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.     

Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.     

Even and Odd Charge Coherent States: Higher-Order Nonclassical Properties and Generation Scheme

We examine the higher-order nonclassical properties of the even and odd charge coherent states as well as proposing a scheme to generate these states whose modes can freely travel in open space. We show that the even and odd charge coherent states exhibit both higher-order antibunching and higher-order squeezing. While the two-mode higher-order antibunching occurs in any order and essentially depends on the charge number, the two-mode higher-order squeezing appears only in the even orders. We also prove that these states are genuinely entangled, and they can be generated by means of cross-Kerr media, beam splitters, phase shifts and threshold detectors. We find that the fidelity and the corresponding success probability to generate these states are dependent on the correlative parameters.     

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.     

Search of sequence databases with uninterpreted high-energy collision-induced dissociation spectra of peptides

We have broadened the utility of the SEQUEST computer algorithms to permit correlation of uninterpreted high-energy collision-induced dissociation spectra of peptides with all sequences in a database. SEQUEST now allows for the additional fragment ion types observed under high-energy conditions. We analyzed spectra from peptides isolated following trypsin digestion of 13 proteins. SEQUEST ranked the correct sequence first for 90% (18/20) of the spectra in searches of the OWL database, without constraint by enzyme cleavage specificity or species of origin. All false-positives were flagged by the scoring system. SEQUEST searches databases for sequences that correspond to the precursor ion mass ±0.5 u. Preliminary ranking of the top 500 candidates is done by calculation of fragment ion masses for each sequence, and comparison to the measured ion masses on the basis of ion series continuity, summed ion intensity, and immonium ion presence. Final ranking is done by construction of model spectra for the 500 candidates and constructing/performing of a cross-correlation analysis with the actual spectrum. Given the need to relate mounting genome sequence information with corresponding suites of proteins that comprise the cellular molecular machinery, tandem mass spectrometry appears destined to play the leading role in accelerating protein identification on the large scale required.     

Activation of α-Fe2O3 for Photoelectrochemical Water Splitting Strongly Enhanced by Low Temperature Annealing in Low Oxygen Containing Ambient

Photoelectrochemical (PEC) water splitting is a promising method for the conversion of solar energy into chemical energy stored in the form of hydrogen. Nanostructured hematite (α-Fe₂O₃) is one of the most attractive materials for a highly efficient charge carrier generation and collection due to its large specific surface area and the short minority carrier diffusion length. In the present work, the PEC water splitting performance of nanostructured α-Fe₂O₃ is investigated which was prepared by anodization followed by annealing in a low oxygen ambient (0.03 % O₂ in Ar). It was found that low oxygen annealing can activate a significant PEC response of α-Fe₂O₃ even at a low temperature of 400 °C and provide an excellent PEC performance compared with classic air annealing. The photocurrent of the α-Fe₂O₃ annealed in the low oxygen at 1.5 V vs. RHE results as 0.5 mA cm⁻², being 20 times higher than that of annealing in air. The obtained results show that the α-Fe₂O₃ annealed in low oxygen contains beneficial defects and promotes the transport of holes; it can be attributed to the improvement of conductivity due to the introduction of suitable oxygen vacancies in the α-Fe₂O₃. Additionally, we demonstrate the photocurrent of α-Fe₂O₃ annealed in low oxygen ambient can be further enhanced by Zn-Co LDH, which is a co-catalyst of oxygen evolution reaction. This indicates low oxygen annealing generates a promising method to obtain an excellent PEC water splitting performance from α-Fe₂O₃ photoanodes.     

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.