Lithium‐Salt Mediated Synthesis of a Covalent Triazine Framework for Highly Stable Lithium Metal Batteries

A new strategy for the synthesis of a covalent triazine framework (CTF‐1) was introduced based on the cyclotrimerization reaction of 1,4‐dicyanobenzene using lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) under ionothermal conditions. LiTFSI not only served as a catalyst, but also facilitated the in situ generation and homogeneous distribution of LiF particles across the framework. The hierarchical structure resulting upon integration of CTF‐LiF onto an airlaid‐paper (AP) offered unique features for lithium metal anodes, such as lithiophilicity from CTF, interface stabilization from LiF, and sufficient lithium storage space from AP. Based on this synergistic effect, the AP‐CTF‐LiF anode exhibited stable cycling performance even at a current density of 10 mA cm^?2.     

Toward standardization of quality assessment in laboratory medicine by using the same matrix samples for both internal and external quality assessments

The main purpose of quality assurance procedures in clinical laboratories is to ensure that test results are appropriate to maintain excellence in the diagnosis, monitoring, and treatment of disease. However, in current practice, no standardized procedure or frequency for the evaluation of methods exists, particularly in external quality assessment. Furthermore, different quality control materials are typically used for internal and external quality assessment. To overcome these discrepancies, we used samples with the same matrix for both internal and external quality assessments of a group test performed in our laboratory. We then calculated total error using real bias (target value obtained by reference method) and the imprecision of each test and compared our results with the total error allowable, derived from biological variation data. We suggest that the strategy of using the same matrix samples for both internal and external quality assessment is cost-effective, can be readily used by staff, and will facilitate the standardization of quality control in clinical laboratories.     

Spatially selective guided growth of high-coverage arrays and random networks of single-walled carbon nanotubes and their integration into electronic devices

The chemical vapor deposition growth of unusual arrangements of single-walled carbon nanotubes (SWNTs) by the combined of use patterned catalysts and quartz substrates is reported. Nearly perfectly aligned, high-coverage arrays of SWNTs can be generated in this manner. High-coverage random networks of SWNTs can also be created in the same growth step, with good spatial alignment and electrical interfaces to the aligned arrays. Tubes with these geometries are ideally suited to applications in thin-film electronic devices. We demonstrate this possibility through the construction of thin-film-type transistors in which the random networks form the source and drain electrodes and the aligned arrays form the channel.     

The nef cone of the moduli space of sheaves and strong Bogomolov inequalities

The paper is devoted to generic translation flows corresponding to Abelian differentials with one zero of order two on flat surfaces of genus two. These flows are weakly mixing by the Avila–Forni theorem. Our main result gives first quantitative estimates on their spectrum, establishing the Hölder property for the spectral measures of Lipschitz functions. The proof proceeds via uniform estimates of twisted Birkhoff integrals in the symbolic framework of random Markov compacta and arguments of Diophantine nature in the spirit of Salem, Erd?s and Kahane.     

The quantum cohomology of flag varieties and the periodicity of the Schubert structure constants

We give conditions on a curve class that guarantee the vanishing of the structure constants of the small quantum cohomology of partial flag varieties F(k ₁, ..., k _r ; n) for that class. We show that many of the structure constants of the quantum cohomology of flag varieties can be computed from the image of the evaluation morphism. In fact, we show that a certain class of these structure constants are equal to the ordinary intersection of Schubert cycles in a related flag variety. We obtain a positive, geometric rule for computing these invariants (see Coskun in A Littlewood–Richardson rule for partial flag varieties, preprint). Our study also reveals a remarkable periodicity property of the ordinary Schubert structure constants of partial flag varieties.     

Combinatorial formulas for certain sequences of multiple numbers

Duke and the second author defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic modular forms of half-integral weight and level 4 and showed that these lifts preserve the integrality of Fourier coefficients. We show that the generalization of these lifts to modular forms of genus 0 odd prime level also preserves the integrality of Fourier coefficients.     

Donor-acceptor oligorotaxanes made to order

Five donor–acceptor oligorotaxanes made up of dumbbells composed of tetraethylene glycol chains, interspersed with three and five 1,5‐dioxynaphthalene units, and terminated by 2,6‐diisopropylphenoxy stoppers, have been prepared by the threading of discrete numbers of cyclobis(paraquat‐p‐phenylene) rings, followed by a kinetically controlled stoppering protocol that relies on click chemistry. The well‐known copper(I)‐catalyzed alkyne–azide cycloaddition between azide functions placed at the ends of the polyether chains and alkyne‐bearing stopper precursors was employed during the final kinetically controlled template‐directed synthesis of the five oligorotaxanes, which were characterized subsequently by ¹H NMR spectroscopy at low temperature (233 K) in deuterated acetonitrile. The secondary structures, as well as the conformations, of the five oligorotaxanes were unraveled by spectroscopic comparison with the dumbbell and ring components. By focusing attention on the changes in chemical shifts of some key probe protons, obtained from a wide range of low‐temperature spectra, a picture emerges of a high degree of folding within the thread protons of the dumbbells of four of the five oligorotaxanes—the fifth oligorotaxane represents a control compound in effect—brought about by a combination of C? H???O and π–π stacking interactions between the π‐electron‐deficient bipyridinium units in the rings and the π‐electron‐rich 1,5‐dioxynaphthalene units and polyether chains in the dumbbells. The secondary structures of a foldamer‐like nature have received further support from a solid‐state superstructure of a related [3]pseudorotaxane and density functional calculations performed thereon.     

Phase diffusion in graphene-based Josephson junctions

We report on graphene-based Josephson junctions with contacts made from lead. The high transition temperature of this superconductor allows us to observe the supercurrent branch at temperatures up to ～2 K, at which point we can detect a small, but nonzero, resistance. We attribute this resistance to the phase diffusion mechanism, which has not been yet identified in graphene. By measuring the resistance as a function of temperature and gate voltage, we can further characterize the nature of the electromagnetic environment and dissipation in our samples.