On the existence of T-direction of algebroid functions: A problem of J.H. Zheng

AbstractIn this paper, we solve a problem of J.H. Zheng (see Problem 5.12 of [J.H. Zheng, On value distribution of meromorphic functions with respect to arguments, preprint]) by proving that for any ν-valued algebroid function satisfying lim supr→∞T(r,w)log2r=+∞, there exists a T-direction dealing with multiple values of w(z)

Effects of ultrasound on electrochemical oxidation mechanisms of p-substituted phenols at BDD and PbO2 anodes

The effects of low-frequency (40 kHz) ultrasound are investigated with regard to the effectiveness and mechanisms of electrochemical oxidation of p-substituted phenols (p-nitrophenol, p-hydroxybenzaldehyde, phenol, p-cresol, and p-methoxyphenol) at BDD (boron-doped diamond) and PbO2 anodes. Although ultrasound improved the disappearance rates of p-substituted phenols at both the BDD and PbO2 anodes, the degree of enhancement varied according to the type of p-substituted phenol and type of anode under consideration. At the BDD anode, the % Increase values were in the range 73-83% for p-substituted phenol disappearance and in the range 60-70% for COD removal. However, at the PbO2 anode, the corresponding %Increase values were in the range 50-70% for disappearance of p-substituted phenols and only 5-25% for COD removal, much lower values than obtained at the BDD anode. Further investigations on the influence of ultrasound on the electrochemical oxidation mechanisms at BDD and PbO2 anodes revealed that the different increase extent were due to the specialized electrochemical oxidation mechanisms at these two anodes. The hydroxyl radicals were mainly free at the BDD electrodes with a larger reaction zone, but adsorbed at the PbO2 electrodes with a smaller reaction zone. Therefore, the enhancement due to ultrasound was greater at the BDD anode than at the PbO2 anode. (C) 2010 Elsevier Ltd. All rights reserved.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000280422800007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701ElectrochemistrySCI(E)EI21ARTICLE205569-55755

Superconductivity and local-moment magnetism in Eu(Fe0.89_{0.89}Co0.11_{0.11})2_{2}As2_{2}

We report the measurements of resistivity and magnetization under magnetic fields parallel and perpendicular to the basal plane, respectively, on a cobalt-doped Eu(Fe$_{0.89}$Co$_{0.11}$)$_{2}$As$_{2}$ single crystal. We observed a resistivity drop at $T_c\sim$ 21 K, which shifts toward lower temperatures under external fields, suggesting a superconducting transition. The upper critical fields near $T_c$ show large anisotropy, in contrast with those of other '122' FeAs-based superconductors. Low-field magnetic susceptibility data also show evidence of superconductivity below 21 K. Instead of expected zero-resistance below $T_c$, however, a resistivity reentrance appears at 17 K under zero field, coincident with the magnetic ordering of Eu$^{2+}$ moments. Based on the temperature and field dependences of anisotropic magnetization, a helical magnetic structure for the Eu$^{2+}$ spins is proposed. External magnetic fields easily changes the helimagnetism into a ferromagnetism with fully polarized Eu$^{2+}$ spins, accompanying by disappearance of the resistivity reentrance. Therefore, superconductivity coexists with ferromagnetic state of Eu$^{2+}$ spins under relatively low magnetic field. The magnetic and superconducting phase diagrams are finally summarized for both $H\parallel ab$ and $H\parallel c$.Comment: 8 pages, 10 figure