Highly edge-connected regular graphs without large factorizable subgraphs

We construct highly edge-connected $r$-regular graphs of even order which do not contain $r?2$ pairwise disjoint perfect matchings. When $r$ is a multiple of 4, the result solves a problem of Thomassen [4].     

High refractive index hyperbranched polyvinylsulfides for planar one‐dimensional all‐polymer photonic crystals

We report on the growth and characterization of one‐dimensional (1D) planar all‐polymer photonic crystals (PhC) with high dielectric contrast (Δn = 0.3) prepared by spin coating using hyperbranched polyvinylsulfide polymers (HB‐PVS) as high refractive index material and cellulose acetate as low refractive index material. Solution processable HB‐PVS show a near ultraviolet absorption inducing an increased refractive index in the visible‐near infrared (n = 1.68, λ = 1000 nm). HBPVS:Cellulose Acetate Distributed Bragg Reflectors show a very clear fingerprint of the photonic band gap possessing the expected polarized dispersion properties as a function of the incidence angle. Moreover, engineered microcavities tuned on the weak fluorescence spectrum of the HB‐PVS show directional fluorescence enhancement effects due to spectral redistribution of the emission oscillator strength. The combination of all these properties testifies the high optical quality of the obtained photonic structures thus indicating HB‐PVS as an interesting material for the preparation of such PhC. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 73–80     

Supramolecular Wiring of Benzo‐1,3‐chalcogenazoles through Programmed Chalcogen Bonding Interactions

The high‐yielding synthesis of 2‐substituted benzo‐1,3‐tellurazoles and benzo‐1,3‐selenazoles through a dehydrative cyclization reaction has been reported, giving access to a large variety of benzo‐1,3‐chalcogenazoles. Exceptionally, these aromatic heterocycles proved to be very stable and thus very handy to form controlled solid‐state organizations in which wire‐like polymeric structures are formed through secondary N???Y bonding interactions (SBIs) engaging the chalcogen (Y=Se or Te) and nitrogen atoms. In particular, it has been shown that the recognition properties of the chalcogen centre at the solid state could be programmed by selectively barring one of its σ‐holes through a combination of electronic and steric effects exerted by the substituent at the 2‐position. As predicted by the electrostatic potential surfaces calculated by quantum chemical modelling, the pyridyl groups revealed to be the stronger chalcogen bonding acceptors, and thus the best ligand candidate for programming the molecular organization at the solid state. In contrast, the thiophenyl group is an unsuitable substituent for establishing SBIs in this molecular system as it gives rise to chalcogen–chalcogen repulsion. The weaker chalcogen donor properties of the Se analogues trigger the formation of feeble N???Se contacts, which are manifested in similar solid‐state polymers featuring longer nitrogen–chalcogen distances.     

Hierarchically Structured Allotropes of Phosphorus from Data-Driven Exploration

The discovery of materials is increasingly guided by quantum-mechanical crystal-structure prediction, but the structural complexity in bulk and nanoscale materials remains a bottleneck. Here we demonstrate how data-driven approaches can vastly accelerate the search for complex structures, combining a machine-learning (ML) model for the potential-energy surface with efficient, fragment-based searching. We use the characteristic building units observed in Hittorf's and fibrous phosphorus to seed stochastic (“random”) structure searches over hundreds of thousands of runs. Our study identifies a family of hierarchically structured allotropes based on a P8 cage as principal building unit, including one-dimensional (1D) single and double helix structures, nanowires, and two-dimensional (2D) phosphorene allotropes with square-lattice and kagome topologies. These findings yield new insight into the intriguingly diverse structural chemistry of phosphorus, and they provide an example for how ML methods may, in the long run, be expected to accelerate the discovery of hierarchical nanostructures.     

A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen.     

Blue-LED Synthesis of Pummerer's Ketones by Peroxidase-Lignin-Catalyzed Oxidative Coupling of Substituted Phenols

Pummerer's ketones resembling the tricyclic scaffold of bioactive natural substances were synthesized by blue-LED driven Horseradish Peroxidase oxidative coupling of substituted phenols in 2-methyltetrahydrofuran by using meso-tetraphenylporphyrin as photosensitizer and dioxygen as primary oxidant. The application of functionalized lignin nanoparticles as a renewable and efficient platform for the immobilization of the enzyme extended the effectiveness of the overall process to heterogeneous catalysis under buffer limiting conditions.     

Sol‐to‐Gel Transition in Fast Evaporating Systems Observed by in Situ Time‐Resolved Infrared Spectroscopy

The in situ observation of a sol‐to‐gel transition in fast evaporating systems is a challenging task and the lack of a suitable experimental design, which includes the chemistry and the analytical method, has limited the observations. We synthesise an acidic sol, employing only tetraethylorthosilicate, SiCl₄ as catalyst and deuterated water; the absence of water added to the sol allows us to follow the absorption from the external environment and the evaporation of deuterated water. The time‐resolved data, obtained by attenuated total reflection infrared spectroscopy on an evaporating droplet, enables us to identify four different stages during evaporation. They are linked to specific hydrolysis and condensation rates that affect the uptake of water from external environment. The second stage is characterized by a decrease in hydroxyl content, a fast rise of condensation rate and an almost stationary absorption of water. This stage has been associated with the sol‐to‐gel transition.     

Holderian Weak Invariance Principle for Stationary Mixing Sequences

We provide some sufficient mixing conditions on a strictly stationary sequence in order to guarantee the weak invariance principle in Hölder spaces. Strong mixing and \(\rho \)-mixing conditions are investigated as well as \(\tau \)-dependent sequences. The main tools are deviation inequalities for mixing sequences.