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.     

Rigidity of Schubert classes in orthogonal Grassmannians

A Schubert class σ in the cohomology of a homogeneous variety X is called rigid if the only projective subvarieties of X representing σ are Schubert varieties. A Schubert class σ is called multi rigid if the only projective subvarieties representing positive integral multiples of σ are unions of Schubert varieties. In this paper, we discuss the rigidity and multi rigidity of Schubert classes in orthogonal Grassmannians. For a large set of non-rigid classes, we provide explicit deformations of Schubert varieties using combinatorially defined varieties called restriction varieties. We characterize rigid and multi rigid Schubert classes of Grassmannian and quadric type. We also characterize all the rigid classes in OG(2, n) if n > 8.     

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 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.     

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.     

Three-point recognition and selective fluorescence sensing of L-DOPA

[reaction: see text] A phenylboronic acid derivative of a well-known dye (Lucifer yellow) recognizes L-DOPA through a combination of reversible esterification, charge transfer, and electrostatic interactions. The selective recognition event is signaled by a drop in the emission intensity of the fluorescent chemosensor.     

Subpicosecond electro-optic measurement of relativistic electron pulses

Time-resolved measurements of the transverse electric field associated with relativistic electron bunches are presented. Using an ultrafast electro-optic sensor close to the electron beam, the longitudinal profile of the electric field was measured with subpicosecond time resolution and without time-reversal ambiguity. Results are shown for two cases: inside the vacuum beam line in the presence of wake fields, and in air behind a beryllium window, effectively probing the near-field transition radiation. Especially in the latter case, reconstruction of the longitudinal electron bunch shape is straightforward.     

A sensitive fluorescent chemosensor for anions based on a styryl-boradiazaindacene framework

Long wavelength emitting, extended conjugation boradiazaindacenes are novel dyes with considerable ICT character. By appending a dipicolylaminylethylamine group, the parent compound was transformed into a fluorescent dye with a strong chelating ability for Zn(II) ions. The zinc complex which has bright orange fluorescence, reversibly signals anions with very large changes in both the absorption and the emission spectra. The remarkable change in the emission intensity is explained in relation to the electron donating capacity of the substituent on the styryl functionality.