Nanoscopic optical sensors based on functional supramolecular hybrid materials

This review highlights how the combination of supramolecular principles and nanoscopic solid structures enables the design of new hybrid sensing ensembles with improved sensitivity and/or selectivity and for the targeting of analytes for which selectivity is hard to achieve by conventional methods. Such ideas are bridging the gap between molecules, materials sciences and nanotechnology. Relevant examples will be detailed, taking into account functional aspects such as (1) enhanced coordination of functionalized solids, (2) enhanced signalling through preorganization, (3) signalling by assembly–disassembly of nanoscopic objects, (4) biomimetic probes utilizing discrimination by polarity and size and (5) distinct switching and gating protocols. These strategies are opening new prospects for sensor research and signalling paradigms at the frontier between nanotechnology, smart materials and supramolecular chemistry.     

On Quillen?s Theorem A for posets

A theorem of McCord of 1966 and Quillen?s Theorem A of 1973 provide sufficient conditions for a map between two posets to be a homotopy equivalence at the level of complexes. We give an alternative elementary proof of this result and we deduce also a stronger statement: under the hypotheses of the theorem, the map is not only a homotopy equivalence but a simple homotopy equivalence. This leads then to stronger formulations of the simplicial version of Quillen?s Theorem A, the Nerve Lemma and other known results. In particular we establish a conjecture of Kozlov on the simple homotopy type of the crosscut complex and we improve a well-known result of Cohen on contractible mappings.     

Toward optomechanics: maximizing the photodeformation of individual molecules

Designing soft organic materials able to directly convert light into macroscopic motion represents one of the grand challenges in modern chemistry. Optomechanical properties originate from the collection and amplification of many local deformation events in individual photoswitching entities due to their 3D organization. The basic concept of optomechanics is introduced, related recent achievements in the photoactuation of soft materials are highlighted, and a new approach, based on the optimization of the individual photoresponse at the single-molecule level, is outlined. Optomechanical systems constitute a fundamental approach to alternative utilization of solar energy and a platform for the development of future responsive soft materials and composites.     

Determination of the helical screw sense and side-group chirality of a synthetic chiral polymer from Raman optical activity

Splitting it up: Excellent agreement between the experimental and the quantum-chemically simulated Raman optical activity (ROA) spectrum of (+)-poly(trityl methacrylate) shows that the polymer backbone adopts a left-handed helical conformation while the trityl side groups display a left-handed propeller conformation. Thus ROA can be used to determine the complete structure of synthetic chiral polymers in solution.     

A new perspective on implementation by voting trees

Voting trees describe an iterative procedure for selecting a single vertex from a tournament. They provide a very general abstract model of decision‐making among a group of individuals, and it has therefore been studied which voting rules have a tree that implements them, i.e., chooses according to the rule for every tournament. While partial results concerning implementable rules and necessary conditions for implementability have been obtained over the past 40 years, a complete characterization of voting rules implementable by trees has proven surprisingly hard to find. A prominent rule that cannot be implemented by trees is the Copeland rule, which singles out vertices with maximum degree. In this paper, we suggest a new angle of attack and re‐examine the implementability of the Copeland solution using paradigms and techniques that are at the core of theoretical computer science. We study the extent to which voting trees can approximate the maximum degree in a tournament, and give upper and lower bounds on the worst‐case ratio between the degree of the vertex chosen by a tree and the maximum degree, both for the deterministic model concerned with a single fixed tree, and for randomizations over arbitrary sets of trees. Our main positive result is a randomization over surjective trees of polynomial size that provides an approximation ratio of at least 1/2. The proof is based on a connection between a randomization over caterpillar trees and a rapidly mixing Markov chain. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 59–82, 2011     

Foliations with persistent singularities

Let ω be a differential q-form defining a foliation of codimension q in a projective variety. In this article we study the singular locus of ω in various settings. We relate a certain type of singularities, which we name persistent, with the unfoldings of ω, generalizing previous work done on foliations of codimension 1 in projective space. We also relate the absence of persistent singularities with the existence of a connection in the sheaf of 1-forms defining the foliation.     

Mass and spin of Poincaré Gauge Theory

We discuss two expressions for the conserved quantities (energy momentum and angular momentum) of the Poincaré Gauge Theory. We show, that the variations of the Hamiltonians, of which the expressions are the respective boundary terms, are well defined, if we choose an appropriate phase space for asymptotic flat gravitating systems. Furthermore, we compare the expressions with others, known from the literature.     

Determination of nitrate with a flow-injection system combining square-wave polarographic detection with on-line deaeration

The combination of a flow-injection system with square-wave polarography and on-line deaeration is applied to the determination of nitrate, utilizing the catalytic reaction between nitrate and uranyl ion. The method is simple, rapid (60 samples h^?1), sensitive and accurate, with a detection limit of 2 μM nitrate. The method has been applied to the determination of nitrate in drinking and river waters.     

Crystallographic report: [N,N‐Methylethylaminopropylalane]2

Dimeric and centrosymmetric [MeEtN(CH₂)₃AlH₂]₂ comprises aluminum centers, coordinated in a distorted trigonal bipyramidal fashion by three hydrogen atoms, one nitrogen atom and one carbon atom. The aluminum atoms are bridged by hydrogen atoms, creating a planar, four‐membered Al₂H₂ ring. Copyright © 2005 John Wiley & Sons, Ltd.     

Homotopy Solution for the Channel Flow of a Third Grade Fluid

The solution for the flow of a third grade fluid bounded by two parallel porous plates is given using homotopy analysis method (HAM). A comparison is made with the exact numerical solution for the various values of the physical parameters. It is found that a proper choice of the auxiliary parameter occurring in HAM solution gives very close results.