A pointwise constrained version of the Liapunov convexity theorem for single integrals

Given any AC solution ${\overline{x} : [a,b] \rightarrow \mathbb{R}^{n}}$ to the convex ordinary differential inclusion $$x^{\prime} ( t) \in co\{v^{1} ( t), \ldots, v^{m} ( t)\} \qquad a.e. on [ a,b], \qquad \qquad (^{*})$$ we aim at solving the associated nonconvex inclusion $$x^{\prime} ( t) \in \{v^{1} ( t), \ldots, v^{m} ( t)\} \qquad a.e.,x( a) = \overline{x} ( a), x( b) = \overline{x} ( b), \qquad \qquad (^{**})$$ under an extra pointwise constraint (e.g. on the first coordinate): $$x_{1} ( t) \leq \overline{x}_{1} ( t) \qquad \forall t \in [ a,b]. \qquad \qquad \qquad (^{***})$$ While the unconstrained inclusion (**) had been solved already in 1940 by Liapunov, its constrained version, with (***), was solved in 1994 by Amar and Cellina in the scalar n = 1 case. In this paper we add an extra geometrical hypothesis which is necessary and sufficient, in the vector n > 1 case, for it existence of solution to the constrained inclusion (**) and (***). We also present many examples and counterexamples to the 2 × 2 case.     

Exposure risk assessment of uranium intake of the milk products from the region of Pernambuco,Brazil

Journal of Radioanalytical and Nuclear Chemistry - Haloperidol (HP) is a dopamine blocking agent. HP was radiolabeled with 125I using direct electrophilic substitution. Different HP formulations...     

Temperature and quantum effects in the stability of pure and doped gold nanowires

We investigate, using ab initio molecular dynamics simulations, the effect of temperature on the stability of pure, C and H doped, atomically thin gold nanowires. We show how thermal fluctuations lead to local instabilities that result in the rupture of the nanowires, and how appropriate impurities may help to stabilize these wires. We also show that when light impurity atoms, such as hydrogen, are incorporated in the Au nanowires, quantum effects will affect the nuclear dynamical evolution.     

The analyticity of a generalized Ruelle’s operator

In this work we propose a generalization of the concept of Ruelle’s operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle’s operator. Our operator generalizes both the Ruelle operator proposed in [2] and the Perron Frobenius operator defined in [7]. We suppose the alphabet is given by a compact metric space, and consider a general a-priori measure to define the operator. We also consider the case where the set of symbols that can follow a given symbol of the alphabet depends on such symbol, which is an extension of the original concept of transition matrices from the theory of subshifts of finite type. We prove the analyticity of the Ruelle’s operator and present some examples.     

Zirconocene-mediated synthesis of cyclobutabenzenes

A new, mild, one-pot method for the synthesis of cyclobutabenzenes by the zirconium-promoted cross-coupling reaction of aryllithium compounds and alkenyl bromides is reported. Formation of an arynezirconocene complex and its regioselective coupling with an alkenyl bromide are the key steps of the process. This method allows the regio- and diastereoselective synthesis of functionalized cyclobutabenzene derivatives from simple and easily available starting materials.     

Removal of envelope protein-free retroviral vectors by anion-exchange chromatography to improve product quality

We have investigated the role of the retroviral lipid bilayer and envelope proteins in the adsorption of retroviral vectors (RVs) to a Fractogel DEAE matrix. Intact RVs and their degradation components (envelope protein-free vectors and solubilized vector components) were adsorbed to this matrix and eluted using a linear gradient. Envelope protein-free RVs (Env(-)) and soluble envelope proteins (gp70) eluted in a significantly lower range of conductivities than intact RVs (Env(+)) (13.7-30 mS/cm for Env(-) and gp70 proteins vs. 47-80 mS/cm for Env(+)). The zeta (zeta)-potential of Env(+) and Env(-) vectors was evaluated showing that envelope proteins define the pI of the viral particles (pI (Env(+)) < 2 versus 3 < pI (Env(-)) < 4) and that Env(+) and Env(-) vectors have similar zeta-potentials within pH 5 and 8. The results presented herein indicate that the adsorption of retroviral particles occurs through multi-point interaction of the envelope proteins with the cationic groups on the chromatographic matrix. The strength of this adsorption is thus dependent on the amount of envelope protein present in the viral lipid bilayer. In conclusion, AEXc enables the separation of gp70 proteins as well as envelope protein-free vectors constituting a significant improvement to the quality of retroviral preparations for gene therapy applications.     

Antioxidant activity of (+)-bergenin: a phytoconstituent isolated from the bark of Sacoglottis uchi Huber (Humireaceae)

(+)-Bergenin (1) was isolated from Sacoglottis uchi, a species of vegetable found in the Amazon region and popularly used for the treatment of several hepatic problems. The structure of 1 was fully characterized using IR, GC-MS and NMR (1D and 2D) analyses. This phytoconstituent has been used as an oriental folk medicine for the treatment of many diseases and shows antihepatotoxic properties. Tests with beta-carotene, DPPH and a heterogeneous Fenton system were carried out, confirming the antioxidant activity of 1. Theoretical calculations were performed to investigate the formation of the radical derivatives of 1 using *H, *OH, *CH(3), and *CCl(3) as initiator radicals. DFT thermodynamic calculations showed that the methoxyl group (O-6-CH(3)) is the most favorable site for radical attack. Frontier molecular orbital analysis showed that nucleophilic radical attack is favored on the aromatic ring of 1 where the LUMO is localized, with antibonding character with respect to the O-6-CH(3) bond. The possibilities of attack at other sites on 1 were investigated in detail in order to understand the regiospecificity of this reaction.     

Adaptation of a commercial ion selective fluoride electrode to a tubular configuration for analysis by flow methodologies

The determination of fluoride ions in water samples is accomplished by using a tubular flow through detector constructed by drilling a channel through a commercially available LaF(3) crystal electrode in such a way that the original contacts of the non-modified unit are maintained. Its performance when incorporated in both FIA and SIA systems was evaluated and the results show that the tubular unit retains the characteristics of the non-modified electrode. In SIA conditions an extended linear range of response and lower detection limit were achieved when compared with the electrode performance in FIA conditions. These aspects together with the additional advantage of low sample and reagent consumptions in SIA when compared to FIA, makes the incorporation of the proposed tubular ISE in a SIA system the preferred approach for on line determination and monitoring of fluoride content in natural water samples.