Lithium–Bromide Exchange versus Nucleophilic Addition of Schiff's base: Unprecedented Tandem Cyclisation Pathways

By exploring lithium–bromide exchange reactivity of aromatic Schiff's bases with tert-butyllithium (tBuLi), we have revealed unprecedented competitive intermolecular and intramolecular cascade annulation pathways, leading to valuable compounds, such as iso-indolinones and N-substituted anthracene derivatives. A series of reaction parameters were probed, including solvent, stoichiometry, sterics and organolithium reagent choice, in order to understand the influences that limit such ring-closing pathways. With two viable reactivity options for the organolithium on the imine; namely, nucleophilic addition or lithium–bromide exchange, a surprising competitive nature was observed, where nucleophilic addition dominated, even under cryogenic conditions. Considering the most commonly used solvents for lithium–bromide exchange, tetrahydrofuran (THF) and diethyl ether (Et₂O), contrasting reactivity outcomes were revealed with nucleophilic addition promoted in THF, while Et₂O yielded almost double the conversion of cyclic products than in THF.     

Linear covering codes and error-correcting codes for limited-magnitude errors

The concepts of a linear covering code and a covering set for the limited-magnitude-error channel are introduced. A number of covering-set constructions, as well as some bounds, are given. In particular, optimal constructions are given for some cases involving small-magnitude errors. A problem of Stein is partially solved for these cases. Optimal packing sets and the corresponding error-correcting codes are also considered for some small-magnitude errors.     

Dynamic investigation of triangles inscribed in a circle,which tend to an equilateral triangle

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner.

First, using geometrical software, we investigate four theorems that represent interesting geometrical properties, after which we present formal proofs that rest on a combination between different fields of mathematics: trigonometry, algebra and geometry, and the use of the concept of standard deviation that is taken from statistics.     

Small Data Can Play a Big Role in Chemical Discovery

The chemistry community is currently witnessing a surge of scientific discoveries in organic chemistry supported by machine learning (ML) techniques. Whereas many of these techniques were developed for big data applications, the nature of experimental organic chemistry often confines practitioners to small datasets. Herein, we touch upon the limitations associated with small data in ML and emphasize the impact of bias and variance on constructing reliable predictive models. We aim to raise awareness to these possible pitfalls, and thus, provide an introductory guideline for good practice. Ultimately, we stress the great value associated with statistical analysis of small data, which can be further boosted by adopting a holistic data-centric approach in chemistry.     

Mechanistic Insight into the Stereochemical Control of Lactide Polymerization by Salan–Aluminum Catalysts

Alkyl aluminum complexes of chiral salan ligands assembled around the 2,2′‐bipyrrolidine core form as single diastereomers that have identical configurations of the N donors. Active catalysts for the polymerization of lactide were formed upon the addition of benzyl alcohol. Polymeryl exchange between enantiomorphous aluminum species had a dramatic effect on the tacticity of the poly(lactic acid) (PLA) in the polymerization of racemic lactide (rac‐LA): The enantiomerically pure catalyst of the nonsubstituted salan ligand led to isotactic PLA, and the racemic catalyst exhibited lower stereocontrol. The enantiomerically pure catalyst of the chloro‐substituted salan ligand led to PLA with a slight tendency toward heterotacticity, whereas the racemic catalyst led to PLA of almost perfect heterotacticity following an insertion/auto‐inhibition/exchange mechanism.     

Ultraviolet Absorption Induces Hydrogen‐Atom Transfer in G⋅C Watson–Crick DNA Base Pairs in Solution

Ultrafast deactivation pathways bestow photostability on nucleobases and hence preserve the structural integrity of DNA following absorption of ultraviolet (UV) radiation. One controversial recovery mechanism proposed to account for this photostability involves electron‐driven proton transfer (EDPT) in Watson–Crick base pairs. The first direct observation is reported of the EDPT process after UV excitation of individual guanine–cytosine (G?C) Watson–Crick base pairs by ultrafast time‐resolved UV/visible and mid‐infrared spectroscopy. The formation of an intermediate biradical species (G[?H]?C[+H]) with a lifetime of 2.9 ps was tracked. The majority of these biradicals return to the original G?C Watson–Crick pairs, but up to 10 % of the initially excited molecules instead form a stable photoproduct G*?C* that has undergone double hydrogen‐atom transfer. The observation of these sequential EDPT mechanisms across intermolecular hydrogen bonds confirms an important and long debated pathway for the deactivation of photoexcited base pairs, with possible implications for the UV photochemistry of DNA.     

Various solution methods,accompanied by dynamic investigation,for the same problem as a means for enriching the mathematical toolbox

A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive ‘mathematical toolbox’. Investigation of the property that appears in the task was carried out using a computerized tool.