Non-Completeness of Zograf–Takhtajan's Kähler Metric for Teichmüller Space of Punctured Riemann Surfaces

Zograf and Takhtajan introduced a new K?hler metric on the Teichmüller space T _g , _n (n>0), in calculating the first Chern form of the Quillen metric for families of -operators. The metric is described in terms of the Eisenstein–Maass series. We prove that it is incomplete. And we also give an alternative proof of non-completeness of the Weil–Petersson metric. For that, we use the pinching family, constructed by Wolpert, whose tangent vectors are always represented by using the relative Poincaré series associated with the pinched geodesic. Received: 18 September 1995 / Accepted: 7 March 1999     

Preparation of monodispersed vinylpyridine–divinylbenzene porous copolymer resins and their application to high-performance liquid chromatographic separation of aromatic amines

For the separation of aromatic amines, two types of monodispersed porous polymer resins were prepared by the copolymerization of 2-vinylpyridine and 4-vinylpyridine with divinylbenzene in the presence of template silica gel particles (particle size 5 μm), followed by dissolution of the template silica gel in an alkaline solution. The transmission electron micrographs and the scanning electron micrograph revealed that these templated polymer resins have a spherical morphology with a good monodispersity and porous structure. Using these monodispersed polymer resins, the high-performance liquid chromatographic separation of aromatic amines in the mobile phases of pHs 2.0, 2.9, 4.1, 7.2 and 11.7 were carried out. The 2-vinylpyridine–divinylbenzene copolymer resins showed slightly stronger retentions for aromatic amines than the 4-vinylpyridine–divinylbenzene copolymer resins. Under acidic conditions (around pH 2.0), aniline and the toluidines showed no retention on these copolymer resins due to the repulsion between the cationic forms of these amines and pyridinium cations in the stationary phase, whereas less basic aromatic amines or non-basic acetanilide showed slight retentions. Above pH 4.1, the separation of aromatic amines with these polymer resins showed a typical reversed-phase mode separation. Therefore, the separation patterns of aromatic amines are effectively tunable by changing the pH value of the mobile phases. A good separation of eight aromatic amines was achieved at pH 2.9 using the 2-vinylpyridine–divinylbenzene copolymer resins.     

Interaction forces between poly(amidoamine) (PAMAM) dendrimers adsorbed on gold surfaces

Interaction forces between two gold surfaces with adsorbed poly(amidoamine) (PAMAM) dendrimers (generations G3.0 and G5.0) have been investigated using colloidal probe atomic force microscopy (AFM). In the absence of dendrimers or at their low concentrations, an attractive force derived from the van der Waals interaction was observed. On the other hand, this attractive interaction changed to repulsion with increasing dendrimer concentration. The origin of the repulsion can be attributed to either an electric double layer interaction or a steric effect of the adsorbed dendrimers, depending on the concentration of dendrimer. The steric hindrance was also influenced by the generation of the dendrimer; the force-detectable distance in the presence of PAMAM G5.0 dendrimer was slightly longer than that in the presence of G3.0 dendrimer. In order to estimate the occupied area of each dendrimer adsorbed on gold, quartz crystal microbalance (QCM) measurement was also carried out.     

Utilization of microgravity to improve the crystal quality of biologically important proteins: chaperonin-60, GrpE, B-subunit of V-type ATPase, and MIF

Protein crystallization experiments under microgravity were performed by using commercial vapor diffusion apparatus (CVDA) hardware on the STS-84 shuttle mission. Chaperonin-60, GrpE, the B subunit of V-type ATPase, and the selenomethionine substituted proteins of macrophage migration inhibitory factor (MIF) were selected as target proteins. The results indicate that microgravity positively affected their crystal growth, supporting the practical utilization of microgravity for the protein structure determination.     

The conjugate gradient method for computing all the extremal stationary probability vectors of a stochastic matrix

Summary The conjugate gradient method is developed for computing stationary probability vectors of a large sparse stochastic matrixP, which often arises in the analysis of queueing system. When unit vectors are chosen as the initial vectors, the iterative method generates all the extremal probability vectors of the convex set formed by all the stationary probability vectors ofP, which are expressed in terms of the Moore-Penrose inverse of the matrix (P−I). A numerical method is given also for classifying the states of the Markov chain defined byP. One particular advantage of this method is to handle a very large scale problem without resorting to any special form ofP. The Institute of Statistical Mathematics     

Migration-enhanced epitaxy (MEE) growth of five-layer asymmetric coupled quantum well (FACQW) and its cross-sectional STM observation

The five-layer asymmetric coupled quantum well (FACQW) is a new potential-tailored quantum well that is promising for ultra-fast and ultra-low-voltage optical modulators and switches. FACQW samples were grown by the migration-enhanced epitaxy (MEE) and the conventional molecular beam epitaxy methods with steep and flat heterointerfaces in the monolayer accuracy. They were characterized with the cross-sectional scanning tunneling microscopy (STM). In the cross-sectional STM image, double-stripe structures with different contrast were observed. The stripe area corresponds to the FACQW (about 10 nm wide), sandwiched with the AlGaAs barrier layers (15 nm wide). A dark line observed at the middle of the FACQW stripe area corresponds to the 3-monolayer-thick AlAs layer. The cross-sectional STM images of the high-quality heterointerface FACQW structures were successfully observed for the samples grown by the MEE method. More detailed studies of this kind of cross-sectional STM observations will be very effective to obtain the optimized growth conditions for fine and complicated ultra-thin structures.     

Application of ferrous-chromate and iodometric titration for the determination of copper oxidation states in the superconductor YBa2Cu3Oy

Summary Oxidation-reduction titration methods, Fe²⁺-Cr₂C ₇ ^2– and I^–-S₂O ₃ ^2– , were applied to the determination of the oxidation state of copper in the superconductor YBa₂Cu₃O _y , and related compounds. The former method presented problems in the sample dissolution and titration steps. The dissolution of the sample in low concentrations of Fe⁺-phosphoric acid and Fe²⁺-perchloric acid takes place in two steps, the oxidation of Fe²⁺ to Fe³⁺ and the liberation of oxygen gas, when the liberation results in low analytical values for Cu⁺. In addition the coexistence of cuprous ion and acids induces the oxidation of ferrous ion by dissolved oxygen and air. The problems were resolved by dissolution in 0.1 mol/l Fe²⁺-phosphoric acid and titration in an argon atmosphere. The latter method gave good results by controlling the amounts of potassium chloride, the concentration of acetic acid, and by elimination of the dissolved oxygen in acetic acid solution. The results of the two titration methods coincided with each other.

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Anwendung der Eisen(II)-Chromat- und der iodometrischen Titration zur Bestimmung der Oxidationsstufe des Kupfers im Supraleiter YBa₂Cu₃O _y

     

Vapor-liquid equilibria for binary mixtures of carbon dioxide and fatty acid ethyl esters

Vapor-liquid equilibria were measured and correlated using the Peng-Robinson equation of state for five binary systems of carbon dioxide and fatty acid ethyl esters (ethyl stearate, ethyl oleate, ethyl linoleate, ethyl eicosapentanoate, ethyl docosahexanoate) at 313.15 K, 323.15 K and 333.15 K. Solubility in CO₂ of fatty acid ethyl esters of equal chain length but of various degrees of unsaturation was compared. Although there was no distinct difference in solubility at lower pressures, at higher pressures (more than 15 MPa), those with a higher degree of unsaturation showed a slightly higher solubility. When the solubility in CO₂ of methyl esters and the corresponding ethyl esters were compared, it was noted that the former showed a slightly higher solubility at all system pressures measured in this work.     

CELL SURFACE DAMAGE IN CULTURED MAMMALIAN CELLS WITH SYNCHROTRON RADIATION AT 160 nm

Cultured mammalian cells (HeLa) were allowed to attach onto a membrane filter and were irradiated with 160 nm synchrotron radiation. The cells then were rinsed with medium, fixed, and stained. Some of the cells became detached from the membrane filter during irradiation before post-irradiation incubation at 37°C. The cells remaining attached to the membrane filter were released by trypsinization, collected and examined for dye-exclusion ability with eosin Y. The number of stained cells was increased when the cells were irradiated at 160 nm, while no such increase was observed in cells irradiated with synchrotron radiation at 220 nm, with a low pressure Hg lamp (predominantly 254 nm), or with gamma-rays of ⁶⁰Co. These results indicated that the cell surface was injured by irradiation with synchrotron radiation at 160 nm.