Elliptic Apostol sums and their reciprocity laws

We introduce an elliptic analogue of the Apostol sums, which we call elliptic Apostol sums. These sums are defined by means of certain elliptic functions with a complex parameter having positive imaginary part. When , these elliptic Apostol sums represent the well-known Apostol generalized Dedekind sums. Also these elliptic Apostol sums are modular forms in the variable . We obtain a reciprocity law for these sums, which gives rise to new relations between certain modular forms (of one variable).

     

An HPLC assay of hydroxyl radicals by the hydroxylation reaction of terephthalic acid

An HPLC assay for hydroxyl radicals is described. The hydroxyl radical was trapped by terephthalic acid (non-fluorescent), and 2-hydroxyl terephthalic acid (fluorescent) was quantitated by HPLC-fluorescence detection. At a terephthalic acid concentration of 4.25 mmol/L, the hydroxyl radical formed in the Fenton reaction was successfully assayed in the concentration range of hydrogen peroxide of 2.5-50 micro mol/L, where the concentration of Fe(II) was 50 micro mol/L. The fluorescence of 2-hydroxy terephthalate was stable at 24 h, and its detection limit by this method was 5 nmol/L (100 fmol).     

The first samarium(II)-mediated aryl radical cyclisation onto an aromatic ring

Intramolecular arylation of aryl radicals was mediated by SmI(2)/HMPA in the presence of i-PrOH to give spirocycles and/or reduced cine-cyclised products, while the reaction in the absence of i-PrOH gave the rearomatised fused rings.     

Topological structure of the space of composition operators onH ∞

Components and isolated points of the topological space of composition operators onH in the uniform operator topology are characterized. Compact differences of two composition operators are also characterized. With the aid of these results, we show that a component inC(H ) is not in general the set of all composition operators that differ from the given one by a compact operator.Supported by the Grant-in-Aid for Scientific Research (C), the Ministory of Education, Science and Culture, No. 09640218, and the Nippon Institute of Technology No. 111Supported by the Japan Society for the Promotion of Science     

Electron paramagnetic resonance imaging using magnetic-field-gradient spinning

A novel X-band CW EPR imaging has been developed using magnetic-field-gradient (MFG) spinning to obtain spatial distributions of electron paramagnetic species. Spinning MFG EPR imaging for 65 projection spectra required just 55 s while conventional imaging took 11 min 40 s, that is, the acquisition time for the new system is one order of magnitude shorter than that for conventional EPR imaging. Spinning MFG EPR imaging allows one to measure reconstructed images in an interactive manner where resolution and condition can be changed quickly.     

Photoinduced dissociation reactions of silver fluoride cluster ions

Photoinduced dissociation in the ultraviolet region has been investigated for Ag _nF _n-1 ⁺ cluster ions. Photodissociation spectrum of Ag₂F⁺ in the energy of 3.8–5.6 eV exhibits several sharp bands corresponding to the transition to electronically excited states. In this dissociation, only the Ag₂ ⁺ ion was observed as a fragment ion. Theoretical calculation indicates that the parent Ag₂F⁺ ion has a linear Ag-F-Ag equilibrium geometries in the ground and excited states. Since conformational changes by excitation of bending vibration are necessary for the fragmentation of an F atom, this indicates that production of Ag₂ ⁺ from Ag₂F⁺ is a result of internal conversion and following conformational changes.     

Many-body effect in the M45–N23N45–N45N45N45 coincidence spectroscopy spectra of metallic elements around Cd

The quasi-particle approximation for the 4p4d state of the metallic elements around Cd breaks down because of very rapid 4p4d–4d³ super Coster–Kroning (sCK) decay of the 4p hole in the presence of the spectator 4d hole. Here the underbar is a hole. As a result, the 4p4d multiplet coupling breaks down. We can examine the presence or absence of the 4p4d multiplet by Auger-electron sCK-electron coincidence spectroscopy measurement of the 3d–4p4d–4d³ Auger-preceded sCK transitions. We collect the sCK-electrons in coincidence with the Auger-electrons of a selected kinetic energy (KE) and vice versa. If the multiplet coupling breaks down and does not exist, the coincidence sCK-electron (or Auger-electron) lines shift as much as the Auger-electron (or sCK-electron) analyzer's selected KE is varied. We can determine not only the three 4d-hole sCK final-state energy but also the presence or absence of the 4p4d multiplet by Auger-electron sCK-electron coincidence spectroscopy. The unique capability of the coincidence measurement by which one can determine the correlation between an Auger-electron and a sCK electron generated, respectively, by creation and annihilation of the same Auger two-hole final state is very useful, even when the quasi-particle approximation of the two-hole state breaks down.