The best constant of Sobolev inequality on a bounded interval

The best constants Cm,j of Sobolev embedding of Hm(0,a) into Cj[0,a](0?j?m−1) are obtained. Especially, when a=∞, these constants can be represented in a closed form.     

Reaction of alkynylsilanes with CuCl in polar solvents leading to alkynyl group transfer from Si to Cu

The reaction of 1-phenyl-2-trimethylsilylethyne with CuCl at 80–100°C in N,N-dimethylformamide (DMF) or N,N-dimethylimidazolidinone (DMI) yielded the alkynylcopper species [Cu₂Cl(CCPh)]_n (1) in 56–63% yields. Heating 1 at 80°C under aerobic conditions gave 1,4-diphenyl-1,3-butadiyne in 82% yield via an oxidative coupling of the phenylethynyl ligands.     

Dipolar Nanocars Based on a Porphyrin Backbone

The design and synthesis of a new family of nanocars is reported. To control their motion, we integrated a dipole which can be tuned thanks to strategic donor and acceptor substituents at the 5- and 15-positions of the porphyrin backbone. The two other meso positions are substituted with ethynyltriptycene moieties which are known to act as wheels. Full characterization of nine nanocars is presented as well as the electrochemistry of these push-pull molecules. DFT calculations allowed us to evaluate the magnitude of the dipoles and to understand the electrochemical behavior and how it is affected by the electron donating and accepting groups present. An X-ray crystal structure of one nanocar has also been obtained.     

Lévy’s Zero–One Law in Game-Theoretic Probability

We prove a nonstochastic version of Lévy’s zero–one law and deduce several corollaries from it, including nonstochastic versions of Kolmogorov’s zero–one law and the ergodicity of Bernoulli shifts. Our secondary goal is to explore the basic definitions of game-theoretic probability theory, with Lévy’s zero–one law serving a useful role.     

Isolation,preparation, and characterization of nanofibers from oil palm empty-fruit-bunch (OPEFB)

Cellulose nanofibers were produced by hydrolyzing oil palm empty-fruit-bunches with sulfuric acid. The effect of hydrolysis time on the structure and properties of the nanofibers was investigated. Fourier transform infrared spectroscopy was employed to evaluate the change of chemical composition. Atomic force microscope images showed that the average thickness of the nanofibers ranged from 1 to 3.5 nm as the hydrolysis time was varied. Longer hydrolysis time produced a higher yield of dispersed nanofibers; whereas the degree of crystallinity and the degree of polymerization decreased with increasing hydrolysis time. The degradation of nanofibers with higher sulfate group content started at a lower temperature.     

Desktop near-field thermal-lens microscope for thermo-optical detection in microfluidics

A new compact near-field desktop-sized diode laser thermal-lens microscope for analysis in microfluidics was proposed. A novel beam-alignment and detection systems provided high signal stability and, along with reduced number of optical elements rendered the instrument portable. The detection of nonfluorescent model species (Fe(II)-bathophenanthroline chelate) in water showed good linearity in the range of 5 × 10(-9) to 1 × 10(-4) M, and the limit of detection was 3.5 × 10(-9) M, which corresponded to 3.5 × 10(-7) absorbance units and provided a 20-fold enhancement in sensitivity compared with existing schematic.     

Global air quality and climate

Emissions of air pollutants and their precursors determine regional air quality and can alter climate. Climate change can perturb the long-range transport, chemical processing, and local meteorology that influence air pollution. We review the implications of projected changes in methane (CH(4)), ozone precursors (O(3)), and aerosols for climate (expressed in terms of the radiative forcing metric or changes in global surface temperature) and hemispheric-to-continental scale air quality. Reducing the O(3) precursor CH(4) would slow near-term warming by decreasing both CH(4) and tropospheric O(3). Uncertainty remains as to the net climate forcing from anthropogenic nitrogen oxide (NO(x)) emissions, which increase tropospheric O(3) (warming) but also increase aerosols and decrease CH(4) (both cooling). Anthropogenic emissions of carbon monoxide (CO) and non-CH(4) volatile organic compounds (NMVOC) warm by increasing both O(3) and CH(4). Radiative impacts from secondary organic aerosols (SOA) are poorly understood. Black carbon emission controls, by reducing the absorption of sunlight in the atmosphere and on snow and ice, have the potential to slow near-term warming, but uncertainties in coincident emissions of reflective (cooling) aerosols and poorly constrained cloud indirect effects confound robust estimates of net climate impacts. Reducing sulfate and nitrate aerosols would improve air quality and lessen interference with the hydrologic cycle, but lead to warming. A holistic and balanced view is thus needed to assess how air pollution controls influence climate; a first step towards this goal involves estimating net climate impacts from individual emission sectors. Modeling and observational analyses suggest a warming climate degrades air quality (increasing surface O(3) and particulate matter) in many populated regions, including during pollution episodes. Prior Intergovernmental Panel on Climate Change (IPCC) scenarios (SRES) allowed unconstrained growth, whereas the Representative Concentration Pathway (RCP) scenarios assume uniformly an aggressive reduction, of air pollutant emissions. New estimates from the current generation of chemistry-climate models with RCP emissions thus project improved air quality over the next century relative to those using the IPCC SRES scenarios. These two sets of projections likely bracket possible futures. We find that uncertainty in emission-driven changes in air quality is generally greater than uncertainty in climate-driven changes. Confidence in air quality projections is limited by the reliability of anthropogenic emission trajectories and the uncertainties in regional climate responses, feedbacks with the terrestrial biosphere, and oxidation pathways affecting O(3) and SOA.     

Markov degree of the Birkhoff model

We prove the conjecture by Diaconis and Eriksson (J. Symbolic Comput. 41(2):182–195, 2006) that the Markov degree of the Birkhoff model is three. In fact, we prove the conjecture in a generalization of the Birkhoff model, where each voter is asked to rank a fixed number, say r, of candidates among all candidates.     

Hexa‐ and Octagold Chains from Flexible Tetragold Molecular Units Supported by Linear Tetraphosphine Ligands

A flexible building block : Flexible tetragold(I) chain complexes supported by a new single methylene‐bridged tetraphosphine ligand were synthesized and further transformed into discrete linear octagold(I) {Au₈} and cyclic hexagold(I) {Au₆} structures by reaction with KI and NaAuCl₄, respectively (see picture, Au purple, Cl dark green, PF₆ light green, I pink). The tetragold complexes are also luminescent at room temperature.