Error bounds,facial residual functions and applications to the exponential cone

Mathematical Programming - We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be...     

High‐performance liquid chromatography separation of unsaturated organic compounds by a monolithic silica column embedded with silver nanoparticles

The optimization of a porous structure to ensure good separation performances is always a significant issue in high‐performance liquid chromatography column design. Recently we reported the homogeneous embedment of Ag nanoparticles in periodic mesoporous silica monolith and the application of such Ag nanoparticles embedded silica monolith for the high‐performance liquid chromatography separation of polyaromatic hydrocarbons. However, the separation performance remains to be improved and the retention mechanism as compared with the Ag ion high‐performance liquid chromatography technique still needs to be clarified. In this research, Ag nanoparticles were introduced into a macro/mesoporous silica monolith with optimized pore parameters for high‐performance liquid chromatography separations. Baseline separation of benzene, naphthalene, anthracene, and pyrene was achieved with the theoretical plate number for analyte naphthalene as 36 000 m^?1. Its separation function was further extended to cis/trans isomers of aromatic compounds where cis/trans stilbenes were chosen as a benchmark. Good separation of cis/trans‐stilbene with separation factor as 7 and theoretical plate number as 76 000 m^?1 for cis‐stilbene was obtained. The trans isomer, however, is retained more strongly, which contradicts the long‐ established retention rule of Ag ion chromatography. Such behavior of Ag nanoparticles embedded in a silica column can be attributed to the differences in the molecular geometric configuration of cis/trans stilbenes.     

On the electronic character of localized singlet 2,2-dimethoxycyclopentane-1,3-diyl diradicals: substituent effects on the lifetime

Photodenitrogenation of the diazenes 4 affords exclusively the housanes 5 through intramolecular cyclization of the spectrally detected and characterized singlet diradicals 3. The lifetime of singlet diradical 3, determined by transient absorption measurements, depends on the Y and Z substituents at the para position of the phenyl ring and has the following order: Y, Z = OMe, OMe > OMe, CN > CN, CN > OMe, H > Cl, Cl approximately CN, H approximately Me, Me > H, H. This unprecedented substituent effect reveals stabilization of the singlet 2,2-dimethoxycyclopentane-1,3-diyl diradicals 3 through radical, zwitterionic, pi-bonding, and hyperconjugative structures.     

Reversible photoredox switching of porphyrin-bridged bis-2,6-di-tert-butylphenols

Porphyrin derivatives bearing 2,6-di-tert-butylphenol substituents at their 5,15-positions undergo reversible photoredox switching between porphyrin and porphodimethene states as revealed by UV-vis spectroscopy, fluorescence spectroscopy, and X-ray single-crystal analyses. Photoredox interconversion is accompanied by substantial variations in electronic absorption and fluorescence emission spectra and a change of conformation of the tetrapyrrole macrocycle from planar to roof-shaped. Oxidation proceeds only under photoillumination of a dianionic state prepared through deprotonation using fluoride anions. Conversely, photoreduction occurs in the presence of a sacrificial electron donor. Transient absorption spectroscopy and electron spin resonance spectroscopy were applied to investigate the processes in photochemical reaction, and radical intermediates were characterized. That is, photooxidation initially results in a phenol-substituent-centered radical, while the reduction process occurs via a delocalized radical state involving both the macrocycle and 5,15-substituents. Forward and reverse photochemical processes are governed by different chemical mechanisms, giving the important benefit that conversion reactions are completely isolated, leading to better separation of the end states. Furthermore, energy diagrams based on electrochemical analyses (cyclic voltammetry) were used to account for the processes occurring during the photochemical reactions. Our molecular design indicates a simple and versatile method for producing photoredox macrocyclic compounds, which should lead to a new class of advanced functional materials suitable for application in molecular devices and machines.     

Gas collection efficiency of annular denuders: A spreadsheet-based calculator

Denuders are widely used for atmospheric analysis. Annular denuders are especially well-suited for preconcentration of trace gases compared to simpler single tube designs. While traditionally coated annular denuders have both bounding surfaces that behave as sinks, annular denuders/membrane-based scrubbers with the same basic geometric design and with only one of the annular surfaces functioning as sink (e.g., a membrane tube whose outer surface behaves as a sink disposed within an inert jacket tube) have become common. However, the gas collection efficiency of such devices cannot be expressed as a simple equation with fixed constants and there is no presently available tool to a priori determine the denuder performance or to design denuders with specific removal efficiencies at specific sampling rates. This paper presents a simple to use “spreadsheet calculator” for concentric annular denuders of any dimension based on known solutions to analogous heat transfer problems. The results from the present spreadsheet calculator are compared with results from a commercial computational fluid dynamics package (Fluent™; this takes significant expertise and development effort to run)—the two approaches produce essentially the same results. The present spreadsheet calculator can be used easily and simply without training and will be a useful tool for denuder users and designers.