FROM 1,3-DIPHOSPHETANE-2,4-DIYLS TO CYCLIC ANIONS AND CATIONS

The interest in diradicals has grown by the increasing number of stable diradicals which have been synthesized during the last few years. The diphosphacyclobutane-diyles have a diradicaloid molecular structure and they were the first diradicals to be prepared in the gramme scale. The combination of stability and high yield synthesis creates the opportunity both to change the substitution pattern or to prepare different valence isomers. Current experimental and computational studies reveal that electron transfer reactions of maintain the cyclic system. In the contribution, the oxidation reaction of 1 to the radical cation 2 and the cyclic diphosphaallyl cation 3 will be reported. Additionally, the remarkable mechanism of the reaction of 1 at first to the radical anion 4 but particularly to the diphosphacyclobutadiene dianion 5 under reductive conditions will be presented in detail.     

Bayesian Error Propagation for a Kinetic Model of n‐Propylbenzene Oxidation in a Shock Tube

We apply a Bayesian parameter estimation technique to a chemical kinetic mechanism for n‐propylbenzene oxidation in a shock tube to propagate errors in experimental data to errors in Arrhenius parameters and predicted species concentrations. We find that, to apply the methodology successfully, conventional optimization is required as a preliminary step. This is carried out in two stages: First, a quasi‐random global search using a Sobol low‐discrepancy sequence is conducted, followed by a local optimization by means of a hybrid gradient‐descent/Newton iteration method. The concentrations of 37 species at a variety of temperatures, pressures, and equivalence ratios are optimized against a total of 2378 experimental observations. We then apply the Bayesian methodology to study the influence of uncertainties in the experimental measurements on some of the Arrhenius parameters in the model as well as some of the predicted species concentrations. Markov chain Monte Carlo algorithms are employed to sample from the posterior probability densities, making use of polynomial surrogates of higher order fitted to the model responses. We conclude that the methodology provides a useful tool for the analysis of distributions of model parameters and responses, in particular their uncertainties and correlations. Limitations of the method are discussed. For example, we find that using second‐order response surfaces and assuming normal distributions for propagated errors is largely adequate, but not always.     

Isothermic constrained Willmore tori in 3-space

Annals of Global Analysis and Geometry - We show that the homogeneous and the 2-lobe Delaunay tori in the 3-sphere provide the only isothermic constrained Willmore tori in 3-space with Willmore...     

The lonely runner problem for lacunary sequences

The paper contains a new proof with a small improvement of a theorem of A. Dubickas on The Lonely Runner Conjecture and lacunary sequences. The proof is an adaptation of the Bernshteyn’s proof of the Lopsided Local lemma from his Local Cut Lemma (Bernshteyn, 2017).     

Probing o‐Diphenylphosphanyl Benzoate (o‐DPPB)‐Directed CC Bond Formation: Total Synthesis of Dictyostatin

Herein, we report a robust total synthesis of dictyostatin. This polyketide natural product has attracted much attention because of its impressive antiproliferative activity against several human cancer‐cell lines. We accomplished its synthesis in a highly convergent manner from three fragments of equal complexity, which were prepared on multigram scale. The southern and northwestern subunits were constructed through application of our o‐DPPB‐directed hydroformylation and allylic substitution methodology, respectively. These methods generated the C6 and C14 stereocenters of dictyostatin with good diastereoselectivities and simultaneously allowed further elaboration of the fragments by Wittig olefination and Sharpless asymmetric epoxidation, respectively. The compelling performance of the hydroformylation and allylic substitution with regard to practicability, selectivity, and scale underline their value for the construction of propionate motifs.