l1 solution of linear inequalities

The numerical solution of a possible inconsistent system oflinear inequalities in the l₁ sense is considered. The non-differentiablel₁ norm minimization problem is approximated by a piecewisequadratic Huber smooth function. A continuation algorithm isdesigned to find an l₁ solution of the inequality system. Inthe case where the linear inequality system is consistent, asolution is obtained by solving any smoothed problem. Otherwise,the algorithm is shown to terminate in a finite number of iterations.We also consider an alternative smoothing scheme which sharessimilar properties with the first one, but results in an improvedcomputational performance of the continuation algorithm on inconsistentsystems. Numerical experiments are conducted to test the efficiencyof the algorithm.     

The nature of paramagnetic species in nitrogen doped TiO2 active in visible light photocatalysis

Nitrogen doped TiO2, a novel photocatalyst active in the decomposition of organic pollutants using visible light, contains two different types of paramagnetic centres (neutral NO radicals and NO2(2-) type radical ions respectively) which are likely related to specific properties of the solid.     

Dead Ends and Detours En Route to Total Syntheses of the 1990s A list of abbreviations can be found at the end of the article

From the very beginning organic chemistry and total synthesis have been intimately joined. In fact, one of the first things that freshmen in organic chemistry learn is how to join two molecules together to obtain a more complex one. Of course they still have a long way to go to become fully mature synthetic chemists, but they must have the primary instinct to build molecules, as synthesis is the essence of organic chemistry. With the different points of view that actually coexist in the chemical community about the maturity of the science (art, or both) of organic synthesis, it is clear that nowadays we know how to make almost all of the most complex molecules ever isolated. The primary question is how easy is it to accomplish? For the readers of papers describing the total synthesis of either simple or complex molecules, it appears that the routes followed are, most of the time, smooth and free of troubles. The synthetic scheme written on paper is, apparently, done in the laboratory with few, if any, modifications and these, essentially, seem to be based on finding the optimal experimental conditions to effect the desired reaction. Failures in the planned synthetic scheme to achieve the goal, detours imposed by unexpected reactivity, or the absence of reactivity are almost never discussed, since they may diminish the value of the work reported. This review attempts to look at total synthesis from a different side; it will focus on troubles found during the synthetic work that cause detours from the original synthetic plan, or on the dead ends that eventually may force redesign. From there, the evolution from the original route to the final successful one that achieves the synthetic target will be presented. The syntheses discussed in this paper have been selected because they contain explicit information about the failures of the original synthetic plan, together with the evolution of the final route to the target molecule. Therefore, they contain a lot of useful negative information that may otherwise be lost.     

Probing the local environment of Ti3+ ions in TiO2 (rutile) by 17O HYSCORE

Reduced states in TiO(2) : (17)O hyperfine sublevel correlation spectroscopy was used to monitor the local environment of stable Ti(3+) ions generated in a (17)O-enriched polycrystalline TiO(2) (rutile) sample. A hyperfine interaction of about 8 MHz is found, which is analogous to that observed for molecular Ti(3+) aqua complex cations and suggests a localized nature of the unpaired electron wave function for these centers at 4 K.     

Improving selectivity in gas chromatography by using chemically modified multi-walled carbon nanotubes as stationary phase

Amino-terminated alkyl MWCNTs (MWCNTs-R-NH₂), synthesized by chemical modification of the nanotube skeleton by nucleophilic substitution with 2,2′-(ethylenedioxy)diethylamine, were successfully used as stationary phases for gas chromatographic separation of esters and chloroaromatics. The presence of alkyl chains with polar embedded groups made the functionalized MWCNTs (f-MWCNTs) a mixed-mode GC separation material able to interact in different ways with the analytes. Compared with non-functionalized MWCNTs (nf-MWCNTs), MWCNTs-R-NH₂ had higher selectivity, enhanced resolution, and optimum retention behaviour, and they were proved to perform better than the commercial stationary phase Porapak QS (PQS), claimed to be suitable for similar applications. The so-prepared stationary phase was used for analysis of a synthetic mixture containing different classes of analytes, viz. esters, ketones, alcohols, alkanes, and aromatic hydrocarbons, and finally used for investigation of similar real matrices. In particular, the constituents of a commercial paint thinner were determined by direct injection of the sample, with good reproducibility (inter-day precision RSDs from 5 to 19%). Two unknown samples of commercial white spirit were also analysed for determination of the aromatic hydrocarbon content, and their composition was profiled on the basis of the different compounds identified.     

Origin of photoactivity of nitrogen-doped titanium dioxide under visible light

Nitrogen-doped titanium dioxide (N-TiO2), a photocatalytic material active in visible light, has been investigated by a combined experimental and theoretical approach. The material contains single-atom nitrogen impurities that form either diamagnetic (Nb-) or paramagnetic (Nb*) bulk centers. Both types of Nb centers give rise to localized states in the band gap of the oxide. The relative abundance of these species depends on the oxidation state of the solid, as, upon reduction, electron transfer from Ti3+ ions to Nb* results in the formation of Ti4+ and Nb-. EPR spectra measured under irradiation show that Nb centers are responsible for visible light absorption with promotion of electrons from the band gap localized states to the conduction band or to surface-adsorbed electron scavengers. These results provide a characterization of the electronic states associated with N impurities in TiO2 and, for the first time, a picture of the processes occurring in the solid under irradiation with visible light.