Minimal entropy and collapsing with curvature bounded from below

We show that if a closed manifold M admits an ℱ-structure (not necessarily polarized, possibly of rank zero) then its minimal entropy vanishes. In particular, this is the case if M admits a non-trivial S ¹-action. As a corollary we obtain that the simplicial volume of a manifold admitting an ℱ-structure is zero.?We also show that if M admits an ℱ-structure then it collapses with curvature bounded from below. This in turn implies that M collapses with bounded scalar curvature or, equivalently, its Yamabe invariant is non-negative.?We show that ℱ-structures of rank zero appear rather frequently: every compact complex elliptic surface admits one as well as any simply connected closed 5-manifold.?We use these results to study the minimal entropy problem. We show the following two theorems: suppose that M is a closed manifold obtained by taking connected sums of copies of S ⁴, ℂP ², ²,S ²×S ²and the K3 surface. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S ⁴,ℂP ²,S ²×S ²,ℂP ²#  ² or ℂP ²# ℂP ². Finally, suppose that M is a closed simply connected 5-manifold. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S ⁵,S ³×S ², then on trivial S ³-bundle over S ² or the Wu-manifold SU(3)/SO(3). Oblatum 13-III-2002 & 12-VIII-2002?Published online: 8 November 2002 G.P. Paternain was partially supported by CIMAT, Guanajuato, México.?J. Petean is supported by grant 37558-E of CONACYT.     

A simple and general method for the synthesis of multicomponent Na2V6O16.3H2O single-crystal nanobelts

Multicomponent Na2V6O16.3H2O (barnesite) single-crystalline nanobelts were synthesized by a direct reaction-crystallization growth of bulk V2O5 and NaF powders under hydrothermal treatment without using any templates or catalysts. This new strategy could be extended to prepare other one-dimensional multicomponent nanomaterials including ammonium, alkali-metal or alkali-earth metal vanadium oxide bronzes and other transition metal oxyfluorides. This is an efficient and mild solution method with clear advantages over the traditional high-temperature approach for the large-scale production of 1D multicomponent nanomaterials. The applicability of this approach toward the preparation of other inorganic systems, such as tungstates and molybdates, will be explored.     

Microwave-assisted synthesis and in-situ self-assembly of coaxial Ag/C nanocables

We have successfully developed a new one-pot solution-phase route, namely microwave-assisted hydrothermal reduction/carbonization (MAHRC), for a rapid synthesis of coaxial Ag/C nanocables. The nanocables can self-assemble in situ in an end-to-end fashion into interconnected chains.     

syn-2,3-Disubstituted-2,3-dihydro-1,4-benzoxathiin rings: preparation from quinone ketals and 2-mercaptoethanols

A general method for the preparation of syn-2,3-disubstituted-2,3-dihydro-1,4-benzoxathiin rings from 2-mercaptoethanols and quinone ketals is presented. This ring system is produced by Michael addition of a 2-mercaptoethanol to a quinone ketal, followed by cyclization of the initial Michael adduct, and subsequent aromatization to afford a syn-2,3-disubstituted-1,4-benzoxathiin in fair to good chemical yield. Several chiral syn-2,3-disubstituted-2,3-dihydro-1,4-benzoxathiin rings were prepared with this method from enantioenriched 2-mercaptoethanols. No loss of enantiopurity was observed.     

An alternative sampling algorithm for use in liquid chromatography/tandem mass spectrometry experiments

In liquid chromatography/tandem mass spectrometry (LC/MS/MS) analyses of complex peptide mixtures, dynamic exclusion functions are used to minimize repeat selections of identical precursors for collision induced dissociation (CID). We describe a new algorithm for the dynamic exclusion of m/z values during LC/MS/MS. Full-scan based peak exclusion (Fulspec) uses a simplified model of chromatographic peak formation to detect and exclude contaminants present throughout the run or that lead to broad peaks. Therefore, instead of excluding peptides from fragment analysis according to a rigidly predefined time window, the chromatographic properties of the detected analytes are used. The algorithm was tested on two datasets derived from previously published experiments. Fulspec achieves a distribution of CID spectra with minimal tailing on the retention time axis, without resorting to rigid exclusion of m/z values. The procedure further excludes intensities with a bias towards low-quality CID spectra. This combination frees up valuable analytical capacity. The underlying intensity vs. quality analyses challenge the assumption that abundant precursors automatically give the best identifications. Further validation of the algorithm will require its incorporation by equipment manufacturers into the instrument control programs.     

A mesoporous Pt/TiO2 nanoarchitecture with catalytic and photocatalytic functions

A novel metal/semiconductor nanocomposite with catalytic and photocatalytic functions has been prepared. The new material consists of highly dispersed platinum (Pt) nanoparticles embedded in a cubic mesoporous nanocrystalline anatase (meso-nc-TiO2) thin film. The porous thin film possesses a narrow pore-size distribution and a large surface area. The diameter of the Pt cluster can be controlled to below 5 nm, and the high dispersion of these clusters gives rise to catalytic activity for the oxidation of carbon monoxide, an important reaction for automobile exhaust treatment. This novel ordered mesoporous Pt/TiO2 nanoarchitecture is also a promising photochemical material, as demonstrated by the photo-driven killing of Micrococcus lylae cells on the film.     

Preconcentration using diethylenetriaminetetraacetic acid-functionalized polysiloxane (DETAP) for determination of molybdenum(VI) in seawater by ICP–OES

This paper reports a new method for preconcentration and separation of trace amounts of molybdenum in seawater samples prior to determination by inductively coupled plasma–atomic emission spectroscopy (ICP–OES). Diethylenetriaminetetraacetic acid-functionalized polysiloxane (DETAP) was synthesized by carboxymethylation of amino groups on triamine immobilized polymer, which was prepared by modification of 3-chloropropylpolysiloxane with diethylenetriamine. The resulting polysiloxane is highly selective and efficient in chelating Mo(VI) at trace levels. It can be used as a column packing material. The polysiloxane column can be reused over ten times without losing its original properties, so it is suitable for preconcentration of molybdenum species in seawater samples before determination. The parameters governing the characteristics of polysiloxane for adsorption of Mo(VI) were investigated. These include the effect of pH, amount of polysiloxane, equilibrium time, adsorption isotherm, maximum adsorption capacity, interfering ions, flow rate, capacity for reuse, and desorption. The precision of the preconcentration method, calculated as the relative standard deviation of seawater samples, was 3%. The preconcentration factor was 100. The detection limit, defined as 3 times the standard deviation of five replicate measurements of the blank sample at pH 3, was 0.17 g L^–1. Measurement results for standard reference materials were in good agreement with the certified values [(CRMs), NASS-2 Seawater (Open Ocean) and CASS-2 Seawater (Coastal)].     

Systematic synthesis and characterization of single-crystal lanthanide orthophosphate nanowires

A simple hydrothermal method has been developed for the systematic synthesis of lanthanide orthophosphate crystals with different crystalline phases and morphologies. It has been shown that pure LnPO(4) compounds change structure with decreasing Ln ionic radius: i.e., the orthophosphates from Ho to Lu as well as Y exist only in the tetragonal zircon (xenotime) structure, while the orthophosphates from La to Dy exist in the hexagonal structure under hydrothermal treatment. The obtained hexagonal structured lanthanide orthophosphate LnPO(4) (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, and Dy) products have a wirelike morphology. In contrast, tetragonal LnPO(4) (Ln = Ho, Er, Tm, Yb, Lu, Y) samples prepared under the same experimental conditions consist of nanoparticles. The obtained hexagonal LnPO(4) (Ln = La --> Tb) can convert to the monoclinic monazite structured products, and their morphologies remained the same after calcination at 900 degrees C in air (Hexagonal DyPO(4) is an exceptional case, it transformed to tetragonal DyPO(4) by calcination), while the tetragonal structure for (Ho--> Lu, Y)PO(4) remains unchanged by calcination. The resulting LnPO(4) (Ln = La --> Dy) products consist almost entirely of nanowires/nanorods with diameters of 5-120 nm and lengths ranging from several hundreds of nanometers to several micrometers. Europium doped LaPO(4) nanowires were also prepared, and their photoluminescent properties were reported. The optical absorption spectrum of CePO(4) nanowires was measured and showed some differences from that of bulk CePO(4) materials. The possible growth mechanism of lanthanide phosphate nanowires was explored in detail. X-ray diffraction, field-emission scanning electron microscopy, transmission electron microscopy, electron diffraction, infrared absorption spectra, X-ray photoelectron spectroscopy, optical absorption spectra, and photoluminescence spectra have been employed to characterize these materials.     

Studies on diacetylenic vinyl compounds. VI. ESR studies on the polymerization of diacetylene containing acrylate and methacrylates

A number of diacetylene containing acrylate and methacrylates have been synthesized and the interaction between their propagating radicals and the diacetylene groups was studied by ESR spectroscopy. In the case of polymerization at 70°C using AIBN as an initiator, the propagating radicals of methacrylates are temporarily trapped with the diacetylenes with rapid exchange of the electron, thus showing strong signals of the propagating radicals. Gamma irradiation of the frozen state produces a blue color in samples, and the ESR signals were found to be those of uninteracted acrylate and methacrylates. From a comparison of spectral widths, there seems to exist an intramolecular interaction between the radicals and the diacetylene group at the frozen state. © 1992 John Wiley & Sons, Inc.     

Efficient degradation of organic pollutants mediated by immobilized iron tetrasulfophthalocyanine under visible light irradiation

Supported iron tetrasulfophthalocyanine can efficiently catalyze the degradation of organic pollutants by H2O2 under visible light irradiation in an aqueous solution, and the catalyst can be easily recycled without apparent loss of activity.