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.     

Statistical radical copolymerization of styrene and methyl methacrylate in a room temperature ionic liquid

Use of a room temperature ionic liquid as the medium for conventional free radical copolymerization of styrene and methyl methacrylate resulted in reactivity ratios that were significantly different from those obtained in conventional organic solvents or in bulk, demonstrating that polymerization in this alternative medium offers potential to create copolymers having new monomer sequences.     

MNDO Study of reaction pathways for SN2 reactions. Menschutkin reaction potential energy surfaces

MNDO molecular orbital calculations have been employed to investigate limited reaction pathways and potential energy surfaces for a series of S_N2 reactions. Model calculations for X^? + CH₃X (X = H, F, OH, OCH₃, and CN) indicate that the MNDO method gives qualitative agreement with ab initio studies except for the hydride–CH₄ exchange. Studies involving alkylation of pyridine (Menschutkin reaction) were also carried out. For the reaction of pyridine with CH₃Cl, which involves charge separation, our MNDO studies (which do not include solvation effects) do not produce a characteristic S_N2 pathway. For the reaction of pyridine with trimethyloxonium cation [(CH₃)₃O⁺] as the alkylating agent, a well defined S_N2 reaction pathway was obtained; this reaction involves charge transfer. A potential energy surface for the pyridine–trimethyloxonium cation reaction shows the presence of a saddle point transition state that resembles starting materials, in agreement with the Hammond postulate for this exothermic reaction.     

The Effect of SiO2 Addition on the Grain Size and Photocatalytic Activity of TiO2 Thin Films

The uniform transparent TiO₂/SiO₂ nanometer composite thin films were prepared via sol-gel method on the soda lime glass substrates, and were characterized by X-ray photoelectron spectroscopy (XPS), FTIR spectroscopy, UV-VIS spectroscopy, transmission electron microscopy (TEM), X-ray diffraction (XRD) and BET surface areas. It was found that the addition of SiO₂ to TiO₂ thin films could suppress the grain growth of TiO₂ crystal and increase the hydroxyl content of the surface of TiO₂ films. The photocatalytic activity of the as-prepared TiO₂/SiO₂ composite thin films increases for SiO₂ content of less than 5 mol%.     

In situ tissue pathology from spatially encoded mass spectrometry classifiers visualized in real time through augmented reality

Integration between a hand-held mass spectrometry desorption probe based on picosecond infrared laser technology (PIRL-MS) and an optical surgical tracking system demonstrates in situ tissue pathology from point-sampled mass spectrometry data. Spatially encoded pathology classifications are displayed at the site of laser sampling as color-coded pixels in an augmented reality video feed of the surgical field of view. This is enabled by two-way communication between surgical navigation and mass spectrometry data analysis platforms through a custom-built interface. Performance of the system was evaluated using murine models of human cancers sampled in situ in the presence of body fluids with a technical pixel error of 1.0 ± 0.2 mm, suggesting a 84% or 92% (excluding one outlier) cancer type classification rate across different molecular models that distinguish cell-lines of each class of breast, brain, head and neck murine models. Further, through end-point immunohistochemical staining for DNA damage, cell death and neuronal viability, spatially encoded PIRL-MS sampling is shown to produce classifiable mass spectral data from living murine brain tissue, with levels of neuronal damage that are comparable to those induced by a surgical scalpel. This highlights the potential of spatially encoded PIRL-MS analysis for in vivo use during neurosurgical applications of cancer type determination or point-sampling in vivo tissue during tumor bed examination to assess cancer removal. The interface developed herein for the analysis and the display of spatially encoded PIRL-MS data can be adapted to other hand-held mass spectrometry analysis probes currently available.

Integration between a hand-held mass spectrometry desorption probe based on picosecond infrared laser technology (PIRL-MS) and an optical surgical tracking system demonstrates in situ tissue pathology from point-sampled mass spectrometry data.     

Determination of total gaseous selenium in atmosphere by honeycomb denuder/differential pulse cathodic stripping voltammetry

A new analytical method has been developed for the determination of total gaseous selenium in the atmosphere by honeycomb denuder collection followed by differential pulse cathodic stripping voltammetry (DPCSV) measurement. Gaseous selenium was collected in a denuder coating solution containing 2% HNO(3) and 2% glycerine. The soluble product, selenious acid, was then extracted by water for DPCSV analysis. The collection efficiency for gaseous selenium was 99.1% at a flow rate of 1 l min(-1) for 3 h. Excellent linearity in DPCSV was maintained up to Se concentration of 40 ng ml(-1). This was equivalent to a working concentration of 220 ng m(-3) of selenium in the atmosphere. A precision of 1.26% RSD (n=5) for 5 ng Se was obtained, and the detection limit (3sigma) and the quantitative determination limit were estimated to be 0.96 and 3.19 ng m(-3). The average recovery of selenium in three standard samples prepared by independent digestion of NIST SRM 1648 (Urban Particulate Matter) using our analytical system was 99.0%. The total content of gaseous selenium in the atmosphere of our laboratories was 3.2-4.4 ng m(-3).     

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.     

Universal quenching of common fluorescent probes by water and alcohols

Although biological imaging is mostly performed in aqueous media, it is hardly ever considered that water acts as a classic fluorescence quencher for organic fluorophores. By investigating the fluorescence properties of 42 common organic fluorophores recommended for biological labelling, we demonstrate that H₂O reduces their fluorescence quantum yield and lifetime by up to threefold and uncover the underlying fluorescence quenching mechanism. We show that the quenching efficiency is significantly larger for red-emitting probes and follows an energy gap law. The fluorescence quenching finds its origin in high-energy vibrations of the solvent (OH groups), as methanol and other linear alcohols are also found to quench the emission, whereas it is restored in deuterated solvents. Our observations are consistent with a mechanism by which the electronic excitation of the fluorophore is resonantly transferred to overtones and combination transitions of high-frequency vibrational stretching modes of the solvent through space and not through hydrogen bonds. Insight into this solvent-assisted quenching mechanism opens the door to the rational design of brighter fluorescent probes by offering a justification for protecting organic fluorophores from the solvent via encapsulation.

Overtones and combinations of O–H vibrations in the solvent efficiently quench red-emitting fluorophores by resonant energy transfer.     

New Monoterpene-Substituted Dihydrochalcones from Piper aduncum

Five New unusual monoterpene-substituted dihydrochalcones, the adunctins A–E (1″S)-1-{2′-hydroxy-4′-methoxy-6′-[4″-methyl-1″-(1?-methylethyl)cyclohex-3″ -en-1″ -yloxy]phenyl}-3-phenylpropan-1-one ( 1 ), (5aR*,8R*,9aR*)-3-phenyl-1-[5′,8′,9′,9′a-tetrahydro-3′-hydroxy-1′-methoxy-8′-(1″-methylethyl)-5′-a-methyldibenzo-[b,d]furan-4′-yl]propan-1-one ( 2 ), (2′R*,4″S*)-1-{6′-hydroxy-4′-methoxy-4″-(1?-methylethyl)spiro[benzo[b]-furan-2′(3′H),1″ -cyclohex-2″ -en]-7′-yl}-3-phenylpropan-1-one ( 3 ), (2′R*,4″R*)-1-{6′-hydroxy-4′-methylethyl-4″-(1?-methylethyl)spiro[benzo[b]furan-2′(3′H),1″-cyclohex-2″-en]-7′-yl}-3-phenypropan-1-one ( 4 ), and (5′aR*,6′S*, 9′R*,9′aS*)-1-[5′a,6′,7′,8′,9′a-hexahydro-3′,6′-methoxy-6′-methyl-9′-(1″-methylethyl)dibenzo[b,d]-furan-4′-yl]-3-phenylpropan-1-one ( 5 ) were isolated from the leaves of Piper aduncum (Piperaceae) by preparative liquid chromatography. In addition, (?)-methyllindaretin ( 6 ), trans-phytol, and α-tocopherol ( = vitamin E) were also isolated and identified. The structures were elucidated by spectroscopic methods, including 1D- and 2D-NMR spectroscopy as well as single-crystal X-ray diffraction analysis. The antibacterial and cytotoxic potentials of the isolates were also investigated.     

β-Cyclodextrin epichlorohydrin copolymer as a solid-phase extraction adsorbent for aromatic compounds in water samples

A novel solid-phase extraction (SPE) procedure for trace aromatic compounds in water samples has been developed using 12 aromatic compounds as model compounds and GC-MS and UV spectrophotometry for detection. The method is based on the fact that β-cyclodextrin (β-CD) epichlorohydrin (ECH) copolymer (β-CDEP) can extract non-ionized aromatic compounds quantitatively from aqueous samples. The polymer used is a colorless, transparent and insoluble solid with a maximum capacity of 0.82 μmol aromatic compounds per gram. It was synthesized by co-polymerization of β-CD and ECH and characterized by FT-IR and UV. β-CDEP does not contain double bonds, and therefore it does not have appreciable absorbance in the UV region. The optimum pH range for the extraction of aromatic compounds is 2.5-5.0. The method has high extraction efficiency with the recoveries between 90 and 101% for aromatic compounds at 0.02-1.67 ppm levels, and the analytes can be easily eluted by methanol washing after preconcentration.