Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints

In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general linearly constrained quasiconvex minimization problems. For this method, we prove global convergence when the regularization parameters go to zero. The latter assumption can be dropped when the function is assumed to be pseudoconvex. We also obtain convergence results for quasimonotone variational inequalities, which are more general than monotone ones.     

Application of 4D-QSAR studies to a series of raloxifene analogs and design of potential selective estrogen receptor modulators

Four-dimensional quantitative structure-activity relationship (4D-QSAR) analysis was applied on a series of 54 2-arylbenzothiophene derivatives, synthesized by Grese and coworkers, based on raloxifene (an estrogen receptor-alpha antagonist), and evaluated as ERa ligands and as inhibitors of estrogen-stimulated proliferation of MCF-7 breast cancer cells. The conformations of each analogue, sampled from a molecular dynamics simulation, were placed in a grid cell lattice according to three trial alignments, considering two grid cell sizes (1.0 and 2.0 ?). The QSAR equations, generated by a combined scheme of genetic algorithms (GA) and partial least squares (PLS) regression, were evaluated by "leave-one-out" cross-validation, using a training set of 41 compounds. External validation was performed using a test set of 13 compounds. The obtained 4D-QSAR models are in agreement with the proposed mechanism of action for raloxifene. This study allowed a quantitative prediction of compounds' potency and supported the design of new raloxifene analogs.     

Antioxidant effect of Stryphnodendron rotundifolium Martius extracts from Cariri-Ceará State (Brazil): potential involvement in its therapeutic use

Stryphnodendron rotundifolium is a phytotherapic used in the northeast of Brazil for the treatment of inflammatory processes which normally are associated with oxidative stress. Consequently, we have tested the antioxidant properties of hydroalcoholic (HAB) and aqueous extracts (AB) from the bark and aqueous extract (AL) from the leaves of Stryphnodendron rotundifolium to determine a possible association between antioxidant activity and the popular use of this plant. Free radical scavenger properties were assessed by the quenching of 1',1'-diphenil-2-picrylhydrazyl (DPPH) and the calculated IC(50) were: HAB = 5.4 ± 0.7, AB = 12.0 ± 2.6, and AL = 46.3 ± 12.3 μg/mL. Total phenolic contents were: HAB = 102.7 ± 2.8, AB = 114.4 ± 14.6, and AL = 93.8 ± 9.1 μg/mg plant). HPLC/DAD analyses indicated that gallic acid, catechin, rutin and caffeic acid were the major components of the crude extracts of S. rotundifolium. Plant extracts inhibited Fe(II)-induced lipid peroxidation in brain homogenates. Iron chelation was also investigated and only HBA exhibited a weak activity. Taken together, the results suggest that S. rotundifolium could be considered an effective agent in the prevention of diseases associated with oxidative stress.     

Extraction of volatile oil from aromatic plants with supercritical carbon dioxide: experiments and modeling

An overview of the studies carried out in our laboratories on supercritical fluid extraction (SFE) of volatile oils from seven aromatic plants: pennyroyal (Mentha pulegium L.), fennel seeds (Foeniculum vulgare Mill.), coriander (Coriandrum sativum L.), savory (Satureja fruticosa Béguinot), winter savory (Satureja montana L.), cotton lavender (Santolina chamaecyparisus) and thyme (Thymus vulgaris), is presented. A flow apparatus with a 1 L extractor and two 0.27 L separators was built to perform studies at temperatures ranging from 298 to 353 K and pressures up to 30.0 MPa. The best compromise between yield and composition compared with hydrodistillation (HD) was achieved selecting the optimum experimental conditions of extraction and fractionation. The major differences between HD and SFE oils is the presence of a small percentage of cuticular waxes and the relative amount of thymoquinone, an oxygenated monoterpene with important biological properties, which is present in the oils from thyme and winter savory. On the other hand, the modeling of our data on supercritical extraction of volatile oil from pennyroyal is discussed using Sovová's models. These models have been applied successfully to the other volatile oil extractions. Furthermore, other experimental studies involving supercritical CO₂ carried out in our laboratories are also mentioned.     

The size of the proton

The root-mean-square (rms) charge radius r _p of the proton has so far been known only with a surprisingly low precision of about 1% from both electron scattering and precision spectroscopy of hydrogen. We have recently determined r _p by means of laser spectroscopy of the Lamb shift in the exotic “muonic hydrogen” atom. Here, the muon, which is the 200 times heavier cousin of the electron, orbits the proton with a 200 times smaller Bohr radius. This enhances the sensitivity to the proton’s finite size tremendously. Our new value r _p?=?0.84184 (67) fm is ten times more precise than the generally accepted CODATA-value, but it differs by 5 standard deviations from it. A lively discussion about possible solutions to the “proton size puzzle” has started. Our measurement, together with precise measurements of the 1S–2S transition in regular hydrogen and deuterium, also yields improved values of the Rydberg constant, R _?∞??=?10,973,731.568160 (16) m^???1.     

Structural organization of cetyltrimethylammonium sulfate in aqueous solution: The effect of Na2SO4

We used dynamic light scattering (DLS), steady-state fluorescence, time resolved fluorescence quenching (TRFQ), tensiometry, conductimetry, and isothermal titration calorimetry (ITC) to investigate the self-assembly of the cationic surfactant cetyltrimethylammonium sulfate (CTAS) in aqueous solution, which has SO(2-)4 as divalent counterion. We obtained the critical micelle concentration (cmc), aggregation number (N(agg)), area per monomer (a0), hydrodynamic radius (R(H)), and degree of counterion dissociation (alpha) of CTAS micelles in the absence and presence of up to 1 M Na2SO4 and at temperatures of 25 and 40 degrees C. Between 0.01 and 0.3 M salt the hydrodynamic radius of CTAS micelle R(H) approximately 16 A is roughly independent on Na2SO4 concentration; below and above this concentration range R(H) increases steeply with the salt concentration, indicating micelle structure transition, from spherical to rod-like structures. R(H) increases only slightly as temperature increases from 25 to 40 degrees C, and the cmc decreases initially very steeply with Na2SO4 concentration up to about 10 mM, and thereafter it is constant. The area per surfactant at the water/air interface, a0, initially increases steeply with Na2SO4 concentration, and then decreases above ca. 10 mM. Conductimetry gives alpha = 0.18 for the degree of counterion dissociation, and N(agg) obtained by fluorescence methods increases with surfactant concentration but it is roughly independent of up to 80 mM salt. The ITC data yield cmc of 0.22 mM in water, and the calculated enthalpy change of micelle formation, Delta H(mic) = 3.8 kJ mol(-1), Gibbs free energy of micellization of surfactant molecules, Delta G(mic) = -38.0 kJ mol(-1) and entropy TDelta S(mic) = 41.7 kJ mol(-1) indicate that the formation of CTAS micelles is entropy-driven.     

Transient shear and elongational behavior of blends of PET with a LCP

Blends of polyethylene terephthalate (PET) with a liquid crystalline polymer (LCP) and a compatibilizer were produced by twin screw extrusion and injection molding. Transesterification and compatibilization studies were made in a torque rheometer. The morphology of the injection-molded plaques was studied by scanning electron microscopy. The blends shear growth function was measured in a cone and plate rheometer. The elongational growth function was measured in a modified rotational rheometer. Transesterification was observed in the PET/LCP/compatibilizer 95/5/0 blend. The injection-molded plaques displayed the usual “skin-core” morphology. All the blends were highly shear-thinning, even at low shear rates; thus, a zero-shear viscosity could not be calculated. The compatibilized blend had the highest shear viscosity of all the blends, confirming the strong PET/LCP interphase and the effectiveness of the compatibilizing agent. On the other hand, the 90/10/0 blend had the lowest shear viscosity. All the blends showed strain softening behavior, similar to the PET. The 90/10/0 blend had the highest elongational growth function, while the 95/5/0 had the lowest. The compatibilized blend had an intermediate behavior between both blends.     

Symmetry of Mountain Pass Solutions of Some Vector Field Equations

We prove radial symmetry (or axial symmetry) of the mountain pass solution of variational elliptic systems − AΔu(x) + ∇ F(u(x)) = 0 (or − ∇.(A(r) ∇ u(x)) + ∇ F(r,u(x)) = 0,) u(x) = (u ₁(x),...,u _N (x)), where A (or A(r)) is a symmetric positive definite matrix. The solutions are defined in a domain Ω which can be , a ball, an annulus or the exterior of a ball. The boundary conditions are either Dirichlet or Neumann (or any one which is invariant under rotation). The mountain pass solutions studied here are given by constrained minimization on the Nehari manifold. We prove symmetry using the reflection method introduced in Lopes [(1996), J. Diff. Eq. 124, 378–388; (1996), Eletron. J. Diff. Eq. 3, 1–14].     

A new method for the synthesis of 2-hydroxy-3-nitro-1,4-naphthoquinones: application to regiospecific preparation of unsymmetrical nitrobiquinones

Novel 2-hydroxy-3-nitro-1,4-naphthoquinones were synthesized by an improved method utilizing nitronium tetrafluoroborate in high yields. A subsequent conversion to 2-chloro-3-nitro-1,4-naphthoquinones and a substitution of the chlorine by hydroxyquinone anions yielded 3-nitro-2,2'-binaphthoquinones with a complete regiocontrol.