Microlocal study of topological Radon transforms and real projective duality

Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.     

Limit cycles and Lie symmetries

Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a prescribed number of hyperbolic limit cycles. Finally we show how this procedure solves the problem of the hyperbolicity of periodic orbits in problems where other criteria, like the classical one of the divergence, fail.     

用分光光度法测定蜂胶超临界CO2萃取物中总黄酮含量

利用碱性条件下黄酮与Al3 生成粉红色络合物在可见光区510 nm处有最大吸收的特性,以芦丁为标样,采用分光光度法测定蜂胶超临界CO2萃取物中总黄酮含量,并与HPLC标准方法测定结果进行比较,发现各平行样的测定结果基本一致,最大偏差为268.38 mg/100 g,最小偏差为52.77 mg/100 g.该法简便快捷,结果相对准确,可作为蜂胶超临界CO2萃取物中总黄酮含量快速评估的一种方法.     

Algorithms for finding proper essential surfaces in 3-manifolds

In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold M, verifies whether M contains an essential orientable surface (possibly, with boundary), whose genus is at most N. The algorithm is based on Haken’s theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold.     

On the 2-rainbow domination in graphs

The concept of 2-rainbow domination of a graph G coincides with the ordinary domination of the prism G□K₂. In this paper, we show that the problem of deciding if a graph has a 2-rainbow dominating function of a given weight is NP-complete even when restricted to bipartite graphs or chordal graphs. Exact values of 2-rainbow domination numbers of several classes of graphs are found, and it is shown that for the generalized Petersen graphs GP(n,k) this number is between ⌈4n/5⌉ and n with both bounds being sharp.     

Upper semifinite hyperspaces as unifying tools in normal Hausdorff topology

In this paper we use the upper semifinite topology in hyperspaces to get results in normal Hausdorff topology. The advantage of this point of view is that the upper semifinite topology, although highly non-Hausdorff, is very easy to handle. By this way we treat different topics and relate topological properties on spaces with some topological properties in hyperspaces. This hyperspace is, of course, determined by the base space. We prove here some reciprocals which are not true for the usual Vietoris topology. We also point out that this framework is a very adequate one to construct the ?ech-Stone compactification of a normal space. We also describe compactness in terms of the second countability axiom and of the fixed point property. As a summary we relate non-Hausdorff topology with some facts in the core of normal Hausdorff topology. In some sense, we reinforce the unity of the subject.     

Degradation of 4-chlorophenol in aqueous solution by γ-radiation and ozone oxidation

The application of radiation technology in the en-vironmental protection was listed as one of the mostimportant research fields by the International AtomicEnergy Agency (IAEA) for the peaceful use of nuclearenergy. It has great research value and potential appli-cation. Because of their broad-spectrum antimicrobialproperties, Cholophenols (CPs) have been used aspreservative agents for wood, paints, vegetable fibersand leather and as disinfectants. In addition, they havebeen widely employed…     

Optical properties of In2O3 oxidized from InN deposited by reactive magnetron sputtering

Unintentionally doped and zinc-doped indium nitride (U-InN and InN:Zn) films were deposited on (0 0 0 1) sapphire substrates by radio-frequency reactive magnetron sputtering, and all samples were then treated by annealing to form In₂O₃ films. U-InN and InN:Zn films have similar photon absorption characteristics. The as-deposited U-InN and InN:Zn film show the absorption edge, ∼1.8-1.9 eV. After the annealing process at 500 °C for 20 min, the absorption coefficient at the visible range apparently decreases, and the absorption edge is about 3.5 eV. Two emission peaks at 3.342 eV (371 nm) and 3.238 eV (383 nm) in the 20 K photoluminescence (PL) spectrum of In₂O₃:Zn films were identified as the free-exciton (FE) or the near band-to-band (B-B) and conduction-band-to-acceptor (C-A) recombination, respectively.     

Preparation and characterization of activated carbons from impregnation pitch by ZnCl2

Using an impregnation pitch from bituminous coal tar (OP) supplied by Industrias Químicas del Nalon Company as raw material, two phases (isotropic and anisotropic) have been obtained. The latter was used as precursor for the preparation of activated carbons. First, a chemical activation process was carried out with ZnCl₂ as activating agent. The process was conducted at different concentrations and temperatures and by means of impregnation with solid zinc chloride. Optimal values were obtained for samples prepared by using a ZnCl₂:pitch ratio equal to 3:1 (sample AZn3). Next, this sample was thermally treated at two different temperatures, i.e., 700 and 800 °C. A lose of specific surface area, microporosity and mesoporosity was observed with respect to sample AZn3, such a lose being more remarkable as temperature increased. Moreover, impregnation of the anisotropic phase of the original pitch with an aqueous solution of ZnCl₂ followed by thermal treatment resulted in a poorly developed surface area and porous texture, probably due to the presence of Zn complexes, which interfere with the activation process.