Minimal, rigid foliations by curves on ℂℙ n

We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space ℂℙ ⁿ for every dimension n≥2 and every degree d≥2. Precisely, we construct a foliation ℱ which is induced by a homogeneous vector field of degree d, has a finite singular set and all the regular leaves are dense in the whole of ℂℙ ⁿ . Moreover, ℱ satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if ℱ is conjugate to another holomorphic foliation by a homeomorphism sufficiently close to the identity, then these foliations are also conjugate by a projective transformation. Finally, all these properties are persistent for small perturbations of ℱ.?This is done by considering pseudo-groups generated on the unit ball 𝔹 ⁿ ⊆ℂ ⁿ by small perturbations of elements in Diff(ℂ ⁿ ,0). Under open conditions on the generators, we prove the existence of many pseudo-flows in their closure (for the C ⁰-topology) acting transitively on the ball. Dynamical features as minimality, ergodicity, positive entropy and rigidity may easily be derived from this approach. Finally, some of these pseudo-groups are realized in the transverse dynamics of polynomial vector fields in ℂℙ ⁿ . Received March 7, 2002 / final version received November 26, 2002?Published online February 7, 2003 Most of this work has been carried out during a visit of the first author to IMPA/RJ and a visit of the second author to the University of Lille 1. We would like to thank these institutes for hospitality and express our gratitude to CNPq-Brazil and CNRS-France for the financial support which made these visits possible. We are also indebted to Paulo Sad, Marcel Nicolau and the referee whose comments helped us to improve on the preliminary version. Finally, the second author has partially conducted this research for the Clay Mathematics Institute.     

Actinide heterobimetallic oxides (Th, U): reduction studies

In our laboratories we have been studying the synthesis and reactivity of binary actinide and lanthanide intermetallic compounds. In this work, the air-oxidation of ThCu₂ and AnNi₂ (An = Th, U) was followed by thermogravimetry (TG) and the products were characterized by X-ray powder diffraction (XRD). The heterobimetallic oxides obtained are described by the formulas 2MO·ThO₂ (M = Cu, Ni) and 2NiO·UO₃. The thermogravimetric analysis under hydrogen of these heterobimetallic oxides show one mass loss for 2MO·ThO₂ and two mass losses for 2NiO·UO₃ over a wide range of temperature (293–1273 K). The characterization by XRD shows that the reduction products are 2M·ThO₂ (M = Cu, Ni) and 2Ni·UO₂, with all the actinides in the 4+ oxidation state. The actinide heterobimetallic oxides were described as copper or nickel supported catalysts.     

Development of an HPLC method with electrochemical detection of femtomoles of 8-oxo-7,8-dihydroguanine and 8-oxo-7,8-dihydro-2'-deoxyguanosine in the presence of uric acid

A selective method based on high performance liquid chromatography with electrochemical detection (HPLC-ECD) was developed to enable simultaneous detection of 8-oxo-7,8-dihydroguanine (8-oxoGua) and 8-oxo-7,8-dihydro-2′-deoxyguanosine (8-oxodGuo), products of DNA oxidative damage, in the presence of uric acid (UA), a strong interferent in their electrochemical detection. The method developed consists of HPLC isocratic elution with amperometric detection on a glassy carbon electrode, enabling a detection limit for 8-oxoGua and 8-oxodGuo lower than 1 nM in standard mixtures. Detection of low concentrations up to 25 nM of 8-oxoGua and 8-oxodGuo in the presence of UA in a 10⁴-fold higher concentration was achieved after one-step solid phase extraction (SPE). The method was tested with urine samples and it was possible to detect and quantify the presence of 8-oxoGua, and to confirm that UA was eliminated after uricase degradation and SPE. The LOD found in urine samples was about 80 nM, a value higher than in standard mixtures, due to the increase of background current in the urine matrix. The results presented here contribute to the development of a methodological approach to simultaneous determination of 8-oxoGua and 8-oxodGuo in urine samples.     

Amidomethylation of amodiaquine: antimalarial N-Mannich base derivatives

Novel N-Mannich base-type derivatives of the antimalarial drug amodiaquine were synthesised by reaction with tertiary N-chloromethylamides. With the exception of the derivative of ethyl hippurate, all the so-formed (1-amidomethyl-1H-quinolin-4-ylidene)arylamines displayed high chemical and enzymatic stability. These compounds displayed antimalarial activity against the multi-drug resistant Plasmodium falciparum strain Dd2 (IC₅₀ values 15-31 nM) and demonstrated no significant loss in activity compared to amodiaquine (IC₅₀ 30 nM).     

Synthesis, crystal structure, spectroscopic and electrochemical characterization of the dinuclear complex {tetra-μ-[(±)-2-(p-methoxyphenoxy)-propionato-O,O′]bis(aqua)dicopper(II)}

Structural, electrochemical and spectroscopic data of a new dinuclear copper(II) complex with (±)-2-(p-methoxyphenoxy)propionic acid are reported. The complex {tetra-μ-[(±)-2-(p-methoxyphenoxy)propionato-O,O′]-bis(aqua)dicopper(II)} crystallizes in the monoclinic system, space group P2₁/n with a = 14.149(1) ?, b = 7.495(1) ?, c = 19.827(1) ?, β = 90.62(1) and Z = 4. X-ray diffraction data show that the two copper(II) ions are held together through four carboxylate bridges, coordinated as equatorial ligands in square pyramidal geometry. The coordination sphere around each copper ion is completed by two water molecules as axial ligands. Thermogravimetric data are consistent with such results. The ligand has an “L” type shape due to the angle formed by the β-carbon of the propionic chain and the linked p-methoxyphenoxy group. This conformation contributes to the occurrence of a peculiar structure of the complex. The complex retains its dinuclear nature when dissolved in acetonitrile, but it decomposes into the corresponding mononuclear species if dissolved in ethanol, according to the EPR measurements. Further, cyclic voltammograms of the complex in acetonitrile show that the dinuclear species maintains the same structure, in agreement with the EPR data in this solvent. The voltammogram shows two irreversible reduction waves at E _pc = −0.73 and −1.04 V vs. Ag/AgCl assigned to the Cu(II)/Cu(I) and Cu(I)/Cu° redox couples, respectively, and two successive oxidation waves at E _pa =− 0.01 and +1.41 V vs. Ag/AgCl, assigned to the Cu°/Cu(I) and Cu(I)/Cu(II) redox couples, respectively, in addition to the oxidation waves of the carboxylate ligand.     

Synthesis of tricyclic isoindoles and thiazolo[3,2-c][1,3]benzoxazines

The thermolysis of (3R,9bS)-5-oxo-2,3,5,9b-tetrahydrothiazolo[2,3-a]isoindole-3-carboxylic acids in Ac₂O led to novel 3-methylene-2,5-dioxo-3H,9bH-oxazolo[2,3-a]isoindoles and chiral (9bS)-5-oxo-2,3,5,9b-tetrahydrothiazolo[2,3-a]isoindoles were obtained on FVP. Starting from l-cysteine methyl ester (3R,10bR)-5-oxo-2,3-dihydro-10bH-[1.3]thiazolo[3,2-c][1,3]benzoxazines were obtained as single stereoisomers. The thermolysis of (3R,10bR)-5-oxo-2,3-dihydro-10bH-[1.3]thiazolo[3,2-c][1,3]benzoxazine-3-carboxylic acid in Ac₂O gave 5-acetyl-2-phenyl-2,3-dihydrothiazole. The structures of methyl (3R,9bS)-5-oxo-2,3,5,9b-tetrahydrothiazolo[2,3-a]isoindole-3-carboxylate 1a and methyl (2R,4R)-N-chlorocarbonyl-2-(2-hydroxyphenyl)thiazolidine-4-carboxylate 9 were determined by X-ray crystallography.     

Healable dual organic–inorganic crosslinked sol–gel based polymers: Crosslinking density and tetrasulfide content effect

In this article, the first generation of healable sol–gel based polymers is reported. A dual organic–inorganic crosslinked network is developed containing non‐reversible crosslinks and reversible (tetrasulfide) groups. The designed polymer architecture allows thermally induced mesoscale flow leading to damage closure followed by interfacial strength restoration due to reformation of the reversible groups. While the reversible bonds are responsible for the flow and the interface restoration, the irreversible crosslinks control the required mechanical integrity during the healing process. The temperature dependent gap closure kinetics is strongly affected by the crosslinking density and tetrasulfide content. Raman spectroscopy is used to explain the gap closure kinetics in air and dry nitrogen. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1953–1961     

On-off scheduling schemes for power-constrained electric vehicle charging

In this paper, we study the problem of establishing a dynamic charging schedule of electric vehicles (EVs) at a charging station, assuming that limited power implies that only a limited number of EVs can charge simultaneously. The only control we assume to be available to the charging station is the ability to (at any given time) turn on or off the power supply to any EV, with this tool we want to develop a charging schedule that will satisfy the energy demands of the EVs in their intended deadlines. We propose two distinct approaches to this problem: a discretized time version, based on a greedy-like algorithm, and a continuous time version, based on linear programming. We compare these two approaches and numerically study the improvement they yield in the efficiency of the charging procedure, when applied to simulated data based on real parking data. Finally, we illustrate the flexibility of the models by sketching several possible extensions.