On necessary and sufficient conditions for near-optimal singular stochastic controls

In this paper we discuss the necessary and sufficient conditions for near-optimal singular stochastic controls for the systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland’s variational principle and some delicate estimates of the state and adjoint processes. It is well known that optimal singular controls may fail to exist even in simple cases. This justifies the use of near-optimal singular controls, which exist under minimal conditions and are sufficient in most practical cases. Moreover, since there are many near-optimal singular controls, it is possible to choose suitable ones, that are convenient for implementation. This result is a generalization of Zhou’s stochastic maximum principle for near-optimality to singular control problem.     

An acceleration scheme for cyclic subgradient projections method

An algorithm for solving convex feasibility problem for a finite family of convex sets is considered. The acceleration scheme of De Pierro (em Methodos de projeção para a resolução de sistemas gerais de equações algébricas lineares. Thesis (tese de Doutoramento), Instituto de Matemática da UFRJ, Cidade Universitária, Rio de Janeiro, Brasil, 1981), which is designed for simultaneous algorithms, is used in the algorithm to speed up the fully sequential cyclic subgradient projections method. A convergence proof is presented. The advantage of using this strategy is demonstrated with some examples.     

Luminescence properties of europium (III) cryptates trapped in sol-gel glass

The Lanthanide complexes Eu-2.2.1 and Eu-2.2.2 were synthesized and then incorporated into silica based transparent organic-inorganic hybrid material by the sol-gel method as an example of how doped xerogel materials are emerging as an important means of producing new materials. The produced gels were diagnosed to monitor emission spectra of the luminescent trivalent europium (Eu³⁺) complexes; emissions were compared to those for gels containing uncomplexed Eu³⁺. Results of the experiments (emission and lifetimes) concerning the coordination sphere composition showed that a cryptand ligand with aromatic groups (short range effect) and the hydrophobic gel host (long range effect) settle efficient action in the antenna effect and isolate the central ion from efficient quenchers, as e.g. water molecules. Each ligand imposed a distinct splitting pattern on the europium emission bands that helps identify them.     

A switchable ionic liquid with polarity swing-assisted regeneration properties used for the preconcentration of cadmium in biological samples

In the present study the cadmium (Cd) was determined in serum samples of psoriatic patients. The severity of psoriasis was evaluated according to criteria based on standard clinical diagnosis using Psoriasis Area Severity Index (PASI) score. In present study, an innovative tunable green solvent system based microextraction (TSS-ME) was applied for the enrichment of Cd in acid digested serum samples prior to determination with flame atomic absorption spectrometry. The hydrophobic complex of Cd-ammonium pyrrolidine thiocarbamate was extracted in a tunable solvent system which was prepared from a polybasic amine (N, N, N′, N′-tetramethyl-1, 4-diaminobutane), decanol and water system. The tunable green solvent system (TSS) which has zero ionic strength was converted to homogeneous monophasic polar hydrophilic phase via exposure to CO₂ at different pressure and time duration. Then hydrophobic enriched Cd- ammonium pyrrolidine thiocarbamate was back extracted, using HNO₃ (0.1 to 0.5 mol L⁻¹) then the second round of TSS-ME was applied. The acidic aqueous phase enrich with analyte was separated from tunable solvent. The separated TSS was easily reused for up to 10 time for preconcentration purposes without loss of its enrichment character. The smoker and nonsmoker psoriatic patients at PASI >10, have two to three folds higher Cd levels in serum samples than healthy persons.     

Crystal and molecular structure of a steroidal spirocyclic lactone, C29H34O4

The X-ray crystal structure of the title compound, as crystallized from methanol–methylene chloride was determined. The asymmetric unit contains two steroid molecules, which differ primarily in the orientation of the aromatic rings of the benzyl ethers. The title compound crystallizes in the noncentrosymmetric space group P2(1), with a = 7.558(2), b = 16.673(3), c = 18.735(4) Å, = 97.610(10)°, and D _calc = 1.268 g cm^–1 for Z = 4.     

The crystal and molecular structure of a trifluoroacetylacetonate complex of scandium,Sc(CH<Subscript>3</Subscript>COCHCOCF<Subscript>3</Subscript>)<Subscript>3</Subscript>

The crystal and molecular structure of Sc(CH₃COCHCOCF₃)₃ has been determined by X-ray diffraction. The compound crystallizes as pure mer-isomer in the orthorhombic space group Pbca with lattice parameters a=15.166(8) ?, b=13.560(7) ?, c=19.327(10) ?, α=β=γ=90°, V=3974(4) ?³, Z=8. The complex at 100 K is partially disordered in the crystal structure in an approximate 5:1 ratio with 83% fluorine population at C-11 and 17% at C-15. NMR data is compared to that previously reported.     

Interaction of Ca2+ with uracil and its thio derivatives in the gas phase

The structures and relative stabilities of the complexes formed by uracil and its sulfur derivatives, namely, 2-thio-, 4-thio, and 2,4-dithio-uracil when interacting with Ca(2+) in the gas phase have been analyzed by means of density functional theory (DFT) calculations carried out at the B3LYP/6-311++G(3df,2p)//B3LYP/6-31+G(d,p) level. For uracil and 2,4-dithiouracil, where the two basic sites are the same, Ca(2+) attachment to the heteroatom at position 4 is preferred. However, for the systems where both types of basic centers, a carbonyl or a thiocarbonyl group, are present, Ca(2+)-oxygen association is favored. The most stable complexes correspond to structures with Ca(2+) bridging between the heteroatom at position 2 of the 4-enol (or the 4-enethiol) tautomer and the dehydrogenated ring nitrogen, N3. The enhanced stability of these enolic forms is two-fold, on the one hand Ca(2+) interacts with two basic sites and on the other triggers a significant aromatization of the ring. Besides, Ca(2+) association has a clear catalytic effect on the tautomerization processes which connect the oxo-thione forms with the enol-enethiol tautomers. Hence, although the enol-enethiol tautomers of uracil and its thio derivatives should not be observed in the gas phase, the corresponding Ca(2+) complexes are the most stable species and should be accessible, because the tautomerization barriers are smaller than the Ca(2+) binding energies.     

Effects of substituents in the beta-position of 1,3-dicarbonyl compounds in bromodimethylsulfonium bromide-catalyzed multicomponent reactions: a facile access to functionalized piperidines

1,3-Dicarbonyl compounds can be converted to Mannich-type products A or highly functionalized piperidines B in the presence of a catalytic amount of bromodimethylsulfonium bromide (BDMS). The combination of aromatic aldehyde, amine, and 1,3-dicarbonyl compounds in the presence of a catalytic amount of BDMS leads to the formation of Mannich-type product A when R is a non-enolizable carbon or an alkoxy group, whereas in cases when R = CH3, the same combination yielded highly functionalized piperidines B. A synthetic study and mechanistic proposal are presented.