Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

Structural changes upon reduction of dipyrido[2,3-a:3',2'-c]phenazine probed by vibrational spectroscopy, ab initio calculations, and deuteration studies

A series of bridging ligands, dipyrido[2,3-a:3',2'-c]phenazine (ppb), dipyrido[2,3-a:3',2'-c]-6,7-dichlorophenazine (ppbCl2), and dipyrido[2,3-a:3',2'-c]-6,7-dimethylphenazine (ppbMe2), and their binuclear copper(I) complexes have been synthesized, and their spectral properties were measured. The single-crystal structure of the complex, [(PPh3)2Cu(mu-ppbCl2)Cu(PPh3)2](BF4)2 in the monoclinic space group P21/c, 18.2590(1), 21.1833(3), 23.2960(3) A with Z = 4 is reported. The copper(I) complexes are deeply colored through MLCT transitions in the visible region. The vibrational spectra of the ligands have been modeled using ab initio hybrid density functional theory (DFT) methods (B3LYP/6-31G(d)) and compared to experimental FT-Raman and IR data. The DFT calculations are used to interpret the resonance Raman spectra, and thus the electronic spectra, of the complexes. The preferential enhancement of modes associated with the phenanthroline section of the ligands with blue excitation (lambda(exc) = 457.9 nm) over phenazine-based modes with redder excitation (lambda(exc) = 514.5 and 632.8 nm) suggests the 2 MLCT transitions terminated on different unoccupied MOs are present under the visible absorption envelope. The radical anion species of the ligands are prepared by the electrochemical reduction of the binuclear copper(I) complexes; no evidence of dechelation prevalent in other copper(I) complexes is observed. The resonance Raman spectra of the reduced complexes are dramatically different from those of the parent species. Across the series common bands are observed at about 1590 and 1570 cm(-1) which do not shift with reduction but are altered in intensity. The normal-mode analysis of the radical anion species suggests that these normal modes primarily involve bond length distortions that are unaffected by reduction.     

Bi2223带材临界电流沿长度方向的统计分布

本文采用四引线法测量了Bi2223带材临界电流沿长度方向的分布,采用正态分布、对数正态分布、威布尔分布和最小极值分布对临界电流分布进行了拟合检验,确定了临界电流的最优统计分布模型.