A variational principle and best proximity points

We generalize Ekeland's Variational Principle for cyclic maps. We present applications of this version of the variational principle for proving of existence and uniqueness of best proximity points for different classes of cyclic maps.     

Sequential anaerobic/aerobic treatment of dye-containing wastewaters: colour and COD removals, and ecotoxicity tests

Colour and COD removals of the azo dyes Congo Red (CR) and Reactive Black 5 (RB5) were individually evaluated in a sequential anaerobic/aerobic treatment system. Additionally, dye toxicity was assessed by using acute ecotoxicity tests with Daphnia magna as the indicator-organism. The anaerobic reactor was operated at approximately 27 °C and with hydraulic retention times of 12 and 24 h. The aerobic reactor was operated in batch mode with a total cycle of 24 h. During anaerobic step, high colour removals were obtained, 96.3% for CR (400 mg/L) and 75% for RB5 (200 mg/L). During the aerobic phase, COD effluent was considerably reduced, with an average removal efficiency of 52% for CR and 85% for RB5, which resulted in an overall COD removal of 88% for both dyes. Ecotoxicity tests with CR revealed that the anaerobic effluent presented a higher toxicity compared with the influent, and an aerobic post-treatment was not efficient in reducing toxicity. However, the results with RB5 showed that both anaerobic and aerobic steps could decrease dye toxicity, especially the aerobic phase, which removed completely the toxicity in D. magna. Therefore, the anaerobic/aerobic treatment is not always effective in detoxifying dye-containing wastewaters, sometimes even increasing dye toxicity.     

Dynamics and mechanism of bridge-dependent charge separation in pyrenylurea-nitrobenzene pi-stacked protophanes

Herein are reported the synthesis, structure, and electronic properties of a series of tertiary di- and polyarylureas possessing pyrene and nitrobenzene end groups separated by a variable number of internal phenylenediamine bridging groups. These molecules adopt folded "protophane" structures in which the adjacent arenes are loosely pi-stacked. The behavior of both the pyrene and nitrobenzene singlet states has been investigated by means of femtosecond broadband pump-probe spectroscopy, and the transients have been assigned on the basis of comparison to reference molecules. Femtosecond time resolution permits direct observation of the fast internal conversion process for both the pyrene and nitrobenzene upper singlet states, as well as the intersystem crossing of nitrobenzene. The ultrafast (ca. 100 fs) charge separation of the donor-acceptor urea having no bridging group is attributed to an internal conversion process. The slower charge separation and charge recombination of the donor-acceptor urea having a single bridging group occur via a bridge-mediated superexchange process. Addition of a second bridging unit results in a role reversal for the pyrene singlet state, which now serves as an excited-state acceptor with the bridging units serving as the electron donors. The change in the directionality of electron transfer upon addition of a second bridging phenylenediamine is a consequence of a decrease in the bridge oxidation potential as well as a decrease in the rate constant for single-step superexchange electron transfer.     

T3P-assisted esterification and amidation of phosphinic acids

A few phosphinic acids, such as phenylphosphinic acids, 1-hydroxy-3-phospholene 1-oxides and 1-hydroxyphospholane oxides are esterified with simple alcohols in the presence of propylphosphonic anhydride (T3P^®). If 1.1 equiv of the T3P^® reagent is used, the esterifications are fast and efficient at 25° C. In the case of more reactive models it was enough to apply 0.66 equiv of T3P^® at 85° C under microwave conditions. The amidation of 1-hydroxy-3-methyl-3-phospholene oxide could also be accomplished under similar conditions.     

T3P®-promoted Kabachnik–Fields reaction: an efficient synthesis of α-aminophosphonates

A simple and efficient synthesis of α-aminophosphonates has been developed via the one-pot three-component reactions of aldehydes, amines, and trialkyl phosphites. The reactions occurred rapidly at room temperature in the presence of 1 equiv of propylphosphonic anhydride (T3P®) as the condensing agent, and the α-aminophosphonate products were obtained in high yields.     

Solid–Liquid Phase Alkylation of N-Heterocycles: Microwave-Assisted Synthesis as an Environmentally Friendly Alternative

The solid–liquid phase alkylation of a variety of five-membered N-heterocycles (carbazole, imidazole, benzimidazole, and indole-3-carbaldehyde) was carried out under different conditions. The use of alkali carbonate in dimethylformamide or in MeCN (in the latter case, in the presence of a phase-transfer catalyst) is a suitable method to prepare the corresponding N-alkylated products in an efficient way. In most cases, the solventless, microwave-assisted reaction is an environmentally friendly alternative to traditional methods.