Blowing‐up solutions to two‐times fractional differential equations

Nonexistence results for a class of two‐times differential equations with fractional derivatives of orders between zero and one are presented. Furthermore, the result is extended to a two‐times system of two differential equations with fractional derivatives of orders between zero and one.     

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.     

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.     

Uniform and weak stability of Bresse system with two infinite memories

In this paper, we consider one-dimensional linear Bresse systems in a bounded open domain under Dirichlet–Neumann–Neumann boundary conditions with two infinite memories acting only on two equations. First, we establish the well-posedness in the sense of semigroup theory. Then, we prove two (uniform and weak) decay estimates depending on the speeds of wave propagations, the smoothness of initial data and the arbitrarily growth at infinity of the two relaxation functions.     

Gas-phase reactivity of 2,7-dimethyl-[1,2,4]-triazepine thio derivatives toward Cu+ cation: a DFT study

The gas-phase interactions of 2,7-dimethyl-[1,2,4]-triazepine and its thio derivatives with Cu+ were studied through the use of high-level density functional theory (DFT) calculations. The structure of all possible tautomers and their conformers was optimized at the B3LYP/6-31G(d) level of theory. Final energies were obtained at the B3LYP/6-311+G(2df,2p) level. It has been found that the direct association of Cu+ occurs at the oxygen atom attached to position 3 in the case of the dioxo derivative and at the sulfur atom in all other cases. For the dithio derivatives, the global minimum of the PES corresponds to the structure in which the metal ion bridges between the heteroatom at position 3 and the nitrogen atom at position 4 of the corresponding enolic tautomer, forming a four-membered ring structure; for the dioxo derivative, this conformer competes with the ketone tautomer. Moreover, the isomerization processes leading from the most stable adduct to the other stable conformers were investigated. Among all the considered compounds, the 3,5-dithiotriazepines-Cu+ is found to be the one that associates Cu+ more tightly in the gas phase. The calculated Cu+ binding energies show a good correlation with the experimental proton affinities.     

The mechanism of double proton transfer in dimers of uracil and 2-thiouracil--the reaction force perspective

The intermolecular double proton transfer in dimers of uracil and 2-thiouracil is studied through density functional theory calculations. The reaction force framework provides the basis for characterizing the mechanism that in all cases has been associated to a dynamic balance between polarization and charge transfer effects. It has been found that the barriers for proton transfer depend upon the nature of the acceptor atoms and its position within the seminal monomer. Actually, the change in the nature of the hydrogen bonds connecting the two monomers along the reaction coordinate may favor or disfavor the double-proton transfer.