A Nadel vanishing theorem via injectivity theorems

The purpose of this paper is to establish Nadel type vanishing theorems with multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu’s metrics). For this purpose, we generalize Kollár’s injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics, by making use of the theory of harmonic integrals. Moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles.     

Enantioselective Darzens reaction using organoselenide-lithium hydroxide complexes

Asymmetric Darzens reaction catalyzed by chiral selenides is described. A novel Lewis acid/Brønsted base catalyst formed by C₂ symmetric chiral selenide-bearing isoborneol skeletons, which were readily prepared from (1S)-10-camphorsulfonic acid, and LiOH promoted the reaction of phenacyl bromide with aldehydes to afford the desired trans oxiranes with up to 62% ee.     

Square integrability of representations on p-adic symmetric spaces

A symmetric space analogue of Casselman's criterion for square integrability of representations of a p-adic group is established. It is described in terms of exponents of Jacquet modules along parabolic subgroups associated to the symmetric space.     

Thermal phase transition of RbMnFe(CN)6 observed by X-ray emission and absorption spectroscopy

The thermal phase transition of RbMnFe(CN)₆ has been observed by Mn and Fe 3p-1s X-ray emission spectroscopy (XES) and 1s X-ray absorption spectroscopy (XAS). The thermal variations of the spin states and the valences of Mn and Fe were determined to be Mn²⁺(S=5/2)-NC-Fe³⁺(S=1/2) for the high-temperature (HT) phase and Mn³⁺(S=2)-NC-Fe²⁺(S=0) for the low-temperature (LT) phase. These transitions are thus caused by charge transfer between Mn and Fe. The temperature dependences of Mn and Fe 3p-1s XES and 1s XAS were observed as the composition of the spectra of the HT and LT phases. The ratios of the HT component in each spectrum show good agreement with the thermal transition curves observed with magnetic susceptibility measurements.     

Upper limit of enhancement of boiling heat transfer in a narrow vertical rectangular channel due to passing bubbles

An experimental study has been made of saturated boiling heat transfer for water and R113 in a narrow vertical rectangular channel (2 mm space, 20 mm wide, and 200 mm long) at atmospheric pressure, in which the vertical heated surface (10 mm long and 20 mm wide) is located on one side at a position of 150 mm from its entrance and bubbles are forcibly passed through it at a designated period from 0.33 to 1.0 sec. The experiment shows that the heat transfer coefficients are increased by the bubble passing through the heated surface for the value of thermal diffusivity,a, times period, T₀, of the passing bubbles above about 6×10^–9 m² (a T ₀>6×10^–9 m²) while fora T ₀< 6×10^–9 m², the heat transfer coefficients become independent of the period and the effectiveness of the enhancement of the heat transfer owing to the passing bubble disappears.

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Die obere Grenze der Verbesserung des Wärmeübergangs beim Sieden in einem vertikalen, rechteckigen Kanal infolge von aufsteigenden Blasen

Zusammenfassung Es wurden Experimente über den Wärmeübergang beim Sättigungssieden mit Wasser und R113 in einem engen, vertikalen, rechteckigen Kanal (2 mm Abstand, 20 mm Breite und 200 mm Länge) bei Umgebungsdruck durchgeführt, wobei die vertikale, beheizte Oberfläche (10 mm lang und 20 mm breit) auf der einen Seite in einem Abstand von 150 mm vom Eintritt angeordnet ist und die Blasen zwangsweise durch den Kanal sich mit einem Periodenabstand von 0,033 bis 1,0 s bewegen. Das Experiment zeigt, daß die Wärmeübergangskoeffizienten durch das Vorbeistreichen der Blasen an der beheizten Oberfläche verbessert werden, wenn das Produkt aus Temperaturleitfähigkeit,a, mal der Periode, T₀, der vorbeistreichenden Blasen größer als 6×10^–9 m² liegt, während unterhalb dieses Wertes der Wärmeübergangskoeffizient unabhängig von der Blasenperiode ist und die Effektivität der Wärmeübergangsverbesserung infolge der Blasenströmung verschwindet.

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Nomenclature a thermal diffusivity of liquid - ¯h time-averaged heat transfer coefficient - q _w heat flux at wall - T ₀ period of passing bubble - T _w(t) temperature of heated surface - T _w amplitude of heated surface temperature Greek symbols thermal conductivity - thickness of liquid film     

A general extension theorem for cohomology classes on non reduced analytic subspaces

The main purpose of this paper is to generalize the celebrated L~2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is K¨ahler and holomorphically convex, but not necessarily compact.     

Dynamic response of circular plates subjected to transverse impulsive loads

Summary The behaviours of dynamical stresses acting in the circular plate subjected to transverse impulsive loads are investigated. The cases are treated where a rigid body with spring collides with the circular plate having a hole at its center along its inner edge. The relationships between dynamic load factors (D.L.F.) with respect to bending moments, solid viscosities and spring are obtained. Experiments are carried out and theoretical results are compared with experimental ones.

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Übersicht Es werden die dynamischen Spannungen untersucht, die in einer Kreisplatte durch stoßartige Querkräfte hervorgerufen werden. Es wird angenommen, daß ein mit Federn versehener starrer Körper so auf die mit einem konzentrischen Loch versehene Platte fällt, daß der Stoß am inneren Rande der Platte erfolgt. Es werden Beziehungen zwischen den dynamischen Belastungsfaktoren bezüglich der Biegemomente, den viskoelastischen Materialeigenschaften der Platte und den Federkonstanten abgeleitet. Die theoretischen Ergebnisse werden mit Versuchsergebnissen verglichen.

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The author wishes to thank Mr. Toda at National Aeronautical Laboratory for his help with numerical calculations.     

Organocatalytic head-to-tail dimerization of methacrolein via conjugate addition of methanol: an alcohol activation mechanism proved by electrospray ionization mass spectrometry

The head-to-tail dimerization of methacrolein via the conjugate addition of methanol is catalyzed by various organic bases, such as an amine, phosphine, and N-heterocyclic carbene, to give 2,4-dimethyl-2-methoxymethylpentane-1,5-dial in moderate yields. Based on the interpretation of the key intermediates by electrospray ionization mass spectrometry, we propose a reaction mechanism involving the initial conjugate addition of the organic bases to methacrolein to generate a zwitterionic base followed by the activation of methanol.     

Synthesis of hollow CaCO3 nanospheres templated by micelles of poly(styrene-b-acrylic acid-b-ethylene glycol) in aqueous solutions

An asymmetric triblock copolymer, poly(styrene-b-acrylic acid-b-ethylene glycol) (PS-b-PAA-b-PEG), was synthesized via reversible addition-fragmentation chain transfer controlled radical polymerization. Micelles of PS-b-PAA-b-PEG with PS core, PAA shell, and PEG corona were then prepared in aqueous solutions, followed by extensive characterization based on dynamic light scattering, zeta-potential, and transmission electron microscopy (TEM) measurements. The well-characterized micelles were used to fabricate hollow nanospheres of CaCO(3) as a template. It was elucidated from TEM measurements that the hollow nanospheres have a uniform size with cavity diameters of ca. 20 nm. The X-ray diffraction analysis revealed a high purity and crystallinity of the hollow nanospheres. The hollow CaCO(3) nanospheres thus obtained have been used for the controlled release of an anti-inflammatory drug, naproxen. The significance of this study is that we have overcome a previous difficulty in the synthesis of hollow CaCO(3) nanospheres. After mixing of Ca(2+) and CO(3)(2-) ions, the growth of CaCO(3) is generally quite rapid to induce large crystal, which prevented us from obtaining hollow CaCO(3) nanospheres with controlled structure. However, we could solve this issue by using micelles of PS-b-PAA-b-PEG as a template. The PS core acts as a template that can be removed to form a cavity of hollow CaCO(3) nanospheres, the PAA shell is beneficial for arresting Ca(2+) ions to produce CaCO(3), and the PEG corona stabilizes the CaCO(3)/micelle nanocomposite to prevent secondary aggregate formation.     

Non-surface activity and micellization behavior of cationic amphiphilic block copolymer synthesized by reversible addition-fragmentation chain transfer process

Cationic amphiphilic diblock copolymers of poly(n-butylacrylate)-b-poly(3-(methacryloylamino)propyl)trimethylammonium chloride) (PBA-b-PMAPTAC) with various hydrophobic and hydrophilic chain lengths were synthesized by a reversible addition-fragmentation chain transfer (RAFT) process. Their molecular characteristics such as surface activity/nonactivity were investigated by surface tension measurements and foam formation observation. Their micelle formation behavior and micelle structure were investigated by fluorescence probe technique, static and dynamic light scattering (SLS and DLS), etc., as a function of hydrophilic and hydrophobic chain lengths. The block copolymers were found to be non-surface active because the surface tension of the aqueous solutions did not change with increasing polymer concentration. Critical micelle concentration (cmc) of the polymers could be determined by fluorescence and SLS measurements, which means that these polymers form micelles in bulk solution, although they were non-surface active. Above the cmc, the large blue shift of the emission maximum of N-phenyl-1-naphthylamine (NPN) probe and the low micropolarity value of the pyrene probe in polymer solution indicate the core of the micelle is nonpolar in nature. Also, the high value of the relative intensity of the NPN probe and the fluorescence anisotropy of the 1,6-diphenyl-1,3,5-hexatriene (DPH) probe indicated that the core of the micelle is highly viscous in nature. DLS was used to measure the average hydrodynamic radii and size distribution of the copolymer micelles. The copolymer with the longest PBA block had the poorest water solubility and consequently formed micelles with larger size while having a lower cmc. The "non-surface activity" was confirmed for cationic amphiphilic diblock copolymers in addition to anionic ones studied previously, indicating the universality of non-surface activity nature.