Small time heat kernel asymptotics at the cut locus on surfaces of revolution

In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest two-dimensional Riemannian manifolds different from the sphere with non-trivial cut-conjugate locus. We determine the degeneracy of the exponential map near a cut-conjugate point and present the consequences of this result to the small time heat kernel asymptotics at this point. These results give a first example where the minimal degeneration of the asymptotic expansion at the cut locus is attained.     

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.     

Versatile Bisethynyl[60]fulleropyrrolidine Scaffolds for Mimicking Artificial Light‐Harvesting Photoreaction Centers

Fullerene‐based tetrads, triads, and dyads are presented in which [60]fulleropyrrolidine synthons are linked to an oligo(p‐phenyleneethynylene) antenna at the nitrogen atom and to electron‐donor phenothiazine (PTZ) and/or ferrocene (Fc) moieties at the α carbon of the pyrrolidine cycle through an acetylene spacer. Cyclic voltammetry and UV/ Vis absorption spectra evidence negligible ground‐state electronic interactions among the subunits. By contrast, strong excited‐state interactions are detected upon selective light irradiation of the antenna (UV) or of the fullerene scaffold (Vis). When only PTZ is present as electron donor, photoinduced electron transfer to the fullerene unit is unambiguously detected in benzonitrile, but this is not the case when Fc is part of the multicomponent system. These results suggest that Fc is a formidable energy transfer quencher and caution should be used in choosing it as electron donor to promote efficient charge separation in multicomponent arrays.     

Beating untrodden paths: James Gregory and his Italian readers

In this paper, I shall reconstruct the stay in Italy of James Gregory (1638–1675), Regius professor of mathematics at St Andrews. According to a standard account, Gregory spent four years (1664–1668) in Padua, as Stephano degli Angeli's student. However, this claim is problematic. First, Gregory's stay in Padua is confirmed only for the years 1667–1668. Second, the existence of a partial scribal copy of Vera quadratura circuli, ellipseos et hyperbolae in sua propria specie inventa et demonstrata, Gregory's debut work in the domain of quadrature problems, as well as a number of letters preserved at the National Library of Florence, suggest that relations between Gregory and Italian mathematicians were more complex and varied than have been suspected. On the basis of new, albeit scarce, textual evidence, I shall advance a few conjectures regarding scholars and philosophers that Gregory could have met in Padua, Rome and perhaps Florence.     

Catalytic Adventures in Space and Time Using High Energy X-rays

Very high energy X-rays (ca. >40 keV) have long offered great promise in providing great insight into the inner workings of catalysts; insights that may complement the battery of techniques available to researchers in catalysis either in the laboratory or at more conventional X-ray wavelengths. This contribution aims to critically assess the diverse possibilities now available in the high energy domain as a result of the maturation of third generation synchrotron facilities and to look forward to the potential that forthcoming developments in synchrotron source technology may offer the world of catalysis in the near future.     

Synthesis of Copper-Based Nanostructures in Liquid Environments by Means of a Non-equilibrium Atmospheric Pressure Nanopulsed Plasma Jet

The influence of the liquid composition on the chemical and morphological properties of copper-based nanostructures synthesized by a non-equilibrium atmospheric plasma treatment is investigated and discussed. The synthesis approach is simple and environmentally friendly, employs a non-equilibrium nanopulsed atmospheric pressure plasma jet as a contactless cathode and a Cu foil as immersed anode. The process was studied using four distinct electrolyte solutions composed of distilled water and either NaCl?+?NaOH, NaCl only or NaOH only at two different concentrations, without the addition of any copper salts. CuO crystalline structures with limited impurities (e.g. Cu and Cu(OH)₂ phases) were produced from NaCl?+?NaOH containing solutions, mainly CuO and CuCl₂ structures were synthesized in the electrolyte solution containing only NaCl and no synthesis occurred in solutions containing only NaOH. Both aggregated and dispersed nanostructures were produced in the NaCl?+?NaOH and NaCl containing solutions. Reaction pathways leading to the formation of the nanostructures are proposed and discussed.     

Selective C(sp3)−H Aerobic Oxidation Enabled by Decatungstate Photocatalysis in Flow

A mild and selective C(sp³)?H aerobic oxidation enabled by decatungstate photocatalysis has been developed. The reaction can be significantly improved in a microflow reactor enabling the safe use of oxygen and enhanced irradiation of the reaction mixture. Our method allows for the oxidation of both activated and unactivated C?H bonds (30 examples). The ability to selectively oxidize natural scaffolds, such as (?)‐ambroxide, pregnenolone acetate, (+)‐sclareolide, and artemisinin, exemplifies the utility of this new method.     

Autonomous propulsion of carbon nanotubes powered by a multienzyme ensemble

Covalent attachment of the enzymes glucose oxidase and catalase to carbon nanotubes enables the tandem catalytic conversion of glucose and H(2)O(2) formed to power autonomous movement of the nanotubes.