the interaction with laser beam

We present here the experimental, theoretical, and numerical investigations of Kerr solitons generated by self-organization in black and yellow high quality bismuth germanium oxide (Bi₁₂GeO₂₀) single crystals. A picosecond laser beam of increasing power induces competing cubic and quintic nonlinearities. The numerical evolution of two-dimensional complex cubic-quintic nonlinear Schrödinger equation with measured values of nonlinearities shows the compensation of diffraction by competing cubic and quintic nonlinearities of opposite sign, i.e., the self-generation and stable propagation of solitons. Experiments as well as numerical simulations show higher nonlinearity in the black Bi₁₂GeO₂₀ than in the more transparent yellow one.